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This manual documents the release 4.06 of the OCaml system. It is organized as follows.
OCaml runs on several operating systems. The parts of this manual that are specific to one operating system are presented as shown below:
Unix: This is material specific to the Unix family of operating systems, including Linux and MacOS X.
Windows: This is material specific to Microsoft Windows (XP, Vista, 7, 8, 10).
The OCaml system is copyright © 1996–2013 Institut National de Recherche en Informatique et en Automatique (INRIA). INRIA holds all ownership rights to the OCaml system.
The OCaml system is open source and can be freely redistributed. See the file LICENSE in the distribution for licensing information.
The present documentation is copyright © 2013 Institut National de Recherche en Informatique et en Automatique (INRIA). The OCaml documentation and user’s manual may be reproduced and distributed in whole or in part, subject to the following conditions:
The complete OCaml distribution can be accessed via the community Caml Web site and the older Caml Web site. The community Caml Web site contains a lot of additional information on OCaml.
Part I |
This part of the manual is a tutorial introduction to the OCaml language. A good familiarity with programming in a conventional languages (say, Pascal or C) is assumed, but no prior exposure to functional languages is required. The present chapter introduces the core language. Chapter 2 deals with the module system, chapter 3 with the object-oriented features, chapter 4 with extensions to the core language (labeled arguments and polymorphic variants), and chapter 6 gives some advanced examples.
For this overview of OCaml, we use the interactive system, which is started by running ocaml from the Unix shell, or by launching the OCamlwin.exe application under Windows. This tutorial is presented as the transcript of a session with the interactive system: lines starting with # represent user input; the system responses are printed below, without a leading #.
Under the interactive system, the user types OCaml phrases terminated by ;; in response to the # prompt, and the system compiles them on the fly, executes them, and prints the outcome of evaluation. Phrases are either simple expressions, or let definitions of identifiers (either values or functions).
1+2*3;;- : int = 7
let pi = 4.0 *. atan 1.0;;val pi : float = 3.14159265358979312
let square x = x *. x;;val square : float -> float = <fun>
square (sin pi) +. square (cos pi);;- : float = 1.
The OCaml system computes both the value and the type for each phrase. Even function parameters need no explicit type declaration: the system infers their types from their usage in the function. Notice also that integers and floating-point numbers are distinct types, with distinct operators: + and * operate on integers, but +. and *. operate on floats.
1.0 * 2;;Error: This expression has type float but an expression was expected of type int
Recursive functions are defined with the let rec binding:
let rec fib n = if n < 2 then n else fib (n-1) + fib (n-2);;val fib : int -> int = <fun>
fib 10;;- : int = 55
In addition to integers and floating-point numbers, OCaml offers the usual basic data types: booleans, characters, and immutable character strings.
(1 < 2) = false;;- : bool = false
'a';;- : char = 'a'
"Hello world";;- : string = "Hello world"
Predefined data structures include tuples, arrays, and lists. General mechanisms for defining your own data structures are also provided. They will be covered in more details later; for now, we concentrate on lists. Lists are either given in extension as a bracketed list of semicolon-separated elements, or built from the empty list [] (pronounce “nil”) by adding elements in front using the :: (“cons”) operator.
let l = ["is"; "a"; "tale"; "told"; "etc."];;val l : string list = ["is"; "a"; "tale"; "told"; "etc."]
"Life" :: l;;- : string list = ["Life"; "is"; "a"; "tale"; "told"; "etc."]
As with all other OCaml data structures, lists do not need to be explicitly allocated and deallocated from memory: all memory management is entirely automatic in OCaml. Similarly, there is no explicit handling of pointers: the OCaml compiler silently introduces pointers where necessary.
As with most OCaml data structures, inspecting and destructuring lists is performed by pattern-matching. List patterns have the exact same shape as list expressions, with identifier representing unspecified parts of the list. As an example, here is insertion sort on a list:
let rec sort lst = match lst with [] -> [] | head :: tail -> insert head (sort tail) and insert elt lst = match lst with [] -> [elt] | head :: tail -> if elt <= head then elt :: lst else head :: insert elt tail ;;val sort : 'a list -> 'a list = <fun> val insert : 'a -> 'a list -> 'a list = <fun>
sort l;;- : string list = ["a"; "etc."; "is"; "tale"; "told"]
The type inferred for sort, 'a list -> 'a list, means that sort can actually apply to lists of any type, and returns a list of the same type. The type 'a is a type variable, and stands for any given type. The reason why sort can apply to lists of any type is that the comparisons (=, <=, etc.) are polymorphic in OCaml: they operate between any two values of the same type. This makes sort itself polymorphic over all list types.
sort [6;2;5;3];;- : int list = [2; 3; 5; 6]
sort [3.14; 2.718];;- : float list = [2.718; 3.14]
The sort function above does not modify its input list: it builds and returns a new list containing the same elements as the input list, in ascending order. There is actually no way in OCaml to modify in-place a list once it is built: we say that lists are immutable data structures. Most OCaml data structures are immutable, but a few (most notably arrays) are mutable, meaning that they can be modified in-place at any time.
OCaml is a functional language: functions in the full mathematical sense are supported and can be passed around freely just as any other piece of data. For instance, here is a deriv function that takes any float function as argument and returns an approximation of its derivative function:
let deriv f dx = function x -> (f (x +. dx) -. f x) /. dx;;val deriv : (float -> float) -> float -> float -> float = <fun>
let sin' = deriv sin 1e-6;;val sin' : float -> float = <fun>
sin' pi;;- : float = -1.00000000013961143
Even function composition is definable:
let compose f g = function x -> f (g x);;val compose : ('a -> 'b) -> ('c -> 'a) -> 'c -> 'b = <fun>
let cos2 = compose square cos;;val cos2 : float -> float = <fun>
Functions that take other functions as arguments are called “functionals”, or “higher-order functions”. Functionals are especially useful to provide iterators or similar generic operations over a data structure. For instance, the standard OCaml library provides a List.map functional that applies a given function to each element of a list, and returns the list of the results:
List.map (function n -> n * 2 + 1) [0;1;2;3;4];;- : int list = [1; 3; 5; 7; 9]
This functional, along with a number of other list and array functionals, is predefined because it is often useful, but there is nothing magic with it: it can easily be defined as follows.
let rec map f l = match l with [] -> [] | hd :: tl -> f hd :: map f tl;;val map : ('a -> 'b) -> 'a list -> 'b list = <fun>
User-defined data structures include records and variants. Both are defined with the type declaration. Here, we declare a record type to represent rational numbers.
type ratio = {num: int; denom: int};;type ratio = { num : int; denom : int; }
let add_ratio r1 r2 = {num = r1.num * r2.denom + r2.num * r1.denom; denom = r1.denom * r2.denom};;val add_ratio : ratio -> ratio -> ratio = <fun>
add_ratio {num=1; denom=3} {num=2; denom=5};;- : ratio = {num = 11; denom = 15}
Record fields can also be accessed through pattern-matching:
let integer_part r = match r with {num=num; denom=denom} -> num / denom;;val integer_part : ratio -> int = <fun>
Since there is only one case in this pattern matching, it is safe to expand directly the argument r in a record pattern:
let integer_part {num=num; denom=denom} = num / denom;;val integer_part : ratio -> int = <fun>
Unneeded fields can be omitted:
let get_denom {denom=denom} = denom;;val get_denom : ratio -> int = <fun>
Optionally, missing fields can be made explicit by ending the list of fields with a trailing wildcard _::
let get_num {num=num; _ } = num;;val get_num : ratio -> int = <fun>
When both sides of the = sign are the same, it is possible to avoid repeating the field name by eliding the =field part:
let integer_part {num; denom} = num / denom;;val integer_part : ratio -> int = <fun>
This short notation for fields also works when constructing records:
let ratio num denom = {num; denom};;val ratio : int -> int -> ratio = <fun>
At last, it is possible to update few fields of a record at once:
let integer_product integer ratio = { ratio with num = integer * ratio.num };;val integer_product : int -> ratio -> ratio = <fun>
With this functional update notation, the record on the left-hand side of with is copied except for the fields on the right-hand side which are updated.
The declaration of a variant type lists all possible shapes for values of that type. Each case is identified by a name, called a constructor, which serves both for constructing values of the variant type and inspecting them by pattern-matching. Constructor names are capitalized to distinguish them from variable names (which must start with a lowercase letter). For instance, here is a variant type for doing mixed arithmetic (integers and floats):
type number = Int of int | Float of float | Error;;type number = Int of int | Float of float | Error
This declaration expresses that a value of type number is either an integer, a floating-point number, or the constant Error representing the result of an invalid operation (e.g. a division by zero).
Enumerated types are a special case of variant types, where all alternatives are constants:
type sign = Positive | Negative;;type sign = Positive | Negative
let sign_int n = if n >= 0 then Positive else Negative;;val sign_int : int -> sign = <fun>
To define arithmetic operations for the number type, we use pattern-matching on the two numbers involved:
let add_num n1 n2 = match (n1, n2) with (Int i1, Int i2) -> (* Check for overflow of integer addition *) if sign_int i1 = sign_int i2 && sign_int (i1 + i2) <> sign_int i1 then Float(float i1 +. float i2) else Int(i1 + i2) | (Int i1, Float f2) -> Float(float i1 +. f2) | (Float f1, Int i2) -> Float(f1 +. float i2) | (Float f1, Float f2) -> Float(f1 +. f2) | (Error, _) -> Error | (_, Error) -> Error;;val add_num : number -> number -> number = <fun>
add_num (Int 123) (Float 3.14159);;- : number = Float 126.14159
Another interesting example of variant type is the built-in 'a option type which represents either a value of type 'a or an absence of value:
type 'a option = Some of 'a | None;;type 'a option = Some of 'a | None
This type is particularly useful when defining function that can fail in common situations, for instance
let safe_square_root x = if x > 0. then Some(sqrt x) else None;;val safe_square_root : float -> float option = <fun>
The most common usage of variant types is to describe recursive data structures. Consider for example the type of binary trees:
type 'a btree = Empty | Node of 'a * 'a btree * 'a btree;;type 'a btree = Empty | Node of 'a * 'a btree * 'a btree
This definition reads as follows: a binary tree containing values of type 'a (an arbitrary type) is either empty, or is a node containing one value of type 'a and two subtrees containing also values of type 'a, that is, two 'a btree.
Operations on binary trees are naturally expressed as recursive functions following the same structure as the type definition itself. For instance, here are functions performing lookup and insertion in ordered binary trees (elements increase from left to right):
let rec member x btree = match btree with Empty -> false | Node(y, left, right) -> if x = y then true else if x < y then member x left else member x right;;val member : 'a -> 'a btree -> bool = <fun>
let rec insert x btree = match btree with Empty -> Node(x, Empty, Empty) | Node(y, left, right) -> if x <= y then Node(y, insert x left, right) else Node(y, left, insert x right);;val insert : 'a -> 'a btree -> 'a btree = <fun>
Though all examples so far were written in purely applicative style, OCaml is also equipped with full imperative features. This includes the usual while and for loops, as well as mutable data structures such as arrays. Arrays are either given in extension between [| and |] brackets, or allocated and initialized with the Array.make function, then filled up later by assignments. For instance, the function below sums two vectors (represented as float arrays) componentwise.
let add_vect v1 v2 = let len = min (Array.length v1) (Array.length v2) in let res = Array.make len 0.0 in for i = 0 to len - 1 do res.(i) <- v1.(i) +. v2.(i) done; res;;val add_vect : float array -> float array -> float array = <fun>
add_vect [| 1.0; 2.0 |] [| 3.0; 4.0 |];;- : float array = [|4.; 6.|]
Record fields can also be modified by assignment, provided they are declared mutable in the definition of the record type:
type mutable_point = { mutable x: float; mutable y: float };;type mutable_point = { mutable x : float; mutable y : float; }
let translate p dx dy = p.x <- p.x +. dx; p.y <- p.y +. dy;;val translate : mutable_point -> float -> float -> unit = <fun>
let mypoint = { x = 0.0; y = 0.0 };;val mypoint : mutable_point = {x = 0.; y = 0.}
translate mypoint 1.0 2.0;;- : unit = ()
mypoint;;- : mutable_point = {x = 1.; y = 2.}
OCaml has no built-in notion of variable – identifiers whose current value can be changed by assignment. (The let binding is not an assignment, it introduces a new identifier with a new scope.) However, the standard library provides references, which are mutable indirection cells (or one-element arrays), with operators ! to fetch the current contents of the reference and := to assign the contents. Variables can then be emulated by let-binding a reference. For instance, here is an in-place insertion sort over arrays:
let insertion_sort a = for i = 1 to Array.length a - 1 do let val_i = a.(i) in let j = ref i in while !j > 0 && val_i < a.(!j - 1) do a.(!j) <- a.(!j - 1); j := !j - 1 done; a.(!j) <- val_i done;;val insertion_sort : 'a array -> unit = <fun>
References are also useful to write functions that maintain a current state between two calls to the function. For instance, the following pseudo-random number generator keeps the last returned number in a reference:
let current_rand = ref 0;;val current_rand : int ref = {contents = 0}
let random () = current_rand := !current_rand * 25713 + 1345; !current_rand;;val random : unit -> int = <fun>
Again, there is nothing magical with references: they are implemented as a single-field mutable record, as follows.
type 'a ref = { mutable contents: 'a };;type 'a ref = { mutable contents : 'a; }
let ( ! ) r = r.contents;;val ( ! ) : 'a ref -> 'a = <fun>
let ( := ) r newval = r.contents <- newval;;val ( := ) : 'a ref -> 'a -> unit = <fun>
In some special cases, you may need to store a polymorphic function in a data structure, keeping its polymorphism. Without user-provided type annotations, this is not allowed, as polymorphism is only introduced on a global level. However, you can give explicitly polymorphic types to record fields.
type idref = { mutable id: 'a. 'a -> 'a };;type idref = { mutable id : 'a. 'a -> 'a; }
let r = {id = fun x -> x};;val r : idref = {id = <fun>}
let g s = (s.id 1, s.id true);;val g : idref -> int * bool = <fun>
r.id <- (fun x -> print_string "called id\n"; x);;- : unit = ()
g r;;called id called id - : int * bool = (1, true)
OCaml provides exceptions for signalling and handling exceptional conditions. Exceptions can also be used as a general-purpose non-local control structure. Exceptions are declared with the exception construct, and signalled with the raise operator. For instance, the function below for taking the head of a list uses an exception to signal the case where an empty list is given.
exception Empty_list;;exception Empty_list
let head l = match l with [] -> raise Empty_list | hd :: tl -> hd;;val head : 'a list -> 'a = <fun>
head [1;2];;- : int = 1
head [];;Exception: Empty_list.
Exceptions are used throughout the standard library to signal cases where the library functions cannot complete normally. For instance, the List.assoc function, which returns the data associated with a given key in a list of (key, data) pairs, raises the predefined exception Not_found when the key does not appear in the list:
List.assoc 1 [(0, "zero"); (1, "one")];;- : string = "one"
List.assoc 2 [(0, "zero"); (1, "one")];;Exception: Not_found.
Exceptions can be trapped with the try…with construct:
let name_of_binary_digit digit = try List.assoc digit [0, "zero"; 1, "one"] with Not_found -> "not a binary digit";;val name_of_binary_digit : int -> string = <fun>
name_of_binary_digit 0;;- : string = "zero"
name_of_binary_digit (-1);;- : string = "not a binary digit"
The with part is actually a regular pattern-matching on the exception value. Thus, several exceptions can be caught by one try…with construct. Also, finalization can be performed by trapping all exceptions, performing the finalization, then raising again the exception:
let temporarily_set_reference ref newval funct = let oldval = !ref in try ref := newval; let res = funct () in ref := oldval; res with x -> ref := oldval; raise x;;val temporarily_set_reference : 'a ref -> 'a -> (unit -> 'b) -> 'b = <fun>
We finish this introduction with a more complete example representative of the use of OCaml for symbolic processing: formal manipulations of arithmetic expressions containing variables. The following variant type describes the expressions we shall manipulate:
type expression = Const of float | Var of string | Sum of expression * expression (* e1 + e2 *) | Diff of expression * expression (* e1 - e2 *) | Prod of expression * expression (* e1 * e2 *) | Quot of expression * expression (* e1 / e2 *) ;;type expression = Const of float | Var of string | Sum of expression * expression | Diff of expression * expression | Prod of expression * expression | Quot of expression * expression
We first define a function to evaluate an expression given an environment that maps variable names to their values. For simplicity, the environment is represented as an association list.
exception Unbound_variable of string;;exception Unbound_variable of string
let rec eval env exp = match exp with Const c -> c | Var v -> (try List.assoc v env with Not_found -> raise (Unbound_variable v)) | Sum(f, g) -> eval env f +. eval env g | Diff(f, g) -> eval env f -. eval env g | Prod(f, g) -> eval env f *. eval env g | Quot(f, g) -> eval env f /. eval env g;;val eval : (string * float) list -> expression -> float = <fun>
eval [("x", 1.0); ("y", 3.14)] (Prod(Sum(Var "x", Const 2.0), Var "y"));;- : float = 9.42
Now for a real symbolic processing, we define the derivative of an expression with respect to a variable dv:
let rec deriv exp dv = match exp with Const c -> Const 0.0 | Var v -> if v = dv then Const 1.0 else Const 0.0 | Sum(f, g) -> Sum(deriv f dv, deriv g dv) | Diff(f, g) -> Diff(deriv f dv, deriv g dv) | Prod(f, g) -> Sum(Prod(f, deriv g dv), Prod(deriv f dv, g)) | Quot(f, g) -> Quot(Diff(Prod(deriv f dv, g), Prod(f, deriv g dv)), Prod(g, g)) ;;val deriv : expression -> string -> expression = <fun>
deriv (Quot(Const 1.0, Var "x")) "x";;- : expression = Quot (Diff (Prod (Const 0., Var "x"), Prod (Const 1., Const 1.)), Prod (Var "x", Var "x"))
As shown in the examples above, the internal representation (also called abstract syntax) of expressions quickly becomes hard to read and write as the expressions get larger. We need a printer and a parser to go back and forth between the abstract syntax and the concrete syntax, which in the case of expressions is the familiar algebraic notation (e.g. 2*x+1).
For the printing function, we take into account the usual precedence rules (i.e. * binds tighter than +) to avoid printing unnecessary parentheses. To this end, we maintain the current operator precedence and print parentheses around an operator only if its precedence is less than the current precedence.
let print_expr exp = (* Local function definitions *) let open_paren prec op_prec = if prec > op_prec then print_string "(" in let close_paren prec op_prec = if prec > op_prec then print_string ")" in let rec print prec exp = (* prec is the current precedence *) match exp with Const c -> print_float c | Var v -> print_string v | Sum(f, g) -> open_paren prec 0; print 0 f; print_string " + "; print 0 g; close_paren prec 0 | Diff(f, g) -> open_paren prec 0; print 0 f; print_string " - "; print 1 g; close_paren prec 0 | Prod(f, g) -> open_paren prec 2; print 2 f; print_string " * "; print 2 g; close_paren prec 2 | Quot(f, g) -> open_paren prec 2; print 2 f; print_string " / "; print 3 g; close_paren prec 2 in print 0 exp;;val print_expr : expression -> unit = <fun>
let e = Sum(Prod(Const 2.0, Var "x"), Const 1.0);;val e : expression = Sum (Prod (Const 2., Var "x"), Const 1.)
print_expr e; print_newline ();;2. * x + 1. - : unit = ()
print_expr (deriv e "x"); print_newline ();;2. * 1. + 0. * x + 0. - : unit = ()
All examples given so far were executed under the interactive system. OCaml code can also be compiled separately and executed non-interactively using the batch compilers ocamlc and ocamlopt. The source code must be put in a file with extension .ml. It consists of a sequence of phrases, which will be evaluated at runtime in their order of appearance in the source file. Unlike in interactive mode, types and values are not printed automatically; the program must call printing functions explicitly to produce some output. Here is a sample standalone program to print Fibonacci numbers:
(* File fib.ml *) let rec fib n = if n < 2 then 1 else fib (n-1) + fib (n-2);; let main () = let arg = int_of_string Sys.argv.(1) in print_int (fib arg); print_newline (); exit 0;; main ();;
Sys.argv is an array of strings containing the command-line parameters. Sys.argv.(1) is thus the first command-line parameter. The program above is compiled and executed with the following shell commands:
$ ocamlc -o fib fib.ml $ ./fib 10 89 $ ./fib 20 10946
More complex standalone OCaml programs are typically composed of multiple source files, and can link with precompiled libraries. Chapters 9 and 12 explain how to use the batch compilers ocamlc and ocamlopt. Recompilation of multi-file OCaml projects can be automated using third-party build systems, such as the ocamlbuild compilation manager.
This chapter introduces the module system of OCaml.
A primary motivation for modules is to package together related definitions (such as the definitions of a data type and associated operations over that type) and enforce a consistent naming scheme for these definitions. This avoids running out of names or accidentally confusing names. Such a package is called a structure and is introduced by the struct…end construct, which contains an arbitrary sequence of definitions. The structure is usually given a name with the module binding. Here is for instance a structure packaging together a type of priority queues and their operations:
module PrioQueue = struct type priority = int type 'a queue = Empty | Node of priority * 'a * 'a queue * 'a queue let empty = Empty let rec insert queue prio elt = match queue with Empty -> Node(prio, elt, Empty, Empty) | Node(p, e, left, right) -> if prio <= p then Node(prio, elt, insert right p e, left) else Node(p, e, insert right prio elt, left) exception Queue_is_empty let rec remove_top = function Empty -> raise Queue_is_empty | Node(prio, elt, left, Empty) -> left | Node(prio, elt, Empty, right) -> right | Node(prio, elt, (Node(lprio, lelt, _, _) as left), (Node(rprio, relt, _, _) as right)) -> if lprio <= rprio then Node(lprio, lelt, remove_top left, right) else Node(rprio, relt, left, remove_top right) let extract = function Empty -> raise Queue_is_empty | Node(prio, elt, _, _) as queue -> (prio, elt, remove_top queue) end;;module PrioQueue : sig type priority = int type 'a queue = Empty | Node of priority * 'a * 'a queue * 'a queue val empty : 'a queue val insert : 'a queue -> priority -> 'a -> 'a queue exception Queue_is_empty val remove_top : 'a queue -> 'a queue val extract : 'a queue -> priority * 'a * 'a queue end
Outside the structure, its components can be referred to using the “dot notation”, that is, identifiers qualified by a structure name. For instance, PrioQueue.insert is the function insert defined inside the structure PrioQueue and PrioQueue.queue is the type queue defined in PrioQueue.
PrioQueue.insert PrioQueue.empty 1 "hello";;- : string PrioQueue.queue = PrioQueue.Node (1, "hello", PrioQueue.Empty, PrioQueue.Empty)
Another possibility is to open the module, which brings all identifiers defined inside the module in the scope of the current structure.
open PrioQueue;;
insert empty 1 "hello";;- : string PrioQueue.queue = Node (1, "hello", Empty, Empty)
Opening a module enables lighter access to its components, at the cost of making it harder to identify in which module a identifier has been defined. In particular, opened modules can shadow identifiers present in the current scope, potentially leading to confusing errors:
let empty = [] open PrioQueue;;val empty : 'a list = []
let x = 1 :: empty ;;Error: This expression has type 'a PrioQueue.queue but an expression was expected of type int list
A partial solution to this conundrum is to open modules locally, making the components of the module available only in the concerned expression. This can also make the code easier to read – the open statement is closer to where it is used– and to refactor – the code fragment is more self-contained. Two constructions are available for this purpose:
let open PrioQueue in insert empty 1 "hello";;- : string PrioQueue.queue = Node (1, "hello", Empty, Empty)
and
PrioQueue.(insert empty 1 "hello");;- : string PrioQueue.queue = Node (1, "hello", Empty, Empty)
In the second form, when the body of a local open is itself delimited by parentheses, braces or bracket, the parentheses of the local open can be omitted. For instance,
PrioQueue.[empty] = PrioQueue.([empty]);;- : bool = true
PrioQueue.[|empty|] = PrioQueue.([|empty|]);;- : bool = true
PrioQueue.{ contents = empty } = PrioQueue.({ contents = empty });;- : bool = true
becomes
PrioQueue.[insert empty 1 "hello"];;- : string PrioQueue.queue list = [Node (1, "hello", Empty, Empty)]
It is also possible to copy the components of a module inside another module by using an include statement. This can be particularly useful to extend existing modules. As an illustration, we could add functions that returns an optional value rather than an exception when the priority queue is empty.
module PrioQueueOpt = struct include PrioQueue let remove_top_opt x = try Some(remove_top x) with Queue_is_empty -> None let extract_opt x = try Some(extract x) with Queue_is_empty -> None end;;module PrioQueueOpt : sig type priority = int type 'a queue = 'a PrioQueue.queue = Empty | Node of priority * 'a * 'a queue * 'a queue val empty : 'a queue val insert : 'a queue -> priority -> 'a -> 'a queue exception Queue_is_empty val remove_top : 'a queue -> 'a queue val extract : 'a queue -> priority * 'a * 'a queue val remove_top_opt : 'a queue -> 'a queue option val extract_opt : 'a queue -> (priority * 'a * 'a queue) option end
Signatures are interfaces for structures. A signature specifies which components of a structure are accessible from the outside, and with which type. It can be used to hide some components of a structure (e.g. local function definitions) or export some components with a restricted type. For instance, the signature below specifies the three priority queue operations empty, insert and extract, but not the auxiliary function remove_top. Similarly, it makes the queue type abstract (by not providing its actual representation as a concrete type).
module type PRIOQUEUE = sig type priority = int (* still concrete *) type 'a queue (* now abstract *) val empty : 'a queue val insert : 'a queue -> int -> 'a -> 'a queue val extract : 'a queue -> int * 'a * 'a queue exception Queue_is_empty end;;module type PRIOQUEUE = sig type priority = int type 'a queue val empty : 'a queue val insert : 'a queue -> int -> 'a -> 'a queue val extract : 'a queue -> int * 'a * 'a queue exception Queue_is_empty end
Restricting the PrioQueue structure by this signature results in another view of the PrioQueue structure where the remove_top function is not accessible and the actual representation of priority queues is hidden:
module AbstractPrioQueue = (PrioQueue : PRIOQUEUE);;module AbstractPrioQueue : PRIOQUEUE
AbstractPrioQueue.remove_top ;;Error: Unbound value AbstractPrioQueue.remove_top
AbstractPrioQueue.insert AbstractPrioQueue.empty 1 "hello";;- : string AbstractPrioQueue.queue = <abstr>
The restriction can also be performed during the definition of the structure, as in
module PrioQueue = (struct ... end : PRIOQUEUE);;
An alternate syntax is provided for the above:
module PrioQueue : PRIOQUEUE = struct ... end;;
Like for modules, it is possible to include a signature to copy its components inside the current signature. For instance, we can extend the PRIOQUEUE signature with the extract_opt function:
module type PRIOQUEUE_WITH_OPT = sig include PRIOQUEUE val extract_opt : 'a queue -> (int * 'a * 'a queue) option end;;module type PRIOQUEUE_WITH_OPT = sig type priority = int type 'a queue val empty : 'a queue val insert : 'a queue -> int -> 'a -> 'a queue val extract : 'a queue -> int * 'a * 'a queue exception Queue_is_empty val extract_opt : 'a queue -> (int * 'a * 'a queue) option end
Functors are “functions” from structures to structures. They are used to express parameterized structures: a structure A parameterized by a structure B is simply a functor F with a formal parameter B (along with the expected signature for B) which returns the actual structure A itself. The functor F can then be applied to one or several implementations B1 …Bn of B, yielding the corresponding structures A1 …An.
For instance, here is a structure implementing sets as sorted lists, parameterized by a structure providing the type of the set elements and an ordering function over this type (used to keep the sets sorted):
type comparison = Less | Equal | Greater;;type comparison = Less | Equal | Greater
module type ORDERED_TYPE = sig type t val compare: t -> t -> comparison end;;module type ORDERED_TYPE = sig type t val compare : t -> t -> comparison end
module Set = functor (Elt: ORDERED_TYPE) -> struct type element = Elt.t type set = element list let empty = [] let rec add x s = match s with [] -> [x] | hd::tl -> match Elt.compare x hd with Equal -> s (* x is already in s *) | Less -> x :: s (* x is smaller than all elements of s *) | Greater -> hd :: add x tl let rec member x s = match s with [] -> false | hd::tl -> match Elt.compare x hd with Equal -> true (* x belongs to s *) | Less -> false (* x is smaller than all elements of s *) | Greater -> member x tl end;;module Set : functor (Elt : ORDERED_TYPE) -> sig type element = Elt.t type set = element list val empty : 'a list val add : Elt.t -> Elt.t list -> Elt.t list val member : Elt.t -> Elt.t list -> bool end
By applying the Set functor to a structure implementing an ordered type, we obtain set operations for this type:
module OrderedString = struct type t = string let compare x y = if x = y then Equal else if x < y then Less else Greater end;;module OrderedString : sig type t = string val compare : 'a -> 'a -> comparison end
module StringSet = Set(OrderedString);;module StringSet : sig type element = OrderedString.t type set = element list val empty : 'a list val add : OrderedString.t -> OrderedString.t list -> OrderedString.t list val member : OrderedString.t -> OrderedString.t list -> bool end
StringSet.member "bar" (StringSet.add "foo" StringSet.empty);;- : bool = false
As in the PrioQueue example, it would be good style to hide the actual implementation of the type set, so that users of the structure will not rely on sets being lists, and we can switch later to another, more efficient representation of sets without breaking their code. This can be achieved by restricting Set by a suitable functor signature:
module type SETFUNCTOR = functor (Elt: ORDERED_TYPE) -> sig type element = Elt.t (* concrete *) type set (* abstract *) val empty : set val add : element -> set -> set val member : element -> set -> bool end;;module type SETFUNCTOR = functor (Elt : ORDERED_TYPE) -> sig type element = Elt.t type set val empty : set val add : element -> set -> set val member : element -> set -> bool end
module AbstractSet = (Set : SETFUNCTOR);;module AbstractSet : SETFUNCTOR
module AbstractStringSet = AbstractSet(OrderedString);;module AbstractStringSet : sig type element = OrderedString.t type set = AbstractSet(OrderedString).set val empty : set val add : element -> set -> set val member : element -> set -> bool end
AbstractStringSet.add "gee" AbstractStringSet.empty;;- : AbstractStringSet.set = <abstr>
In an attempt to write the type constraint above more elegantly, one may wish to name the signature of the structure returned by the functor, then use that signature in the constraint:
module type SET = sig type element type set val empty : set val add : element -> set -> set val member : element -> set -> bool end;;module type SET = sig type element type set val empty : set val add : element -> set -> set val member : element -> set -> bool end
module WrongSet = (Set : functor(Elt: ORDERED_TYPE) -> SET);;module WrongSet : functor (Elt : ORDERED_TYPE) -> SET
module WrongStringSet = WrongSet(OrderedString);;module WrongStringSet : sig type element = WrongSet(OrderedString).element type set = WrongSet(OrderedString).set val empty : set val add : element -> set -> set val member : element -> set -> bool end
WrongStringSet.add "gee" WrongStringSet.empty ;;Error: This expression has type string but an expression was expected of type WrongStringSet.element = WrongSet(OrderedString).element
The problem here is that SET specifies the type element abstractly, so that the type equality between element in the result of the functor and t in its argument is forgotten. Consequently, WrongStringSet.element is not the same type as string, and the operations of WrongStringSet cannot be applied to strings. As demonstrated above, it is important that the type element in the signature SET be declared equal to Elt.t; unfortunately, this is impossible above since SET is defined in a context where Elt does not exist. To overcome this difficulty, OCaml provides a with type construct over signatures that allows enriching a signature with extra type equalities:
module AbstractSet2 = (Set : functor(Elt: ORDERED_TYPE) -> (SET with type element = Elt.t));;module AbstractSet2 : functor (Elt : ORDERED_TYPE) -> sig type element = Elt.t type set val empty : set val add : element -> set -> set val member : element -> set -> bool end
As in the case of simple structures, an alternate syntax is provided for defining functors and restricting their result:
module AbstractSet2(Elt: ORDERED_TYPE) : (SET with type element = Elt.t) = struct ... end;;
Abstracting a type component in a functor result is a powerful technique that provides a high degree of type safety, as we now illustrate. Consider an ordering over character strings that is different from the standard ordering implemented in the OrderedString structure. For instance, we compare strings without distinguishing upper and lower case.
module NoCaseString = struct type t = string let compare s1 s2 = OrderedString.compare (String.lowercase_ascii s1) (String.lowercase_ascii s2) end;;module NoCaseString : sig type t = string val compare : string -> string -> comparison end
module NoCaseStringSet = AbstractSet(NoCaseString);;module NoCaseStringSet : sig type element = NoCaseString.t type set = AbstractSet(NoCaseString).set val empty : set val add : element -> set -> set val member : element -> set -> bool end
NoCaseStringSet.add "FOO" AbstractStringSet.empty ;;Error: This expression has type AbstractStringSet.set = AbstractSet(OrderedString).set but an expression was expected of type NoCaseStringSet.set = AbstractSet(NoCaseString).set
Note that the two types AbstractStringSet.set and NoCaseStringSet.set are not compatible, and values of these two types do not match. This is the correct behavior: even though both set types contain elements of the same type (strings), they are built upon different orderings of that type, and different invariants need to be maintained by the operations (being strictly increasing for the standard ordering and for the case-insensitive ordering). Applying operations from AbstractStringSet to values of type NoCaseStringSet.set could give incorrect results, or build lists that violate the invariants of NoCaseStringSet.
All examples of modules so far have been given in the context of the interactive system. However, modules are most useful for large, batch-compiled programs. For these programs, it is a practical necessity to split the source into several files, called compilation units, that can be compiled separately, thus minimizing recompilation after changes.
In OCaml, compilation units are special cases of structures and signatures, and the relationship between the units can be explained easily in terms of the module system. A compilation unit A comprises two files:
These two files together define a structure named A as if the following definition was entered at top-level:
module A: sig (* contents of file A.mli *) end = struct (* contents of file A.ml *) end;;
The files that define the compilation units can be compiled separately using the ocamlc -c command (the -c option means “compile only, do not try to link”); this produces compiled interface files (with extension .cmi) and compiled object code files (with extension .cmo). When all units have been compiled, their .cmo files are linked together using the ocamlc command. For instance, the following commands compile and link a program composed of two compilation units Aux and Main:
$ ocamlc -c Aux.mli # produces aux.cmi $ ocamlc -c Aux.ml # produces aux.cmo $ ocamlc -c Main.mli # produces main.cmi $ ocamlc -c Main.ml # produces main.cmo $ ocamlc -o theprogram Aux.cmo Main.cmo
The program behaves exactly as if the following phrases were entered at top-level:
module Aux: sig (* contents of Aux.mli *) end
= struct (* contents of Aux.ml *) end;;
module Main: sig (* contents of Main.mli *) end
= struct (* contents of Main.ml *) end;;
In particular, Main can refer to Aux: the definitions and declarations contained in Main.ml and Main.mli can refer to definition in Aux.ml, using the Aux.ident notation, provided these definitions are exported in Aux.mli.
The order in which the .cmo files are given to ocamlc during the linking phase determines the order in which the module definitions occur. Hence, in the example above, Aux appears first and Main can refer to it, but Aux cannot refer to Main.
Note that only top-level structures can be mapped to separately-compiled files, but neither functors nor module types. However, all module-class objects can appear as components of a structure, so the solution is to put the functor or module type inside a structure, which can then be mapped to a file.
(Chapter written by Jérôme Vouillon, Didier Rémy and Jacques Garrigue)
This chapter gives an overview of the object-oriented features of OCaml. Note that the relation between object, class and type in OCaml is very different from that in mainstream object-oriented languages like Java or C++, so that you should not assume that similar keywords mean the same thing.
3.1 Classes and objects
3.2 Immediate objects
3.3 Reference to self
3.4 Initializers
3.5 Virtual methods
3.6 Private methods
3.7 Class interfaces
3.8 Inheritance
3.9 Multiple inheritance
3.10 Parameterized classes
3.11 Polymorphic methods
3.12 Using coercions
3.13 Functional objects
3.14 Cloning objects
3.15 Recursive classes
3.16 Binary methods
3.17 Friends
The class point below defines one instance variable x and two methods get_x and move. The initial value of the instance variable is 0. The variable x is declared mutable, so the method move can change its value.
class point = object val mutable x = 0 method get_x = x method move d = x <- x + d end;;class point : object val mutable x : int method get_x : int method move : int -> unit end
We now create a new point p, instance of the point class.
let p = new point;;val p : point = <obj>
Note that the type of p is point. This is an abbreviation automatically defined by the class definition above. It stands for the object type <get_x : int; move : int -> unit>, listing the methods of class point along with their types.
We now invoke some methods to p:
p#get_x;;- : int = 0
p#move 3;;- : unit = ()
p#get_x;;- : int = 3
The evaluation of the body of a class only takes place at object creation time. Therefore, in the following example, the instance variable x is initialized to different values for two different objects.
let x0 = ref 0;;val x0 : int ref = {contents = 0}
class point = object val mutable x = incr x0; !x0 method get_x = x method move d = x <- x + d end;;class point : object val mutable x : int method get_x : int method move : int -> unit end
new point#get_x;;- : int = 1
new point#get_x;;- : int = 2
The class point can also be abstracted over the initial values of the x coordinate.
class point = fun x_init -> object val mutable x = x_init method get_x = x method move d = x <- x + d end;;class point : int -> object val mutable x : int method get_x : int method move : int -> unit end
Like in function definitions, the definition above can be abbreviated as:
class point x_init = object val mutable x = x_init method get_x = x method move d = x <- x + d end;;class point : int -> object val mutable x : int method get_x : int method move : int -> unit end
An instance of the class point is now a function that expects an initial parameter to create a point object:
new point;;- : int -> point = <fun>
let p = new point 7;;val p : point = <obj>
The parameter x_init is, of course, visible in the whole body of the definition, including methods. For instance, the method get_offset in the class below returns the position of the object relative to its initial position.
class point x_init = object val mutable x = x_init method get_x = x method get_offset = x - x_init method move d = x <- x + d end;;class point : int -> object val mutable x : int method get_offset : int method get_x : int method move : int -> unit end
Expressions can be evaluated and bound before defining the object body of the class. This is useful to enforce invariants. For instance, points can be automatically adjusted to the nearest point on a grid, as follows:
class adjusted_point x_init = let origin = (x_init / 10) * 10 in object val mutable x = origin method get_x = x method get_offset = x - origin method move d = x <- x + d end;;class adjusted_point : int -> object val mutable x : int method get_offset : int method get_x : int method move : int -> unit end
(One could also raise an exception if the x_init coordinate is not on the grid.) In fact, the same effect could here be obtained by calling the definition of class point with the value of the origin.
class adjusted_point x_init = point ((x_init / 10) * 10);;class adjusted_point : int -> point
An alternate solution would have been to define the adjustment in a special allocation function:
let new_adjusted_point x_init = new point ((x_init / 10) * 10);;val new_adjusted_point : int -> point = <fun>
However, the former pattern is generally more appropriate, since the code for adjustment is part of the definition of the class and will be inherited.
This ability provides class constructors as can be found in other languages. Several constructors can be defined this way to build objects of the same class but with different initialization patterns; an alternative is to use initializers, as described below in section 3.4.
There is another, more direct way to create an object: create it without going through a class.
The syntax is exactly the same as for class expressions, but the result is a single object rather than a class. All the constructs described in the rest of this section also apply to immediate objects.
let p = object val mutable x = 0 method get_x = x method move d = x <- x + d end;;val p : < get_x : int; move : int -> unit > = <obj>
p#get_x;;- : int = 0
p#move 3;;- : unit = ()
p#get_x;;- : int = 3
Unlike classes, which cannot be defined inside an expression, immediate objects can appear anywhere, using variables from their environment.
let minmax x y = if x < y then object method min = x method max = y end else object method min = y method max = x end;;val minmax : 'a -> 'a -> < max : 'a; min : 'a > = <fun>
Immediate objects have two weaknesses compared to classes: their types are not abbreviated, and you cannot inherit from them. But these two weaknesses can be advantages in some situations, as we will see in sections 3.3 and 3.10.
A method or an initializer can send messages to self (that is, the current object). For that, self must be explicitly bound, here to the variable s (s could be any identifier, even though we will often choose the name self.)
class printable_point x_init = object (s) val mutable x = x_init method get_x = x method move d = x <- x + d method print = print_int s#get_x end;;class printable_point : int -> object val mutable x : int method get_x : int method move : int -> unit method print : unit end
let p = new printable_point 7;;val p : printable_point = <obj>
p#print;;7- : unit = ()
Dynamically, the variable s is bound at the invocation of a method. In particular, when the class printable_point is inherited, the variable s will be correctly bound to the object of the subclass.
A common problem with self is that, as its type may be extended in subclasses, you cannot fix it in advance. Here is a simple example.
let ints = ref [];;val ints : '_weak1 list ref = {contents = []}
class my_int = object (self) method n = 1 method register = ints := self :: !ints end ;;Error: This expression has type < n : int; register : 'a; .. > but an expression was expected of type 'weak1 Self type cannot escape its class
You can ignore the first two lines of the error message. What matters is the last one: putting self into an external reference would make it impossible to extend it through inheritance. We will see in section 3.12 a workaround to this problem. Note however that, since immediate objects are not extensible, the problem does not occur with them.
let my_int = object (self) method n = 1 method register = ints := self :: !ints end;;val my_int : < n : int; register : unit > = <obj>
Let-bindings within class definitions are evaluated before the object is constructed. It is also possible to evaluate an expression immediately after the object has been built. Such code is written as an anonymous hidden method called an initializer. Therefore, it can access self and the instance variables.
class printable_point x_init = let origin = (x_init / 10) * 10 in object (self) val mutable x = origin method get_x = x method move d = x <- x + d method print = print_int self#get_x initializer print_string "new point at "; self#print; print_newline () end;;class printable_point : int -> object val mutable x : int method get_x : int method move : int -> unit method print : unit end
let p = new printable_point 17;;new point at 10 val p : printable_point = <obj>
Initializers cannot be overridden. On the contrary, all initializers are evaluated sequentially. Initializers are particularly useful to enforce invariants. Another example can be seen in section 6.1.
It is possible to declare a method without actually defining it, using the keyword virtual. This method will be provided later in subclasses. A class containing virtual methods must be flagged virtual, and cannot be instantiated (that is, no object of this class can be created). It still defines type abbreviations (treating virtual methods as other methods.)
class virtual abstract_point x_init = object (self) method virtual get_x : int method get_offset = self#get_x - x_init method virtual move : int -> unit end;;class virtual abstract_point : int -> object method get_offset : int method virtual get_x : int method virtual move : int -> unit end
class point x_init = object inherit abstract_point x_init val mutable x = x_init method get_x = x method move d = x <- x + d end;;class point : int -> object val mutable x : int method get_offset : int method get_x : int method move : int -> unit end
Instance variables can also be declared as virtual, with the same effect as with methods.
class virtual abstract_point2 = object val mutable virtual x : int method move d = x <- x + d end;;class virtual abstract_point2 : object val mutable virtual x : int method move : int -> unit end
class point2 x_init = object inherit abstract_point2 val mutable x = x_init method get_offset = x - x_init end;;class point2 : int -> object val mutable x : int method get_offset : int method move : int -> unit end
Private methods are methods that do not appear in object interfaces. They can only be invoked from other methods of the same object.
class restricted_point x_init = object (self) val mutable x = x_init method get_x = x method private move d = x <- x + d method bump = self#move 1 end;;class restricted_point : int -> object val mutable x : int method bump : unit method get_x : int method private move : int -> unit end
let p = new restricted_point 0;;val p : restricted_point = <obj>
p#move 10 ;;Error: This expression has type restricted_point It has no method move
p#bump;;- : unit = ()
Note that this is not the same thing as private and protected methods in Java or C++, which can be called from other objects of the same class. This is a direct consequence of the independence between types and classes in OCaml: two unrelated classes may produce objects of the same type, and there is no way at the type level to ensure that an object comes from a specific class. However a possible encoding of friend methods is given in section 3.17.
Private methods are inherited (they are by default visible in subclasses), unless they are hidden by signature matching, as described below.
Private methods can be made public in a subclass.
class point_again x = object (self) inherit restricted_point x method virtual move : _ end;;class point_again : int -> object val mutable x : int method bump : unit method get_x : int method move : int -> unit end
The annotation virtual here is only used to mention a method without providing its definition. Since we didn’t add the private annotation, this makes the method public, keeping the original definition.
An alternative definition is
class point_again x = object (self : < move : _; ..> ) inherit restricted_point x end;;class point_again : int -> object val mutable x : int method bump : unit method get_x : int method move : int -> unit end
The constraint on self’s type is requiring a public move method, and this is sufficient to override private.
One could think that a private method should remain private in a subclass. However, since the method is visible in a subclass, it is always possible to pick its code and define a method of the same name that runs that code, so yet another (heavier) solution would be:
class point_again x = object inherit restricted_point x as super method move = super#move end;;class point_again : int -> object val mutable x : int method bump : unit method get_x : int method move : int -> unit end
Of course, private methods can also be virtual. Then, the keywords must appear in this order method private virtual.
Class interfaces are inferred from class definitions. They may also be defined directly and used to restrict the type of a class. Like class declarations, they also define a new type abbreviation.
class type restricted_point_type = object method get_x : int method bump : unit end;;class type restricted_point_type = object method bump : unit method get_x : int end
fun (x : restricted_point_type) -> x;;- : restricted_point_type -> restricted_point_type = <fun>
In addition to program documentation, class interfaces can be used to constrain the type of a class. Both concrete instance variables and concrete private methods can be hidden by a class type constraint. Public methods and virtual members, however, cannot.
class restricted_point' x = (restricted_point x : restricted_point_type);;class restricted_point' : int -> restricted_point_type
Or, equivalently:
class restricted_point' = (restricted_point : int -> restricted_point_type);;class restricted_point' : int -> restricted_point_type
The interface of a class can also be specified in a module signature, and used to restrict the inferred signature of a module.
module type POINT = sig class restricted_point' : int -> object method get_x : int method bump : unit end end;;module type POINT = sig class restricted_point' : int -> object method bump : unit method get_x : int end end
module Point : POINT = struct class restricted_point' = restricted_point end;;module Point : POINT
We illustrate inheritance by defining a class of colored points that inherits from the class of points. This class has all instance variables and all methods of class point, plus a new instance variable c and a new method color.
class colored_point x (c : string) = object inherit point x val c = c method color = c end;;class colored_point : int -> string -> object val c : string val mutable x : int method color : string method get_offset : int method get_x : int method move : int -> unit end
let p' = new colored_point 5 "red";;val p' : colored_point = <obj>
p'#get_x, p'#color;;- : int * string = (5, "red")
A point and a colored point have incompatible types, since a point has no method color. However, the function get_x below is a generic function applying method get_x to any object p that has this method (and possibly some others, which are represented by an ellipsis in the type). Thus, it applies to both points and colored points.
let get_succ_x p = p#get_x + 1;;val get_succ_x : < get_x : int; .. > -> int = <fun>
get_succ_x p + get_succ_x p';;- : int = 8
Methods need not be declared previously, as shown by the example:
let set_x p = p#set_x;;val set_x : < set_x : 'a; .. > -> 'a = <fun>
let incr p = set_x p (get_succ_x p);;val incr : < get_x : int; set_x : int -> 'a; .. > -> 'a = <fun>
Multiple inheritance is allowed. Only the last definition of a method is kept: the redefinition in a subclass of a method that was visible in the parent class overrides the definition in the parent class. Previous definitions of a method can be reused by binding the related ancestor. Below, super is bound to the ancestor printable_point. The name super is a pseudo value identifier that can only be used to invoke a super-class method, as in super#print.
class printable_colored_point y c = object (self) val c = c method color = c inherit printable_point y as super method! print = print_string "("; super#print; print_string ", "; print_string (self#color); print_string ")" end;;class printable_colored_point : int -> string -> object val c : string val mutable x : int method color : string method get_x : int method move : int -> unit method print : unit end
let p' = new printable_colored_point 17 "red";;new point at (10, red) val p' : printable_colored_point = <obj>
p'#print;;(10, red)- : unit = ()
A private method that has been hidden in the parent class is no longer visible, and is thus not overridden. Since initializers are treated as private methods, all initializers along the class hierarchy are evaluated, in the order they are introduced.
Note that for clarity’s sake, the method print is explicitly marked as overriding another definition by annotating the method keyword with an exclamation mark !. If the method print were not overriding the print method of printable_point, the compiler would raise an error:
object method! m = () end;;Error: The method `m' has no previous definition
This explicit overriding annotation also works for val and inherit:
class another_printable_colored_point y c c' = object (self) inherit printable_point y inherit! printable_colored_point y c val! c = c' end;;class another_printable_colored_point : int -> string -> string -> object val c : string val mutable x : int method color : string method get_x : int method move : int -> unit method print : unit end
Reference cells can be implemented as objects. The naive definition fails to typecheck:
class oref x_init = object val mutable x = x_init method get = x method set y = x <- y end;;Error: Some type variables are unbound in this type: class oref : 'a -> object val mutable x : 'a method get : 'a method set : 'a -> unit end The method get has type 'a where 'a is unbound
The reason is that at least one of the methods has a polymorphic type (here, the type of the value stored in the reference cell), thus either the class should be parametric, or the method type should be constrained to a monomorphic type. A monomorphic instance of the class could be defined by:
class oref (x_init:int) = object val mutable x = x_init method get = x method set y = x <- y end;;class oref : int -> object val mutable x : int method get : int method set : int -> unit end
Note that since immediate objects do not define a class type, they have no such restriction.
let new_oref x_init = object val mutable x = x_init method get = x method set y = x <- y end;;val new_oref : 'a -> < get : 'a; set : 'a -> unit > = <fun>
On the other hand, a class for polymorphic references must explicitly list the type parameters in its declaration. Class type parameters are listed between [ and ]. The type parameters must also be bound somewhere in the class body by a type constraint.
class ['a] oref x_init = object val mutable x = (x_init : 'a) method get = x method set y = x <- y end;;class ['a] oref : 'a -> object val mutable x : 'a method get : 'a method set : 'a -> unit end
let r = new oref 1 in r#set 2; (r#get);;- : int = 2
The type parameter in the declaration may actually be constrained in the body of the class definition. In the class type, the actual value of the type parameter is displayed in the constraint clause.
class ['a] oref_succ (x_init:'a) = object val mutable x = x_init + 1 method get = x method set y = x <- y end;;class ['a] oref_succ : 'a -> object constraint 'a = int val mutable x : int method get : int method set : int -> unit end
Let us consider a more complex example: define a circle, whose center may be any kind of point. We put an additional type constraint in method move, since no free variables must remain unaccounted for by the class type parameters.
class ['a] circle (c : 'a) = object val mutable center = c method center = center method set_center c = center <- c method move = (center#move : int -> unit) end;;class ['a] circle : 'a -> object constraint 'a = < move : int -> unit; .. > val mutable center : 'a method center : 'a method move : int -> unit method set_center : 'a -> unit end
An alternate definition of circle, using a constraint clause in the class definition, is shown below. The type #point used below in the constraint clause is an abbreviation produced by the definition of class point. This abbreviation unifies with the type of any object belonging to a subclass of class point. It actually expands to < get_x : int; move : int -> unit; .. >. This leads to the following alternate definition of circle, which has slightly stronger constraints on its argument, as we now expect center to have a method get_x.
class ['a] circle (c : 'a) = object constraint 'a = #point val mutable center = c method center = center method set_center c = center <- c method move = center#move end;;class ['a] circle : 'a -> object constraint 'a = #point val mutable center : 'a method center : 'a method move : int -> unit method set_center : 'a -> unit end
The class colored_circle is a specialized version of class circle that requires the type of the center to unify with #colored_point, and adds a method color. Note that when specializing a parameterized class, the instance of type parameter must always be explicitly given. It is again written between [ and ].
class ['a] colored_circle c = object constraint 'a = #colored_point inherit ['a] circle c method color = center#color end;;class ['a] colored_circle : 'a -> object constraint 'a = #colored_point val mutable center : 'a method center : 'a method color : string method move : int -> unit method set_center : 'a -> unit end
While parameterized classes may be polymorphic in their contents, they are not enough to allow polymorphism of method use.
A classical example is defining an iterator.
List.fold_left;;- : ('a -> 'b -> 'a) -> 'a -> 'b list -> 'a = <fun>
class ['a] intlist (l : int list) = object method empty = (l = []) method fold f (accu : 'a) = List.fold_left f accu l end;;class ['a] intlist : int list -> object method empty : bool method fold : ('a -> int -> 'a) -> 'a -> 'a end
At first look, we seem to have a polymorphic iterator, however this does not work in practice.
let l = new intlist [1; 2; 3];;val l : '_weak2 intlist = <obj>
l#fold (fun x y -> x+y) 0;;- : int = 6
l;;- : int intlist = <obj>
l#fold (fun s x -> s ^ string_of_int x ^ " ") "" ;;Error: This expression has type int but an expression was expected of type string
Our iterator works, as shows its first use for summation. However, since objects themselves are not polymorphic (only their constructors are), using the fold method fixes its type for this individual object. Our next attempt to use it as a string iterator fails.
The problem here is that quantification was wrongly located: it is not the class we want to be polymorphic, but the fold method. This can be achieved by giving an explicitly polymorphic type in the method definition.
class intlist (l : int list) = object method empty = (l = []) method fold : 'a. ('a -> int -> 'a) -> 'a -> 'a = fun f accu -> List.fold_left f accu l end;;class intlist : int list -> object method empty : bool method fold : ('a -> int -> 'a) -> 'a -> 'a end
let l = new intlist [1; 2; 3];;val l : intlist = <obj>
l#fold (fun x y -> x+y) 0;;- : int = 6
l#fold (fun s x -> s ^ string_of_int x ^ " ") "";;- : string = "1 2 3 "
As you can see in the class type shown by the compiler, while polymorphic method types must be fully explicit in class definitions (appearing immediately after the method name), quantified type variables can be left implicit in class descriptions. Why require types to be explicit? The problem is that (int -> int -> int) -> int -> int would also be a valid type for fold, and it happens to be incompatible with the polymorphic type we gave (automatic instantiation only works for toplevel types variables, not for inner quantifiers, where it becomes an undecidable problem.) So the compiler cannot choose between those two types, and must be helped.
However, the type can be completely omitted in the class definition if it is already known, through inheritance or type constraints on self. Here is an example of method overriding.
class intlist_rev l = object inherit intlist l method! fold f accu = List.fold_left f accu (List.rev l) end;;
The following idiom separates description and definition.
class type ['a] iterator = object method fold : ('b -> 'a -> 'b) -> 'b -> 'b end;;
class intlist l = object (self : int #iterator) method empty = (l = []) method fold f accu = List.fold_left f accu l end;;
Note here the (self : int #iterator) idiom, which ensures that this object implements the interface iterator.
Polymorphic methods are called in exactly the same way as normal methods, but you should be aware of some limitations of type inference. Namely, a polymorphic method can only be called if its type is known at the call site. Otherwise, the method will be assumed to be monomorphic, and given an incompatible type.
let sum lst = lst#fold (fun x y -> x+y) 0;;val sum : < fold : (int -> int -> int) -> int -> 'a; .. > -> 'a = <fun>
sum l ;;Error: This expression has type intlist but an expression was expected of type < fold : (int -> int -> int) -> int -> 'a; .. > Types for method fold are incompatible
The workaround is easy: you should put a type constraint on the parameter.
let sum (lst : _ #iterator) = lst#fold (fun x y -> x+y) 0;;val sum : int #iterator -> int = <fun>
Of course the constraint may also be an explicit method type. Only occurences of quantified variables are required.
let sum lst = (lst : < fold : 'a. ('a -> _ -> 'a) -> 'a -> 'a; .. >)#fold (+) 0;;val sum : < fold : 'a. ('a -> int -> 'a) -> 'a -> 'a; .. > -> int = <fun>
Another use of polymorphic methods is to allow some form of implicit subtyping in method arguments. We have already seen in section 3.8 how some functions may be polymorphic in the class of their argument. This can be extended to methods.
class type point0 = object method get_x : int end;;class type point0 = object method get_x : int end
class distance_point x = object inherit point x method distance : 'a. (#point0 as 'a) -> int = fun other -> abs (other#get_x - x) end;;class distance_point : int -> object val mutable x : int method distance : #point0 -> int method get_offset : int method get_x : int method move : int -> unit end
let p = new distance_point 3 in (p#distance (new point 8), p#distance (new colored_point 1 "blue"));;- : int * int = (5, 2)
Note here the special syntax (#point0 as 'a) we have to use to quantify the extensible part of #point0. As for the variable binder, it can be omitted in class specifications. If you want polymorphism inside object field it must be quantified independently.
class multi_poly = object method m1 : 'a. (< n1 : 'b. 'b -> 'b; .. > as 'a) -> _ = fun o -> o#n1 true, o#n1 "hello" method m2 : 'a 'b. (< n2 : 'b -> bool; .. > as 'a) -> 'b -> _ = fun o x -> o#n2 x end;;class multi_poly : object method m1 : < n1 : 'b. 'b -> 'b; .. > -> bool * string method m2 : < n2 : 'b -> bool; .. > -> 'b -> bool end
In method m1, o must be an object with at least a method n1, itself polymorphic. In method m2, the argument of n2 and x must have the same type, which is quantified at the same level as 'a.
Subtyping is never implicit. There are, however, two ways to perform subtyping. The most general construction is fully explicit: both the domain and the codomain of the type coercion must be given.
We have seen that points and colored points have incompatible types. For instance, they cannot be mixed in the same list. However, a colored point can be coerced to a point, hiding its color method:
let colored_point_to_point cp = (cp : colored_point :> point);;val colored_point_to_point : colored_point -> point = <fun>
let p = new point 3 and q = new colored_point 4 "blue";;val p : point = <obj> val q : colored_point = <obj>
let l = [p; (colored_point_to_point q)];;val l : point list = [<obj>; <obj>]
An object of type t can be seen as an object of type t' only if t is a subtype of t'. For instance, a point cannot be seen as a colored point.
(p : point :> colored_point);;Error: Type point = < get_offset : int; get_x : int; move : int -> unit > is not a subtype of colored_point = < color : string; get_offset : int; get_x : int; move : int -> unit >
Indeed, narrowing coercions without runtime checks would be unsafe. Runtime type checks might raise exceptions, and they would require the presence of type information at runtime, which is not the case in the OCaml system. For these reasons, there is no such operation available in the language.
Be aware that subtyping and inheritance are not related. Inheritance is a syntactic relation between classes while subtyping is a semantic relation between types. For instance, the class of colored points could have been defined directly, without inheriting from the class of points; the type of colored points would remain unchanged and thus still be a subtype of points.
The domain of a coercion can often be omitted. For instance, one can define:
let to_point cp = (cp :> point);;val to_point : #point -> point = <fun>
In this case, the function colored_point_to_point is an instance of the function to_point. This is not always true, however. The fully explicit coercion is more precise and is sometimes unavoidable. Consider, for example, the following class:
class c0 = object method m = {< >} method n = 0 end;;class c0 : object ('a) method m : 'a method n : int end
The object type c0 is an abbreviation for <m : 'a; n : int> as 'a. Consider now the type declaration:
class type c1 = object method m : c1 end;;class type c1 = object method m : c1 end
The object type c1 is an abbreviation for the type <m : 'a> as 'a. The coercion from an object of type c0 to an object of type c1 is correct:
fun (x:c0) -> (x : c0 :> c1);;- : c0 -> c1 = <fun>
However, the domain of the coercion cannot always be omitted. In that case, the solution is to use the explicit form. Sometimes, a change in the class-type definition can also solve the problem
class type c2 = object ('a) method m : 'a end;;class type c2 = object ('a) method m : 'a end
fun (x:c0) -> (x :> c2);;- : c0 -> c2 = <fun>
While class types c1 and c2 are different, both object types c1 and c2 expand to the same object type (same method names and types). Yet, when the domain of a coercion is left implicit and its co-domain is an abbreviation of a known class type, then the class type, rather than the object type, is used to derive the coercion function. This allows leaving the domain implicit in most cases when coercing form a subclass to its superclass. The type of a coercion can always be seen as below:
let to_c1 x = (x :> c1);;val to_c1 : < m : #c1; .. > -> c1 = <fun>
let to_c2 x = (x :> c2);;val to_c2 : #c2 -> c2 = <fun>
Note the difference between these two coercions: in the case of to_c2, the type #c2 = < m : 'a; .. > as 'a is polymorphically recursive (according to the explicit recursion in the class type of c2); hence the success of applying this coercion to an object of class c0. On the other hand, in the first case, c1 was only expanded and unrolled twice to obtain < m : < m : c1; .. >; .. > (remember #c1 = < m : c1; .. >), without introducing recursion. You may also note that the type of to_c2 is #c2 -> c2 while the type of to_c1 is more general than #c1 -> c1. This is not always true, since there are class types for which some instances of #c are not subtypes of c, as explained in section 3.16. Yet, for parameterless classes the coercion (_ :> c) is always more general than (_ : #c :> c).
A common problem may occur when one tries to define a coercion to a class c while defining class c. The problem is due to the type abbreviation not being completely defined yet, and so its subtypes are not clearly known. Then, a coercion (_ :> c) or (_ : #c :> c) is taken to be the identity function, as in
function x -> (x :> 'a);;- : 'a -> 'a = <fun>
As a consequence, if the coercion is applied to self, as in the following example, the type of self is unified with the closed type c (a closed object type is an object type without ellipsis). This would constrain the type of self be closed and is thus rejected. Indeed, the type of self cannot be closed: this would prevent any further extension of the class. Therefore, a type error is generated when the unification of this type with another type would result in a closed object type.
class c = object method m = 1 end and d = object (self) inherit c method n = 2 method as_c = (self :> c) end;;Error: This expression cannot be coerced to type c = < m : int >; it has type < as_c : c; m : int; n : int; .. > but is here used with type c Self type cannot escape its class
However, the most common instance of this problem, coercing self to its current class, is detected as a special case by the type checker, and properly typed.
class c = object (self) method m = (self :> c) end;;class c : object method m : c end
This allows the following idiom, keeping a list of all objects belonging to a class or its subclasses:
let all_c = ref [];;val all_c : '_weak3 list ref = {contents = []}
class c (m : int) = object (self) method m = m initializer all_c := (self :> c) :: !all_c end;;class c : int -> object method m : int end
This idiom can in turn be used to retrieve an object whose type has been weakened:
let rec lookup_obj obj = function [] -> raise Not_found | obj' :: l -> if (obj :> < >) = (obj' :> < >) then obj' else lookup_obj obj l ;;val lookup_obj : < .. > -> (< .. > as 'a) list -> 'a = <fun>
let lookup_c obj = lookup_obj obj !all_c;;val lookup_c : < .. > -> < m : int > = <fun>
The type < m : int > we see here is just the expansion of c, due to the use of a reference; we have succeeded in getting back an object of type c.
The previous coercion problem can often be avoided by first
defining the abbreviation, using a class type:
class type c' = object method m : int end;;class type c' = object method m : int end
class c : c' = object method m = 1 end and d = object (self) inherit c method n = 2 method as_c = (self :> c') end;;class c : c' and d : object method as_c : c' method m : int method n : int end
It is also possible to use a virtual class. Inheriting from this class simultaneously forces all methods of c to have the same type as the methods of c'.
class virtual c' = object method virtual m : int end;;class virtual c' : object method virtual m : int end
class c = object (self) inherit c' method m = 1 end;;class c : object method m : int end
One could think of defining the type abbreviation directly:
type c' = <m : int>;;
However, the abbreviation #c' cannot be defined directly in a similar way. It can only be defined by a class or a class-type definition. This is because a #-abbreviation carries an implicit anonymous variable .. that cannot be explicitly named. The closer you get to it is:
type 'a c'_class = 'a constraint 'a = < m : int; .. >;;
with an extra type variable capturing the open object type.
It is possible to write a version of class point without assignments on the instance variables. The override construct {< ... >} returns a copy of “self” (that is, the current object), possibly changing the value of some instance variables.
class functional_point y = object val x = y method get_x = x method move d = {< x = x + d >} end;;class functional_point : int -> object ('a) val x : int method get_x : int method move : int -> 'a end
let p = new functional_point 7;;val p : functional_point = <obj>
p#get_x;;- : int = 7
(p#move 3)#get_x;;- : int = 10
p#get_x;;- : int = 7
Note that the type abbreviation functional_point is recursive, which can be seen in the class type of functional_point: the type of self is 'a and 'a appears inside the type of the method move.
The above definition of functional_point is not equivalent to the following:
class bad_functional_point y = object val x = y method get_x = x method move d = new bad_functional_point (x+d) end;;class bad_functional_point : int -> object val x : int method get_x : int method move : int -> bad_functional_point end
While objects of either class will behave the same, objects of their subclasses will be different. In a subclass of bad_functional_point, the method move will keep returning an object of the parent class. On the contrary, in a subclass of functional_point, the method move will return an object of the subclass.
Functional update is often used in conjunction with binary methods as illustrated in section 6.2.1.
Objects can also be cloned, whether they are functional or imperative. The library function Oo.copy makes a shallow copy of an object. That is, it returns a new object that has the same methods and instance variables as its argument. The instance variables are copied but their contents are shared. Assigning a new value to an instance variable of the copy (using a method call) will not affect instance variables of the original, and conversely. A deeper assignment (for example if the instance variable is a reference cell) will of course affect both the original and the copy.
The type of Oo.copy is the following:
Oo.copy;;- : (< .. > as 'a) -> 'a = <fun>
The keyword as in that type binds the type variable 'a to the object type < .. >. Therefore, Oo.copy takes an object with any methods (represented by the ellipsis), and returns an object of the same type. The type of Oo.copy is different from type < .. > -> < .. > as each ellipsis represents a different set of methods. Ellipsis actually behaves as a type variable.
let p = new point 5;;val p : point = <obj>
let q = Oo.copy p;;val q : point = <obj>
q#move 7; (p#get_x, q#get_x);;- : int * int = (5, 12)
In fact, Oo.copy p will behave as p#copy assuming that a public method copy with body {< >} has been defined in the class of p.
Objects can be compared using the generic comparison functions = and <>. Two objects are equal if and only if they are physically equal. In particular, an object and its copy are not equal.
let q = Oo.copy p;;val q : point = <obj>
p = q, p = p;;- : bool * bool = (false, true)
Other generic comparisons such as (<, <=, ...) can also be used on objects. The relation < defines an unspecified but strict ordering on objects. The ordering relationship between two objects is fixed once for all after the two objects have been created and it is not affected by mutation of fields.
Cloning and override have a non empty intersection. They are interchangeable when used within an object and without overriding any field:
class copy = object method copy = {< >} end;;class copy : object ('a) method copy : 'a end
class copy = object (self) method copy = Oo.copy self end;;class copy : object ('a) method copy : 'a end
Only the override can be used to actually override fields, and only the Oo.copy primitive can be used externally.
Cloning can also be used to provide facilities for saving and restoring the state of objects.
class backup = object (self : 'mytype) val mutable copy = None method save = copy <- Some {< copy = None >} method restore = match copy with Some x -> x | None -> self end;;class backup : object ('a) val mutable copy : 'a option method restore : 'a method save : unit end
The above definition will only backup one level. The backup facility can be added to any class by using multiple inheritance.
class ['a] backup_ref x = object inherit ['a] oref x inherit backup end;;class ['a] backup_ref : 'a -> object ('b) val mutable copy : 'b option val mutable x : 'a method get : 'a method restore : 'b method save : unit method set : 'a -> unit end
let rec get p n = if n = 0 then p # get else get (p # restore) (n-1);;val get : (< get : 'b; restore : 'a; .. > as 'a) -> int -> 'b = <fun>
let p = new backup_ref 0 in p # save; p # set 1; p # save; p # set 2; [get p 0; get p 1; get p 2; get p 3; get p 4];;- : int list = [2; 1; 1; 1; 1]
We can define a variant of backup that retains all copies. (We also add a method clear to manually erase all copies.)
class backup = object (self : 'mytype) val mutable copy = None method save = copy <- Some {< >} method restore = match copy with Some x -> x | None -> self method clear = copy <- None end;;class backup : object ('a) val mutable copy : 'a option method clear : unit method restore : 'a method save : unit end
class ['a] backup_ref x = object inherit ['a] oref x inherit backup end;;class ['a] backup_ref : 'a -> object ('b) val mutable copy : 'b option val mutable x : 'a method clear : unit method get : 'a method restore : 'b method save : unit method set : 'a -> unit end
let p = new backup_ref 0 in p # save; p # set 1; p # save; p # set 2; [get p 0; get p 1; get p 2; get p 3; get p 4];;- : int list = [2; 1; 0; 0; 0]
Recursive classes can be used to define objects whose types are mutually recursive.
class window = object val mutable top_widget = (None : widget option) method top_widget = top_widget end and widget (w : window) = object val window = w method window = window end;;class window : object val mutable top_widget : widget option method top_widget : widget option end and widget : window -> object val window : window method window : window end
Although their types are mutually recursive, the classes widget and window are themselves independent.
A binary method is a method which takes an argument of the same type as self. The class comparable below is a template for classes with a binary method leq of type 'a -> bool where the type variable 'a is bound to the type of self. Therefore, #comparable expands to < leq : 'a -> bool; .. > as 'a. We see here that the binder as also allows writing recursive types.
class virtual comparable = object (_ : 'a) method virtual leq : 'a -> bool end;;class virtual comparable : object ('a) method virtual leq : 'a -> bool end
We then define a subclass money of comparable. The class money simply wraps floats as comparable objects. We will extend it below with more operations. We have to use a type constraint on the class parameter x because the primitive <= is a polymorphic function in OCaml. The inherit clause ensures that the type of objects of this class is an instance of #comparable.
class money (x : float) = object inherit comparable val repr = x method value = repr method leq p = repr <= p#value end;;class money : float -> object ('a) val repr : float method leq : 'a -> bool method value : float end
Note that the type money is not a subtype of type comparable, as the self type appears in contravariant position in the type of method leq. Indeed, an object m of class money has a method leq that expects an argument of type money since it accesses its value method. Considering m of type comparable would allow a call to method leq on m with an argument that does not have a method value, which would be an error.
Similarly, the type money2 below is not a subtype of type money.
class money2 x = object inherit money x method times k = {< repr = k *. repr >} end;;class money2 : float -> object ('a) val repr : float method leq : 'a -> bool method times : float -> 'a method value : float end
It is however possible to define functions that manipulate objects of type either money or money2: the function min will return the minimum of any two objects whose type unifies with #comparable. The type of min is not the same as #comparable -> #comparable -> #comparable, as the abbreviation #comparable hides a type variable (an ellipsis). Each occurrence of this abbreviation generates a new variable.
let min (x : #comparable) y = if x#leq y then x else y;;val min : (#comparable as 'a) -> 'a -> 'a = <fun>
This function can be applied to objects of type money or money2.
(min (new money 1.3) (new money 3.1))#value;;- : float = 1.3
(min (new money2 5.0) (new money2 3.14))#value;;- : float = 3.14
More examples of binary methods can be found in sections 6.2.1 and 6.2.3.
Note the use of override for method times. Writing new money2 (k *. repr) instead of {< repr = k *. repr >} would not behave well with inheritance: in a subclass money3 of money2 the times method would return an object of class money2 but not of class money3 as would be expected.
The class money could naturally carry another binary method. Here is a direct definition:
class money x = object (self : 'a) val repr = x method value = repr method print = print_float repr method times k = {< repr = k *. x >} method leq (p : 'a) = repr <= p#value method plus (p : 'a) = {< repr = x +. p#value >} end;;class money : float -> object ('a) val repr : float method leq : 'a -> bool method plus : 'a -> 'a method print : unit method times : float -> 'a method value : float end
The above class money reveals a problem that often occurs with binary methods. In order to interact with other objects of the same class, the representation of money objects must be revealed, using a method such as value. If we remove all binary methods (here plus and leq), the representation can easily be hidden inside objects by removing the method value as well. However, this is not possible as soon as some binary method requires access to the representation of objects of the same class (other than self).
class safe_money x = object (self : 'a) val repr = x method print = print_float repr method times k = {< repr = k *. x >} end;;class safe_money : float -> object ('a) val repr : float method print : unit method times : float -> 'a end
Here, the representation of the object is known only to a particular object. To make it available to other objects of the same class, we are forced to make it available to the whole world. However we can easily restrict the visibility of the representation using the module system.
module type MONEY = sig type t class c : float -> object ('a) val repr : t method value : t method print : unit method times : float -> 'a method leq : 'a -> bool method plus : 'a -> 'a end end;;
module Euro : MONEY = struct type t = float class c x = object (self : 'a) val repr = x method value = repr method print = print_float repr method times k = {< repr = k *. x >} method leq (p : 'a) = repr <= p#value method plus (p : 'a) = {< repr = x +. p#value >} end end;;
Another example of friend functions may be found in section 6.2.3. These examples occur when a group of objects (here objects of the same class) and functions should see each others internal representation, while their representation should be hidden from the outside. The solution is always to define all friends in the same module, give access to the representation and use a signature constraint to make the representation abstract outside the module.
(Chapter written by Jacques Garrigue)
This chapter gives an overview of the new features in OCaml 3: labels, and polymorphic variants.
If you have a look at modules ending in Labels in the standard library, you will see that function types have annotations you did not have in the functions you defined yourself.
ListLabels.map;;- : f:('a -> 'b) -> 'a list -> 'b list = <fun>
StringLabels.sub;;- : string -> pos:int -> len:int -> string = <fun>
Such annotations of the form name: are called labels. They are meant to document the code, allow more checking, and give more flexibility to function application. You can give such names to arguments in your programs, by prefixing them with a tilde ~.
let f ~x ~y = x - y;;val f : x:int -> y:int -> int = <fun>
let x = 3 and y = 2 in f ~x ~y;;- : int = 1
When you want to use distinct names for the variable and the label appearing in the type, you can use a naming label of the form ~name:. This also applies when the argument is not a variable.
let f ~x:x1 ~y:y1 = x1 - y1;;val f : x:int -> y:int -> int = <fun>
f ~x:3 ~y:2;;- : int = 1
Labels obey the same rules as other identifiers in OCaml, that is you cannot use a reserved keyword (like in or to) as label.
Formal parameters and arguments are matched according to their respective labels1, the absence of label being interpreted as the empty label. This allows commuting arguments in applications. One can also partially apply a function on any argument, creating a new function of the remaining parameters.
let f ~x ~y = x - y;;val f : x:int -> y:int -> int = <fun>
f ~y:2 ~x:3;;- : int = 1
ListLabels.fold_left;;- : f:('a -> 'b -> 'a) -> init:'a -> 'b list -> 'a = <fun>
ListLabels.fold_left [1;2;3] ~init:0 ~f:( + );;- : int = 6
ListLabels.fold_left ~init:0;;- : f:(int -> 'a -> int) -> 'a list -> int = <fun>
If several arguments of a function bear the same label (or no label), they will not commute among themselves, and order matters. But they can still commute with other arguments.
let hline ~x:x1 ~x:x2 ~y = (x1, x2, y);;val hline : x:'a -> x:'b -> y:'c -> 'a * 'b * 'c = <fun>
hline ~x:3 ~y:2 ~x:5;;- : int * int * int = (3, 5, 2)
As an exception to the above parameter matching rules, if an application is total (omitting all optional arguments), labels may be omitted. In practice, many applications are total, so that labels can often be omitted.
f 3 2;;- : int = 1
ListLabels.map succ [1;2;3];;- : int list = [2; 3; 4]
But beware that functions like ListLabels.fold_left whose result type is a type variable will never be considered as totally applied.
ListLabels.fold_left ( + ) 0 [1;2;3];;Error: This expression has type int -> int -> int but an expression was expected of type 'a list
When a function is passed as an argument to a higher-order function, labels must match in both types. Neither adding nor removing labels are allowed.
let h g = g ~x:3 ~y:2;;val h : (x:int -> y:int -> 'a) -> 'a = <fun>
h f;;- : int = 1
h ( + ) ;;Error: This expression has type int -> int -> int but an expression was expected of type x:int -> y:int -> 'a
Note that when you don’t need an argument, you can still use a wildcard pattern, but you must prefix it with the label.
h (fun ~x:_ ~y -> y+1);;- : int = 3
An interesting feature of labeled arguments is that they can be made optional. For optional parameters, the question mark ? replaces the tilde ~ of non-optional ones, and the label is also prefixed by ? in the function type. Default values may be given for such optional parameters.
let bump ?(step = 1) x = x + step;;val bump : ?step:int -> int -> int = <fun>
bump 2;;- : int = 3
bump ~step:3 2;;- : int = 5
A function taking some optional arguments must also take at least one non-optional argument. The criterion for deciding whether an optional argument has been omitted is the non-labeled application of an argument appearing after this optional argument in the function type. Note that if that argument is labeled, you will only be able to eliminate optional arguments through the special case for total applications.
let test ?(x = 0) ?(y = 0) () ?(z = 0) () = (x, y, z);;val test : ?x:int -> ?y:int -> unit -> ?z:int -> unit -> int * int * int = <fun>
test ();;- : ?z:int -> unit -> int * int * int = <fun>
test ~x:2 () ~z:3 ();;- : int * int * int = (2, 0, 3)
Optional parameters may also commute with non-optional or unlabeled ones, as long as they are applied simultaneously. By nature, optional arguments do not commute with unlabeled arguments applied independently.
test ~y:2 ~x:3 () ();;- : int * int * int = (3, 2, 0)
test () () ~z:1 ~y:2 ~x:3;;- : int * int * int = (3, 2, 1)
(test () ()) ~z:1 ;;Error: This expression has type int * int * int This is not a function; it cannot be applied.
Here (test () ()) is already (0,0,0) and cannot be further applied.
Optional arguments are actually implemented as option types. If you do not give a default value, you have access to their internal representation, type 'a option = None | Some of 'a. You can then provide different behaviors when an argument is present or not.
let bump ?step x = match step with | None -> x * 2 | Some y -> x + y ;;val bump : ?step:int -> int -> int = <fun>
It may also be useful to relay an optional argument from a function call to another. This can be done by prefixing the applied argument with ?. This question mark disables the wrapping of optional argument in an option type.
let test2 ?x ?y () = test ?x ?y () ();;val test2 : ?x:int -> ?y:int -> unit -> int * int * int = <fun>
test2 ?x:None;;- : ?y:int -> unit -> int * int * int = <fun>
While they provide an increased comfort for writing function applications, labels and optional arguments have the pitfall that they cannot be inferred as completely as the rest of the language.
You can see it in the following two examples.
let h' g = g ~y:2 ~x:3;;val h' : (y:int -> x:int -> 'a) -> 'a = <fun>
h' f ;;Error: This expression has type x:int -> y:int -> int but an expression was expected of type y:int -> x:int -> 'a
let bump_it bump x = bump ~step:2 x;;val bump_it : (step:int -> 'a -> 'b) -> 'a -> 'b = <fun>
bump_it bump 1 ;;Error: This expression has type ?step:int -> int -> int but an expression was expected of type step:int -> 'a -> 'b
The first case is simple: g is passed ~y and then ~x, but f expects ~x and then ~y. This is correctly handled if we know the type of g to be x:int -> y:int -> int in advance, but otherwise this causes the above type clash. The simplest workaround is to apply formal parameters in a standard order.
The second example is more subtle: while we intended the argument bump to be of type ?step:int -> int -> int, it is inferred as step:int -> int -> 'a. These two types being incompatible (internally normal and optional arguments are different), a type error occurs when applying bump_it to the real bump.
We will not try here to explain in detail how type inference works. One must just understand that there is not enough information in the above program to deduce the correct type of g or bump. That is, there is no way to know whether an argument is optional or not, or which is the correct order, by looking only at how a function is applied. The strategy used by the compiler is to assume that there are no optional arguments, and that applications are done in the right order.
The right way to solve this problem for optional parameters is to add a type annotation to the argument bump.
let bump_it (bump : ?step:int -> int -> int) x = bump ~step:2 x;;val bump_it : (?step:int -> int -> int) -> int -> int = <fun>
bump_it bump 1;;- : int = 3
In practice, such problems appear mostly when using objects whose methods have optional arguments, so that writing the type of object arguments is often a good idea.
Normally the compiler generates a type error if you attempt to pass to a function a parameter whose type is different from the expected one. However, in the specific case where the expected type is a non-labeled function type, and the argument is a function expecting optional parameters, the compiler will attempt to transform the argument to have it match the expected type, by passing None for all optional parameters.
let twice f (x : int) = f(f x);;val twice : (int -> int) -> int -> int = <fun>
twice bump 2;;- : int = 8
This transformation is coherent with the intended semantics, including side-effects. That is, if the application of optional parameters shall produce side-effects, these are delayed until the received function is really applied to an argument.
Like for names, choosing labels for functions is not an easy task. A good labeling is a labeling which
We explain here the rules we applied when labeling OCaml libraries.
To speak in an “object-oriented” way, one can consider that each function has a main argument, its object, and other arguments related with its action, the parameters. To permit the combination of functions through functionals in commuting label mode, the object will not be labeled. Its role is clear from the function itself. The parameters are labeled with names reminding of their nature or their role. The best labels combine nature and role. When this is not possible the role is to be preferred, since the nature will often be given by the type itself. Obscure abbreviations should be avoided.
ListLabels.map : f:('a -> 'b) -> 'a list -> 'b list
UnixLabels.write : file_descr -> buf:bytes -> pos:int -> len:int -> unit
When there are several objects of same nature and role, they are all left unlabeled.
ListLabels.iter2 : f:('a -> 'b -> 'c) -> 'a list -> 'b list -> unit
When there is no preferable object, all arguments are labeled.
BytesLabels.blit : src:bytes -> src_pos:int -> dst:bytes -> dst_pos:int -> len:int -> unit
However, when there is only one argument, it is often left unlabeled.
BytesLabels.create : int -> bytes
This principle also applies to functions of several arguments whose return type is a type variable, as long as the role of each argument is not ambiguous. Labeling such functions may lead to awkward error messages when one attempts to omit labels in an application, as we have seen with ListLabels.fold_left.
Here are some of the label names you will find throughout the libraries.
| Label | Meaning |
| f: | a function to be applied |
| pos: | a position in a string, array or byte sequence |
| len: | a length |
| buf: | a byte sequence or string used as buffer |
| src: | the source of an operation |
| dst: | the destination of an operation |
| init: | the initial value for an iterator |
| cmp: | a comparison function, e.g. Pervasives.compare |
| mode: | an operation mode or a flag list |
All these are only suggestions, but keep in mind that the choice of labels is essential for readability. Bizarre choices will make the program harder to maintain.
In the ideal, the right function name with right labels should be enough to understand the function’s meaning. Since one can get this information with OCamlBrowser or the ocaml toplevel, the documentation is only used when a more detailed specification is needed.
Variants as presented in section 1.4 are a powerful tool to build data structures and algorithms. However they sometimes lack flexibility when used in modular programming. This is due to the fact that every constructor is assigned to a unique type when defined and used. Even if the same name appears in the definition of multiple types, the constructor itself belongs to only one type. Therefore, one cannot decide that a given constructor belongs to multiple types, or consider a value of some type to belong to some other type with more constructors.
With polymorphic variants, this original assumption is removed. That is, a variant tag does not belong to any type in particular, the type system will just check that it is an admissible value according to its use. You need not define a type before using a variant tag. A variant type will be inferred independently for each of its uses.
In programs, polymorphic variants work like usual ones. You just have to prefix their names with a backquote character `.
[`On; `Off];;- : [> `Off | `On ] list = [`On; `Off]
`Number 1;;- : [> `Number of int ] = `Number 1
let f = function `On -> 1 | `Off -> 0 | `Number n -> n;;val f : [< `Number of int | `Off | `On ] -> int = <fun>
List.map f [`On; `Off];;- : int list = [1; 0]
[>`Off|`On] list means that to match this list, you should at least be able to match `Off and `On, without argument. [<`On|`Off|`Number of int] means that f may be applied to `Off, `On (both without argument), or `Number n where n is an integer. The > and < inside the variant types show that they may still be refined, either by defining more tags or by allowing less. As such, they contain an implicit type variable. Because each of the variant types appears only once in the whole type, their implicit type variables are not shown.
The above variant types were polymorphic, allowing further refinement. When writing type annotations, one will most often describe fixed variant types, that is types that cannot be refined. This is also the case for type abbreviations. Such types do not contain < or >, but just an enumeration of the tags and their associated types, just like in a normal datatype definition.
type 'a vlist = [`Nil | `Cons of 'a * 'a vlist];;type 'a vlist = [ `Cons of 'a * 'a vlist | `Nil ]
let rec map f : 'a vlist -> 'b vlist = function | `Nil -> `Nil | `Cons(a, l) -> `Cons(f a, map f l) ;;val map : ('a -> 'b) -> 'a vlist -> 'b vlist = <fun>
Type-checking polymorphic variants is a subtle thing, and some expressions may result in more complex type information.
let f = function `A -> `C | `B -> `D | x -> x;;val f : ([> `A | `B | `C | `D ] as 'a) -> 'a = <fun>
f `E;;- : [> `A | `B | `C | `D | `E ] = `E
Here we are seeing two phenomena. First, since this matching is open (the last case catches any tag), we obtain the type [> `A | `B] rather than [< `A | `B] in a closed matching. Then, since x is returned as is, input and return types are identical. The notation as 'a denotes such type sharing. If we apply f to yet another tag `E, it gets added to the list.
let f1 = function `A x -> x = 1 | `B -> true | `C -> false let f2 = function `A x -> x = "a" | `B -> true ;;val f1 : [< `A of int | `B | `C ] -> bool = <fun> val f2 : [< `A of string | `B ] -> bool = <fun>
let f x = f1 x && f2 x;;val f : [< `A of string & int | `B ] -> bool = <fun>
Here f1 and f2 both accept the variant tags `A and `B, but the argument of `A is int for f1 and string for f2. In f’s type `C, only accepted by f1, disappears, but both argument types appear for `A as int & string. This means that if we pass the variant tag `A to f, its argument should be both int and string. Since there is no such value, f cannot be applied to `A, and `B is the only accepted input.
Even if a value has a fixed variant type, one can still give it a larger type through coercions. Coercions are normally written with both the source type and the destination type, but in simple cases the source type may be omitted.
type 'a wlist = [`Nil | `Cons of 'a * 'a wlist | `Snoc of 'a wlist * 'a];;type 'a wlist = [ `Cons of 'a * 'a wlist | `Nil | `Snoc of 'a wlist * 'a ]
let wlist_of_vlist l = (l : 'a vlist :> 'a wlist);;val wlist_of_vlist : 'a vlist -> 'a wlist = <fun>
let open_vlist l = (l : 'a vlist :> [> 'a vlist]);;val open_vlist : 'a vlist -> [> 'a vlist ] = <fun>
fun x -> (x :> [`A|`B|`C]);;- : [< `A | `B | `C ] -> [ `A | `B | `C ] = <fun>
You may also selectively coerce values through pattern matching.
let split_cases = function | `Nil | `Cons _ as x -> `A x | `Snoc _ as x -> `B x ;;val split_cases : [< `Cons of 'a | `Nil | `Snoc of 'b ] -> [> `A of [> `Cons of 'a | `Nil ] | `B of [> `Snoc of 'b ] ] = <fun>
When an or-pattern composed of variant tags is wrapped inside an alias-pattern, the alias is given a type containing only the tags enumerated in the or-pattern. This allows for many useful idioms, like incremental definition of functions.
let num x = `Num x let eval1 eval (`Num x) = x let rec eval x = eval1 eval x ;;val num : 'a -> [> `Num of 'a ] = <fun> val eval1 : 'a -> [< `Num of 'b ] -> 'b = <fun> val eval : [< `Num of 'a ] -> 'a = <fun>
let plus x y = `Plus(x,y) let eval2 eval = function | `Plus(x,y) -> eval x + eval y | `Num _ as x -> eval1 eval x let rec eval x = eval2 eval x ;;val plus : 'a -> 'b -> [> `Plus of 'a * 'b ] = <fun> val eval2 : ('a -> int) -> [< `Num of int | `Plus of 'a * 'a ] -> int = <fun> val eval : ([< `Num of int | `Plus of 'a * 'a ] as 'a) -> int = <fun>
To make this even more comfortable, you may use type definitions as abbreviations for or-patterns. That is, if you have defined type myvariant = [`Tag1 of int | `Tag2 of bool], then the pattern #myvariant is equivalent to writing (`Tag1(_ : int) | `Tag2(_ : bool)).
Such abbreviations may be used alone,
let f = function | #myvariant -> "myvariant" | `Tag3 -> "Tag3";;val f : [< `Tag1 of int | `Tag2 of bool | `Tag3 ] -> string = <fun>
or combined with with aliases.
let g1 = function `Tag1 _ -> "Tag1" | `Tag2 _ -> "Tag2";;val g1 : [< `Tag1 of 'a | `Tag2 of 'b ] -> string = <fun>
let g = function | #myvariant as x -> g1 x | `Tag3 -> "Tag3";;val g : [< `Tag1 of int | `Tag2 of bool | `Tag3 ] -> string = <fun>
After seeing the power of polymorphic variants, one may wonder why they were added to core language variants, rather than replacing them.
The answer is twofold. One first aspect is that while being pretty efficient, the lack of static type information allows for less optimizations, and makes polymorphic variants slightly heavier than core language ones. However noticeable differences would only appear on huge data structures.
More important is the fact that polymorphic variants, while being type-safe, result in a weaker type discipline. That is, core language variants do actually much more than ensuring type-safety, they also check that you use only declared constructors, that all constructors present in a data-structure are compatible, and they enforce typing constraints to their parameters.
For this reason, you must be more careful about making types explicit when you use polymorphic variants. When you write a library, this is easy since you can describe exact types in interfaces, but for simple programs you are probably better off with core language variants.
Beware also that some idioms make trivial errors very hard to find. For instance, the following code is probably wrong but the compiler has no way to see it.
type abc = [`A | `B | `C] ;;type abc = [ `A | `B | `C ]
let f = function | `As -> "A" | #abc -> "other" ;;val f : [< `A | `As | `B | `C ] -> string = <fun>
let f : abc -> string = f ;;val f : abc -> string = <fun>
You can avoid such risks by annotating the definition itself.
let f : abc -> string = function | `As -> "A" | #abc -> "other" ;;Error: This pattern matches values of type [? `As ] but a pattern was expected which matches values of type abc The second variant type does not allow tag(s) `As
This chapter covers more advanced questions related to the limitations of polymorphic functions and types. There are some situations in OCaml where the type inferred by the type checker may be less generic than expected. Such non-genericity can stem either from interactions between side-effect and typing or the difficulties of implicit polymorphic recursion and higher-rank polymorphism.
This chapter details each of these situations and, if it is possible, how to recover genericity.
Maybe the most frequent examples of non-genericity derive from the interactions between polymorphic types and mutation. A simple example appears when typing the following expression
let store = ref None ;;val store : '_weak1 option ref = {contents = None}
Since the type of None is 'a option and the function ref has type 'b -> 'b ref, a natural deduction for the type of store would be 'a option ref. However, the inferred type, '_weak1 option ref, is different. Type variables whose name starts with a _weak prefix like '_weak1 are weakly polymorphic type variables, sometimes shortened as weak type variables. A weak type variable is a placeholder for a single type that is currently unknown. Once the specific type t behind the placeholder type '_weak1 is known, all occurrences of '_weak1 will be replaced by t. For instance, we can define another option reference and store an int inside:
let another_store = ref None ;;val another_store : '_weak2 option ref = {contents = None}
another_store := Some 0; another_store ;;- : int option ref = {contents = Some 0}
After storing an int inside another_store, the type of another_store has been updated from '_weak2 option ref to int option ref. This distinction between weakly and generic polymorphic type variable protects OCaml programs from unsoundness and runtime errors. To understand from where unsoundness might come, consider this simple function which swaps a value x with the value stored inside a store reference, if there is such value:
let swap store x = match !store with | None -> store := Some x; x | Some y -> store := Some x; y;;val swap : 'a option ref -> 'a -> 'a = <fun>
We can apply this function to our store
let one = swap store 1 let one_again = swap store 2 let two = swap store 3;;val one : int = 1 val one_again : int = 1 val two : int = 2
After these three swaps the stored value is 3. Everything is fine up to now. We can then try to swap 3 with a more interesting value, for instance a function:
let error = swap store (fun x -> x);;Error: This expression should not be a function, the expected type is int
At this point, the type checker rightfully complains that it is not possible to swap an integer and a function, and that an int should always be traded for another int. Furthermore, the type checker prevents us to change manually the type of the value stored by store:
store := Some (fun x -> x);;Error: This expression should not be a function, the expected type is int
Indeed, looking at the type of store, we see that the weak type '_weak1 has been replaced by the type int
store;;- : int option ref = {contents = Some 3}
Therefore, after placing an int in store, we cannot use it to store any value other than an int. More generally, weak types protect the program from undue mutation of values with a polymorphic type.
Moreover, weak types cannot appear in the signature of toplevel modules: types must be known at compilation time. Otherwise, different compilation units could replace the weak type with different and incompatible types. For this reason, compiling the following small piece of code
let option_ref = ref None
yields a compilation error
Error: The type of this expression, '_weak1 option ref,
contains type variables that cannot be generalized
To solve this error, it is enough to add an explicit type annotation to specify the type at declaration time:
let option_ref: int option ref = ref None
This is in any case a good practice for such global mutable variables. Otherwise, they will pick out the type of first use. If there is a mistake at this point, this can result in confusing type errors when later, correct uses are flagged as errors.
Identifying the exact context in which polymorphic types should be replaced by weak types in a modular way is a difficult question. Indeed the type system must handle the possibility that functions may hide persistent mutable states. For instance, the following function uses an internal reference to implement a delayed identity function
let make_fake_id () = let store = ref None in fun x -> swap store x ;;val make_fake_id : unit -> 'a -> 'a = <fun>
let fake_id = make_fake_id();;val fake_id : '_weak3 -> '_weak3 = <fun>
It would be unsound to apply this fake_id function to values with different types. The function fake_id is therefore rightfully assigned the type '_weak3 -> '_weak3 rather than 'a -> 'a. At the same time, it ought to be possible to use a local mutable state without impacting the type of a function.
To circumvent these dual difficulties, the type checker considers that any value returned by a function might rely on persistent mutable states behind the scene and should be given a weak type. This restriction on the type of mutable values and the results of function application is called the value restriction. Note that this value restriction is conservative: there are situations where the value restriction is too cautious and gives a weak type to a value that could be safely generalized to a polymorphic type:
let not_id = (fun x -> x) (fun x -> x);;val not_id : '_weak4 -> '_weak4 = <fun>
Quite often, this happens when defining function using higher order function. To avoid this problem, a solution is to add an explicit argument to the function:
let id_again = fun x -> (fun x -> x) (fun x -> x) x;;val id_again : 'a -> 'a = <fun>
With this argument, id_again is seen as a function definition by the type checker and can therefore be generalized. This kind of manipulation is called eta-expansion in lambda calculus and is sometimes referred under this name.
There is another partial solution to the problem of unnecessary weak type, which is implemented directly within the type checker. Briefly, it is possible to prove that weak types that only appear as type parameters in covariant positions –also called positive positions– can be safely generalized to polymorphic types. For instance, the type 'a list is covariant in 'a:
let f () = [];;val f : unit -> 'a list = <fun>
let empty = f ();;val empty : 'a list = []
Remark that the type inferred for empty is 'a list and not '_weak5 list that should have occurred with the value restriction since f () is a function application.
The value restriction combined with this generalization for covariant type parameters is called the relaxed value restriction.
Variance describes how type constructors behave with respect to subtyping. Consider for instance a pair of type x and xy with x a subtype of xy, denoted x :> xy:
type x = [ `X ];;type x = [ `X ]
type xy = [ `X | `Y ];;type xy = [ `X | `Y ]
As x is a subtype of xy, we can convert a value of type x to a value of type xy:
let x:x = `X;;val x : x = `X
let x' = ( x :> xy);;val x' : xy = `X
Similarly, if we have a value of type x list, we can convert it to a value of type xy list, since we could convert each element one by one:
let l:x list = [`X; `X];;val l : x list = [`X; `X]
let l' = ( l :> xy list);;val l' : xy list = [`X; `X]
In other words, x :> xy implies that x list :> xy list, therefore the type constructor 'a list is covariant (it preserves subtyping) in its parameter 'a.
Contrarily, if we have a function that can handle values of type xy
let f: xy -> unit = function | `X -> () | `Y -> ();;val f : xy -> unit = <fun>
it can also handle values of type x:
let f' = (f :> x -> unit);;val f' : x -> unit = <fun>
Note that we can rewrite the type of f and f' as
type 'a proc = 'a -> unit let f' = (f: xy proc :> x proc);;type 'a proc = 'a -> unit val f' : x proc = <fun>
In this case, we have x :> xy implies xy proc :> x proc. Notice that the second subtyping relation reverse the order of x and xy: the type constructor 'a proc is contravariant in its parameter 'a. More generally, the function type constructor 'a -> 'b is covariant in its return type 'b and contravariant in its argument type 'a.
A type constructor can also be invariant in some of its type parameters, neither covariant nor contravariant. A typical example is a reference:
let x: x ref = ref `X;;val x : x ref = {contents = `X}
If we were able to coerce x to the type xy ref as a variable xy, we could use xy to store the value `Y inside the reference and then use the x value to read this content as a value of type x, which would break the type system.
More generally, as soon as a type variable appears in a position describing mutable state it becomes invariant. As a corollary, covariant variables will never denote mutable locations and can be safely generalized. For a better description, interested readers can consult the original article by Jacques Garrigue on http://www.math.nagoya-u.ac.jp/~garrigue/papers/morepoly-long.pdf
Together, the relaxed value restriction and type parameter covariance help to avoid eta-expansion in many situations.
Moreover, when the type definitions are exposed, the type checker is able to infer variance information on its own and one can benefit from the relaxed value restriction even unknowingly. However, this is not the case anymore when defining new abstract types. As an illustration, we can define a module type collection as:
module type COLLECTION = sig type 'a t val empty: unit -> 'a t end module Implementation = struct type 'a t = 'a list let empty ()= [] end;;module type COLLECTION = sig type 'a t val empty : unit -> 'a t end module Implementation : sig type 'a t = 'a list val empty : unit -> 'a list end
module List2: COLLECTION = Implementation;;module List2 : COLLECTION
In this situation, when coercing the module List2 to the module type COLLECTION, the type checker forgets that 'a List2.t was covariant in 'a. Consequently, the relaxed value restriction does not apply anymore:
List2.empty ();;- : '_weak5 List2.t = <abstr>
To keep the relaxed value restriction, we need to declare the abstract type 'a COLLECTION.t as covariant in 'a:
module type COLLECTION = sig type +'a t val empty: unit -> 'a t end module List2: COLLECTION = Implementation;;module type COLLECTION = sig type +'a t val empty : unit -> 'a t end module List2 : COLLECTION
We then recover polymorphism:
List2.empty ();;- : 'a List2.t = <abstr>
The second major class of non-genericity is directly related to the problem of type inference for polymorphic functions. In some circumstances, the type inferred by OCaml might be not general enough to allow the definition of some recursive functions, in particular for recursive function acting on non-regular algebraic data type.
With a regular polymorphic algebraic data type, the type parameters of the type constructor are constant within the definition of the type. For instance, we can look at arbitrarily nested list defined as:
type 'a regular_nested = List of 'a list | Nested of 'a regular_nested list let l = Nested[ List [1]; Nested [List[2;3]]; Nested[Nested[]] ];;type 'a regular_nested = List of 'a list | Nested of 'a regular_nested list val l : int regular_nested = Nested [List [1]; Nested [List [2; 3]]; Nested [Nested []]]
Note that the type constructor regular_nested always appears as 'a regular_nested in the definition above, with the same parameter 'a. Equipped with this type, one can compute a maximal depth with a classic recursive function
let rec maximal_depth = function | List _ -> 1 | Nested [] -> 0 | Nested (a::q) -> 1 + max (maximal_depth a) (maximal_depth (Nested q));;val maximal_depth : 'a regular_nested -> int = <fun>
Non-regular recursive algebraic data types correspond to polymorphic algebraic data types whose parameter types vary between the left and right side of the type definition. For instance, it might be interesting to define a datatype that ensures that all lists are nested at the same depth:
type 'a nested = List of 'a list | Nested of 'a list nested;;type 'a nested = List of 'a list | Nested of 'a list nested
Intuitively, a value of type 'a nested is a list of list …of list of elements a with k nested list. We can then adapt the maximal_depth function defined on regular_depth into a depth function that computes this k. As a first try, we may define
let rec depth = function | List _ -> 1 | Nested n -> 1 + depth n;;Error: This expression has type 'a list nested but an expression was expected of type 'a nested The type variable 'a occurs inside 'a list
The type error here comes from the fact that during the definition of depth, the type checker first assigns to depth the type 'a -> 'b . When typing the pattern matching, 'a -> 'b becomes 'a nested -> 'b, then 'a nested -> int once the List branch is typed. However, when typing the application depth n in the Nested branch, the type checker encounters a problem: depth n is applied to 'a list nested, it must therefore have the type 'a list nested -> 'b. Unifying this constraint with the previous one leads to the impossible constraint 'a list nested = 'a nested. In other words, within its definition, the recursive function depth is applied to values of type 'a t with different types 'a due to the non-regularity of the type constructor nested. This creates a problem because the type checker had introduced a new type variable 'a only at the definition of the function depth whereas, here, we need a different type variable for every application of the function depth.
The solution of this conundrum is to use an explicitly polymorphic type annotation for the type 'a:
let rec depth: 'a. 'a nested -> int = function | List _ -> 1 | Nested n -> 1 + depth n;;val depth : 'a nested -> int = <fun>
depth ( Nested(List [ [7]; [8] ]) );;- : int = 2
In the type of depth, 'a.'a nested -> int, the type variable 'a is universally quantified. In other words, 'a.'a nested -> int reads as “for all type 'a, depth maps 'a nested values to integers”. Whereas the standard type 'a nested -> int can be interpreted as “let be a type variable 'a, then depth maps 'a nested values to integers”. There are two major differences with these two type expressions. First, the explicit polymorphic annotation indicates to the type checker that it needs to introduce a new type variable every times the function depth is applied. This solves our problem with the definition of the function depth.
Second, it also notifies the type checker that the type of the function should be polymorphic. Indeed, without explicit polymorphic type annotation, the following type annotation is perfectly valid
let sum: 'a -> 'b -> 'c = fun x y -> x + y;;val sum : int -> int -> int = <fun>
since 'a,'b and 'c denote type variables that may or may not be polymorphic. Whereas, it is an error to unify an explicitly polymorphic type with a non-polymorphic type:
let sum: 'a 'b 'c. 'a -> 'b -> 'c = fun x y -> x + y;;Error: This definition has type int -> int -> int which is less general than 'a 'b 'c. 'a -> 'b -> 'c
An important remark here is that it is not needed to explicit fully the type of depth: it is sufficient to add annotations only for the universally quantified type variables:
let rec depth: 'a. 'a nested -> _ = function | List _ -> 1 | Nested n -> 1 + depth n;;val depth : 'a nested -> int = <fun>
depth ( Nested(List [ [7]; [8] ]) );;- : int = 2
With explicit polymorphic annotations, it becomes possible to implement any recursive function that depends only on the structure of the nested lists and not on the type of the elements. For instance, a more complex example would be to compute the total number of elements of the nested lists:
let len nested = let map_and_sum f = List.fold_left (fun acc x -> acc + f x) 0 in let rec len: 'a. ('a list -> int ) -> 'a nested -> int = fun nested_len n -> match n with | List l -> nested_len l | Nested n -> len (map_and_sum nested_len) n in len List.length nested;;val len : 'a nested -> int = <fun>
len (Nested(Nested(List [ [ [1;2]; [3] ]; [ []; [4]; [5;6;7]]; [[]] ])));;- : int = 7
Similarly, it may be necessary to use more than one explicitly polymorphic type variables, like for computing the nested list of list lengths of the nested list:
let shape n = let rec shape: 'a 'b. ('a nested -> int nested) -> ('b list list -> 'a list) -> 'b nested -> int nested = fun nest nested_shape -> function | List l -> raise (Invalid_argument "shape requires nested_list of depth greater than 1") | Nested (List l) -> nest @@ List (nested_shape l) | Nested n -> let nested_shape = List.map nested_shape in let nest x = nest (Nested x) in shape nest nested_shape n in shape (fun n -> n ) (fun l -> List.map List.length l ) n;;val shape : 'a nested -> int nested = <fun>
shape (Nested(Nested(List [ [ [1;2]; [3] ]; [ []; [4]; [5;6;7]]; [[]] ])));;- : int nested = Nested (List [[2; 1]; [0; 1; 3]; [0]])
Explicit polymorphic annotations are however not sufficient to cover all the cases where the inferred type of a function is less general than expected. A similar problem arises when using polymorphic functions as arguments of higher-order functions. For instance, we may want to compute the average depth or length of two nested lists:
let average_depth x y = (depth x + depth y) / 2;;val average_depth : 'a nested -> 'b nested -> int = <fun>
let average_len x y = (len x + len y) / 2;;val average_len : 'a nested -> 'b nested -> int = <fun>
let one = average_len (List [2]) (List [[]]);;val one : int = 1
It would be natural to factorize these two definitions as:
let average f x y = (f x + f y) / 2;;val average : ('a -> int) -> 'a -> 'a -> int = <fun>
However, the type of average len is less generic than the type of average_len, since it requires the type of the first and second argument to be the same:
average_len (List [2]) (List [[]]);;- : int = 1
average len (List [2]) (List [[]]);;Error: This expression has type 'a list but an expression was expected of type int
As previously with polymorphic recursion, the problem stems from the fact that type variables are introduced only at the start of the let definitions. When we compute both f x and f y, the type of x and y are unified together. To avoid this unification, we need to indicate to the type checker that f is polymorphic in its first argument. In some sense, we would want average to have type
val average: ('a. 'a nested -> int) -> 'a nested -> 'b nested -> int
Note that this syntax is not valid within OCaml: average has an universally quantified type 'a inside the type of one of its argument whereas for polymorphic recursion the universally quantified type was introduced before the rest of the type. This position of the universally quantified type means that average is a second-rank polymorphic function. This kind of higher-rank functions is not directly supported by OCaml: type inference for second-rank polymorphic function and beyond is undecidable; therefore using this kind of higher-rank functions requires to handle manually these universally quantified types.
In OCaml, there are two ways to introduce this kind of explicit universally quantified types: universally quantified record fields,
type 'a nested_reduction = { f:'elt. 'elt nested -> 'a };;type 'a nested_reduction = { f : 'elt. 'elt nested -> 'a; }
let boxed_len = { f = len };;val boxed_len : int nested_reduction = {f = <fun>}
and universally quantified object methods:
let obj_len = object method f:'a. 'a nested -> 'b = len end;;val obj_len : < f : 'a. 'a nested -> int > = <obj>
To solve our problem, we can therefore use either the record solution:
let average nsm x y = (nsm.f x + nsm.f y) / 2 ;;val average : int nested_reduction -> 'a nested -> 'b nested -> int = <fun>
or the object one:
let average (obj:<f:'a. 'a nested -> _ > ) x y = (obj#f x + obj#f y) / 2 ;;val average : < f : 'a. 'a nested -> int > -> 'b nested -> 'c nested -> int = <fun>
(Chapter written by Didier Rémy)
In this chapter, we show some larger examples using objects, classes and modules. We review many of the object features simultaneously on the example of a bank account. We show how modules taken from the standard library can be expressed as classes. Lastly, we describe a programming pattern known as virtual types through the example of window managers.
In this section, we illustrate most aspects of Object and inheritance by refining, debugging, and specializing the following initial naive definition of a simple bank account. (We reuse the module Euro defined at the end of chapter 3.)
let euro = new Euro.c;;val euro : float -> Euro.c = <fun>
let zero = euro 0.;;val zero : Euro.c = <obj>
let neg x = x#times (-1.);;val neg : < times : float -> 'a; .. > -> 'a = <fun>
class account = object val mutable balance = zero method balance = balance method deposit x = balance <- balance # plus x method withdraw x = if x#leq balance then (balance <- balance # plus (neg x); x) else zero end;;class account : object val mutable balance : Euro.c method balance : Euro.c method deposit : Euro.c -> unit method withdraw : Euro.c -> Euro.c end
let c = new account in c # deposit (euro 100.); c # withdraw (euro 50.);;- : Euro.c = <obj>
We now refine this definition with a method to compute interest.
class account_with_interests = object (self) inherit account method private interest = self # deposit (self # balance # times 0.03) end;;class account_with_interests : object val mutable balance : Euro.c method balance : Euro.c method deposit : Euro.c -> unit method private interest : unit method withdraw : Euro.c -> Euro.c end
We make the method interest private, since clearly it should not be called freely from the outside. Here, it is only made accessible to subclasses that will manage monthly or yearly updates of the account.
We should soon fix a bug in the current definition: the deposit method can be used for withdrawing money by depositing negative amounts. We can fix this directly:
class safe_account = object inherit account method deposit x = if zero#leq x then balance <- balance#plus x end;;class safe_account : object val mutable balance : Euro.c method balance : Euro.c method deposit : Euro.c -> unit method withdraw : Euro.c -> Euro.c end
However, the bug might be fixed more safely by the following definition:
class safe_account = object inherit account as unsafe method deposit x = if zero#leq x then unsafe # deposit x else raise (Invalid_argument "deposit") end;;class safe_account : object val mutable balance : Euro.c method balance : Euro.c method deposit : Euro.c -> unit method withdraw : Euro.c -> Euro.c end
In particular, this does not require the knowledge of the implementation of the method deposit.
To keep track of operations, we extend the class with a mutable field history and a private method trace to add an operation in the log. Then each method to be traced is redefined.
type 'a operation = Deposit of 'a | Retrieval of 'a;;type 'a operation = Deposit of 'a | Retrieval of 'a
class account_with_history = object (self) inherit safe_account as super val mutable history = [] method private trace x = history <- x :: history method deposit x = self#trace (Deposit x); super#deposit x method withdraw x = self#trace (Retrieval x); super#withdraw x method history = List.rev history end;;class account_with_history : object val mutable balance : Euro.c val mutable history : Euro.c operation list method balance : Euro.c method deposit : Euro.c -> unit method history : Euro.c operation list method private trace : Euro.c operation -> unit method withdraw : Euro.c -> Euro.c end
One may wish to open an account and simultaneously deposit some initial amount. Although the initial implementation did not address this requirement, it can be achieved by using an initializer.
class account_with_deposit x = object inherit account_with_history initializer balance <- x end;;class account_with_deposit : Euro.c -> object val mutable balance : Euro.c val mutable history : Euro.c operation list method balance : Euro.c method deposit : Euro.c -> unit method history : Euro.c operation list method private trace : Euro.c operation -> unit method withdraw : Euro.c -> Euro.c end
A better alternative is:
class account_with_deposit x = object (self) inherit account_with_history initializer self#deposit x end;;class account_with_deposit : Euro.c -> object val mutable balance : Euro.c val mutable history : Euro.c operation list method balance : Euro.c method deposit : Euro.c -> unit method history : Euro.c operation list method private trace : Euro.c operation -> unit method withdraw : Euro.c -> Euro.c end
Indeed, the latter is safer since the call to deposit will automatically benefit from safety checks and from the trace. Let’s test it:
let ccp = new account_with_deposit (euro 100.) in let _balance = ccp#withdraw (euro 50.) in ccp#history;;- : Euro.c operation list = [Deposit <obj>; Retrieval <obj>]
Closing an account can be done with the following polymorphic function:
let close c = c#withdraw c#balance;;val close : < balance : 'a; withdraw : 'a -> 'b; .. > -> 'b = <fun>
Of course, this applies to all sorts of accounts.
Finally, we gather several versions of the account into a module Account abstracted over some currency.
let today () = (01,01,2000) (* an approximation *) module Account (M:MONEY) = struct type m = M.c let m = new M.c let zero = m 0. class bank = object (self) val mutable balance = zero method balance = balance val mutable history = [] method private trace x = history <- x::history method deposit x = self#trace (Deposit x); if zero#leq x then balance <- balance # plus x else raise (Invalid_argument "deposit") method withdraw x = if x#leq balance then (balance <- balance # plus (neg x); self#trace (Retrieval x); x) else zero method history = List.rev history end class type client_view = object method deposit : m -> unit method history : m operation list method withdraw : m -> m method balance : m end class virtual check_client x = let y = if (m 100.)#leq x then x else raise (Failure "Insufficient initial deposit") in object (self) initializer self#deposit y method virtual deposit: m -> unit end module Client (B : sig class bank : client_view end) = struct class account x : client_view = object inherit B.bank inherit check_client x end let discount x = let c = new account x in if today() < (1998,10,30) then c # deposit (m 100.); c end end;;
This shows the use of modules to group several class definitions that can in fact be thought of as a single unit. This unit would be provided by a bank for both internal and external uses. This is implemented as a functor that abstracts over the currency so that the same code can be used to provide accounts in different currencies.
The class bank is the real implementation of the bank account (it could have been inlined). This is the one that will be used for further extensions, refinements, etc. Conversely, the client will only be given the client view.
module Euro_account = Account(Euro);;
module Client = Euro_account.Client (Euro_account);;
new Client.account (new Euro.c 100.);;
Hence, the clients do not have direct access to the balance, nor the history of their own accounts. Their only way to change their balance is to deposit or withdraw money. It is important to give the clients a class and not just the ability to create accounts (such as the promotional discount account), so that they can personalize their account. For instance, a client may refine the deposit and withdraw methods so as to do his own financial bookkeeping, automatically. On the other hand, the function discount is given as such, with no possibility for further personalization.
It is important to provide the client’s view as a functor Client so that client accounts can still be built after a possible specialization of the bank. The functor Client may remain unchanged and be passed the new definition to initialize a client’s view of the extended account.
module Investment_account (M : MONEY) = struct type m = M.c module A = Account(M) class bank = object inherit A.bank as super method deposit x = if (new M.c 1000.)#leq x then print_string "Would you like to invest?"; super#deposit x end module Client = A.Client end;;
The functor Client may also be redefined when some new features of the account can be given to the client.
module Internet_account (M : MONEY) = struct type m = M.c module A = Account(M) class bank = object inherit A.bank method mail s = print_string s end class type client_view = object method deposit : m -> unit method history : m operation list method withdraw : m -> m method balance : m method mail : string -> unit end module Client (B : sig class bank : client_view end) = struct class account x : client_view = object inherit B.bank inherit A.check_client x end end end;;
One may wonder whether it is possible to treat primitive types such as integers and strings as objects. Although this is usually uninteresting for integers or strings, there may be some situations where this is desirable. The class money above is such an example. We show here how to do it for strings.
A naive definition of strings as objects could be:
class ostring s = object method get n = String.get s n method print = print_string s method escaped = new ostring (String.escaped s) end;;class ostring : string -> object method escaped : ostring method get : int -> char method print : unit end
However, the method escaped returns an object of the class ostring, and not an object of the current class. Hence, if the class is further extended, the method escaped will only return an object of the parent class.
class sub_string s = object inherit ostring s method sub start len = new sub_string (String.sub s start len) end;;class sub_string : string -> object method escaped : ostring method get : int -> char method print : unit method sub : int -> int -> sub_string end
As seen in section 3.16, the solution is to use functional update instead. We need to create an instance variable containing the representation s of the string.
class better_string s = object val repr = s method get n = String.get repr n method print = print_string repr method escaped = {< repr = String.escaped repr >} method sub start len = {< repr = String.sub s start len >} end;;class better_string : string -> object ('a) val repr : string method escaped : 'a method get : int -> char method print : unit method sub : int -> int -> 'a end
As shown in the inferred type, the methods escaped and sub now return objects of the same type as the one of the class.
Another difficulty is the implementation of the method concat. In order to concatenate a string with another string of the same class, one must be able to access the instance variable externally. Thus, a method repr returning s must be defined. Here is the correct definition of strings:
class ostring s = object (self : 'mytype) val repr = s method repr = repr method get n = String.get repr n method print = print_string repr method escaped = {< repr = String.escaped repr >} method sub start len = {< repr = String.sub s start len >} method concat (t : 'mytype) = {< repr = repr ^ t#repr >} end;;class ostring : string -> object ('a) val repr : string method concat : 'a -> 'a method escaped : 'a method get : int -> char method print : unit method repr : string method sub : int -> int -> 'a end
Another constructor of the class string can be defined to return a new string of a given length:
class cstring n = ostring (String.make n ' ');;class cstring : int -> ostring
Here, exposing the representation of strings is probably harmless. We do could also hide the representation of strings as we hid the currency in the class money of section 3.17.
There is sometimes an alternative between using modules or classes for parametric data types. Indeed, there are situations when the two approaches are quite similar. For instance, a stack can be straightforwardly implemented as a class:
exception Empty;;exception Empty
class ['a] stack = object val mutable l = ([] : 'a list) method push x = l <- x::l method pop = match l with [] -> raise Empty | a::l' -> l <- l'; a method clear = l <- [] method length = List.length l end;;class ['a] stack : object val mutable l : 'a list method clear : unit method length : int method pop : 'a method push : 'a -> unit end
However, writing a method for iterating over a stack is more problematic. A method fold would have type ('b -> 'a -> 'b) -> 'b -> 'b. Here 'a is the parameter of the stack. The parameter 'b is not related to the class 'a stack but to the argument that will be passed to the method fold. A naive approach is to make 'b an extra parameter of class stack:
class ['a, 'b] stack2 = object inherit ['a] stack method fold f (x : 'b) = List.fold_left f x l end;;class ['a, 'b] stack2 : object val mutable l : 'a list method clear : unit method fold : ('b -> 'a -> 'b) -> 'b -> 'b method length : int method pop : 'a method push : 'a -> unit end
However, the method fold of a given object can only be applied to functions that all have the same type:
let s = new stack2;;val s : ('_weak1, '_weak2) stack2 = <obj>
s#fold ( + ) 0;;- : int = 0
s;;- : (int, int) stack2 = <obj>
A better solution is to use polymorphic methods, which were introduced in OCaml version 3.05. Polymorphic methods makes it possible to treat the type variable 'b in the type of fold as universally quantified, giving fold the polymorphic type Forall 'b. ('b -> 'a -> 'b) -> 'b -> 'b. An explicit type declaration on the method fold is required, since the type checker cannot infer the polymorphic type by itself.
class ['a] stack3 = object inherit ['a] stack method fold : 'b. ('b -> 'a -> 'b) -> 'b -> 'b = fun f x -> List.fold_left f x l end;;class ['a] stack3 : object val mutable l : 'a list method clear : unit method fold : ('b -> 'a -> 'b) -> 'b -> 'b method length : int method pop : 'a method push : 'a -> unit end
A simplified version of object-oriented hash tables should have the following class type.
class type ['a, 'b] hash_table = object method find : 'a -> 'b method add : 'a -> 'b -> unit end;;class type ['a, 'b] hash_table = object method add : 'a -> 'b -> unit method find : 'a -> 'b end
A simple implementation, which is quite reasonable for small hash tables is to use an association list:
class ['a, 'b] small_hashtbl : ['a, 'b] hash_table = object val mutable table = [] method find key = List.assoc key table method add key valeur = table <- (key, valeur) :: table end;;class ['a, 'b] small_hashtbl : ['a, 'b] hash_table
A better implementation, and one that scales up better, is to use a true hash table… whose elements are small hash tables!
class ['a, 'b] hashtbl size : ['a, 'b] hash_table = object (self) val table = Array.init size (fun i -> new small_hashtbl) method private hash key = (Hashtbl.hash key) mod (Array.length table) method find key = table.(self#hash key) # find key method add key = table.(self#hash key) # add key end;;class ['a, 'b] hashtbl : int -> ['a, 'b] hash_table
Implementing sets leads to another difficulty. Indeed, the method union needs to be able to access the internal representation of another object of the same class.
This is another instance of friend functions as seen in section 3.17. Indeed, this is the same mechanism used in the module Set in the absence of objects.
In the object-oriented version of sets, we only need to add an additional method tag to return the representation of a set. Since sets are parametric in the type of elements, the method tag has a parametric type 'a tag, concrete within the module definition but abstract in its signature. From outside, it will then be guaranteed that two objects with a method tag of the same type will share the same representation.
module type SET = sig type 'a tag class ['a] c : object ('b) method is_empty : bool method mem : 'a -> bool method add : 'a -> 'b method union : 'b -> 'b method iter : ('a -> unit) -> unit method tag : 'a tag end end;;
module Set : SET = struct let rec merge l1 l2 = match l1 with [] -> l2 | h1 :: t1 -> match l2 with [] -> l1 | h2 :: t2 -> if h1 < h2 then h1 :: merge t1 l2 else if h1 > h2 then h2 :: merge l1 t2 else merge t1 l2 type 'a tag = 'a list class ['a] c = object (_ : 'b) val repr = ([] : 'a list) method is_empty = (repr = []) method mem x = List.exists (( = ) x) repr method add x = {< repr = merge [x] repr >} method union (s : 'b) = {< repr = merge repr s#tag >} method iter (f : 'a -> unit) = List.iter f repr method tag = repr end end;;
The following example, known as the subject/observer pattern, is often presented in the literature as a difficult inheritance problem with inter-connected classes. The general pattern amounts to the definition a pair of two classes that recursively interact with one another.
The class observer has a distinguished method notify that requires two arguments, a subject and an event to execute an action.
class virtual ['subject, 'event] observer = object method virtual notify : 'subject -> 'event -> unit end;;class virtual ['subject, 'event] observer : object method virtual notify : 'subject -> 'event -> unit end
The class subject remembers a list of observers in an instance variable, and has a distinguished method notify_observers to broadcast the message notify to all observers with a particular event e.
class ['observer, 'event] subject = object (self) val mutable observers = ([]:'observer list) method add_observer obs = observers <- (obs :: observers) method notify_observers (e : 'event) = List.iter (fun x -> x#notify self e) observers end;;class ['a, 'event] subject : object ('b) constraint 'a = < notify : 'b -> 'event -> unit; .. > val mutable observers : 'a list method add_observer : 'a -> unit method notify_observers : 'event -> unit end
The difficulty usually lies in defining instances of the pattern above by inheritance. This can be done in a natural and obvious manner in OCaml, as shown on the following example manipulating windows.
type event = Raise | Resize | Move;;type event = Raise | Resize | Move
let string_of_event = function Raise -> "Raise" | Resize -> "Resize" | Move -> "Move";;val string_of_event : event -> string = <fun>
let count = ref 0;;val count : int ref = {contents = 0}
class ['observer] window_subject = let id = count := succ !count; !count in object (self) inherit ['observer, event] subject val mutable position = 0 method identity = id method move x = position <- position + x; self#notify_observers Move method draw = Printf.printf "{Position = %d}\n" position; end;;class ['a] window_subject : object ('b) constraint 'a = < notify : 'b -> event -> unit; .. > val mutable observers : 'a list val mutable position : int method add_observer : 'a -> unit method draw : unit method identity : int method move : int -> unit method notify_observers : event -> unit end
class ['subject] window_observer = object inherit ['subject, event] observer method notify s e = s#draw end;;class ['a] window_observer : object constraint 'a = < draw : unit; .. > method notify : 'a -> event -> unit end
As can be expected, the type of window is recursive.
let window = new window_subject;;val window : < notify : 'a -> event -> unit; _.. > window_subject as 'a = <obj>
However, the two classes of window_subject and window_observer are not mutually recursive.
let window_observer = new window_observer;;val window_observer : < draw : unit; _.. > window_observer = <obj>
window#add_observer window_observer;;- : unit = ()
window#move 1;;{Position = 1} - : unit = ()
Classes window_observer and window_subject can still be extended by inheritance. For instance, one may enrich the subject with new behaviors and refine the behavior of the observer.
class ['observer] richer_window_subject = object (self) inherit ['observer] window_subject val mutable size = 1 method resize x = size <- size + x; self#notify_observers Resize val mutable top = false method raise = top <- true; self#notify_observers Raise method draw = Printf.printf "{Position = %d; Size = %d}\n" position size; end;;class ['a] richer_window_subject : object ('b) constraint 'a = < notify : 'b -> event -> unit; .. > val mutable observers : 'a list val mutable position : int val mutable size : int val mutable top : bool method add_observer : 'a -> unit method draw : unit method identity : int method move : int -> unit method notify_observers : event -> unit method raise : unit method resize : int -> unit end
class ['subject] richer_window_observer = object inherit ['subject] window_observer as super method notify s e = if e <> Raise then s#raise; super#notify s e end;;class ['a] richer_window_observer : object constraint 'a = < draw : unit; raise : unit; .. > method notify : 'a -> event -> unit end
We can also create a different kind of observer:
class ['subject] trace_observer = object inherit ['subject, event] observer method notify s e = Printf.printf "<Window %d <== %s>\n" s#identity (string_of_event e) end;;class ['a] trace_observer : object constraint 'a = < identity : int; .. > method notify : 'a -> event -> unit end
and attach several observers to the same object:
let window = new richer_window_subject;;val window : < notify : 'a -> event -> unit; _.. > richer_window_subject as 'a = <obj>
window#add_observer (new richer_window_observer);;- : unit = ()
window#add_observer (new trace_observer);;- : unit = ()
window#move 1; window#resize 2;;<Window 1 <== Move> <Window 1 <== Raise> {Position = 1; Size = 1} {Position = 1; Size = 1} <Window 1 <== Resize> <Window 1 <== Raise> {Position = 1; Size = 3} {Position = 1; Size = 3} - : unit = ()
Part II |
This document is intended as a reference manual for the OCaml language. It lists the language constructs, and gives their precise syntax and informal semantics. It is by no means a tutorial introduction to the language: there is not a single example. A good working knowledge of OCaml is assumed.
No attempt has been made at mathematical rigor: words are employed with their intuitive meaning, without further definition. As a consequence, the typing rules have been left out, by lack of the mathematical framework required to express them, while they are definitely part of a full formal definition of the language.
The syntax of the language is given in BNF-like notation. Terminal symbols are set in typewriter font (like this). Non-terminal symbols are set in italic font (like that). Square brackets […] denote optional components. Curly brackets {…} denotes zero, one or several repetitions of the enclosed components. Curly brackets with a trailing plus sign {…}+ denote one or several repetitions of the enclosed components. Parentheses (…) denote grouping.
The following characters are considered as blanks: space, horizontal tabulation, carriage return, line feed and form feed. Blanks are ignored, but they separate adjacent identifiers, literals and keywords that would otherwise be confused as one single identifier, literal or keyword.
Comments are introduced by the two characters (*, with no intervening blanks, and terminated by the characters *), with no intervening blanks. Comments are treated as blank characters. Comments do not occur inside string or character literals. Nested comments are handled correctly.
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Identifiers are sequences of letters, digits, _ (the underscore character), and ' (the single quote), starting with a letter or an underscore. Letters contain at least the 52 lowercase and uppercase letters from the ASCII set. The current implementation also recognizes as letters some characters from the ISO 8859-1 set (characters 192–214 and 216–222 as uppercase letters; characters 223–246 and 248–255 as lowercase letters). This feature is deprecated and should be avoided for future compatibility.
All characters in an identifier are meaningful. The current implementation accepts identifiers up to 16000000 characters in length.
In many places, OCaml makes a distinction between capitalized identifiers and identifiers that begin with a lowercase letter. The underscore character is considered a lowercase letter for this purpose.
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An integer literal is a sequence of one or more digits, optionally preceded by a minus sign. By default, integer literals are in decimal (radix 10). The following prefixes select a different radix:
| Prefix | Radix |
| 0x, 0X | hexadecimal (radix 16) |
| 0o, 0O | octal (radix 8) |
| 0b, 0B | binary (radix 2) |
(The initial 0 is the digit zero; the O for octal is the letter O.) The interpretation of integer literals that fall outside the range of representable integer values is undefined.
For convenience and readability, underscore characters (_) are accepted (and ignored) within integer literals.
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Floating-point decimal literals consist in an integer part, a fractional part and an exponent part. The integer part is a sequence of one or more digits, optionally preceded by a minus sign. The fractional part is a decimal point followed by zero, one or more digits. The exponent part is the character e or E followed by an optional + or - sign, followed by one or more digits. It is interpreted as a power of 10. The fractional part or the exponent part can be omitted but not both, to avoid ambiguity with integer literals. The interpretation of floating-point literals that fall outside the range of representable floating-point values is undefined.
Floating-point hexadecimal literals are denoted with the 0x or 0X prefix. The syntax is similar to that of floating-point decimal literals, with the following differences. The integer part and the fractional part use hexadecimal digits. The exponent part starts with the character p or P. It is written in decimal and interpreted as a power of 2.
For convenience and readability, underscore characters (_) are accepted (and ignored) within floating-point literals.
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Character literals are delimited by ' (single quote) characters. The two single quotes enclose either one character different from ' and \, or one of the escape sequences below:
| Sequence | Character denoted |
| \\ | backslash (\) |
| \" | double quote (") |
| \' | single quote (') |
| \n | linefeed (LF) |
| \r | carriage return (CR) |
| \t | horizontal tabulation (TAB) |
| \b | backspace (BS) |
| \space | space (SPC) |
| \ddd | the character with ASCII code ddd in decimal |
| \xhh | the character with ASCII code hh in hexadecimal |
| \oooo | the character with ASCII code ooo in octal |
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String literals are delimited by " (double quote) characters. The two double quotes enclose a sequence of either characters different from " and \, or escape sequences from the table given above for character literals, or a Unicode character escape sequence.
A Unicode character escape sequence is substituted by the UTF-8 encoding of the specified Unicode scalar value. The Unicode scalar value, an integer in the ranges 0x0000...0xD7FF or 0xE000...0x10FFFF, is defined using 1 to 6 hexadecimal digits; leading zeros are allowed.
To allow splitting long string literals across lines, the sequence \newline spaces-or-tabs (a backslash at the end of a line followed by any number of spaces and horizontal tabulations at the beginning of the next line) is ignored inside string literals.
The current implementation places practically no restrictions on the length of string literals.
To avoid ambiguities, naming labels in expressions cannot just be defined syntactically as the sequence of the three tokens ~, ident and :, and have to be defined at the lexical level.
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Naming labels come in two flavours: label for normal arguments and optlabel for optional ones. They are simply distinguished by their first character, either ~ or ?.
Despite label and optlabel being lexical entities in expressions, their expansions ~ label-name : and ? label-name : will be used in grammars, for the sake of readability. Note also that inside type expressions, this expansion can be taken literally, i.e. there are really 3 tokens, with optional blanks between them.
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See also the following language extensions: extension operators and extended indexing operators.
Sequences of “operator characters”, such as <=> or !!, are read as a single token from the infix-symbol or prefix-symbol class. These symbols are parsed as prefix and infix operators inside expressions, but otherwise behave like normal identifiers.
The identifiers below are reserved as keywords, and cannot be employed otherwise:
and as assert asr begin class
constraint do done downto else end
exception external false for fun function
functor if in include inherit initializer
land lazy let lor lsl lsr
lxor match method mod module mutable
new nonrec object of open or
private rec sig struct then to
true try type val virtual when
while with
The following character sequences are also keywords:
!= # & && ' ( ) * + , - -. -> . .. : :: := :> ; ;; < <- = > >] >} ? [ [< [> [| ] _ ` { {< | |] || } ~
Note that the following identifiers are keywords of the Camlp4 extensions and should be avoided for compatibility reasons.
parser value $ $$ $: <: << >> ??
Lexical ambiguities are resolved according to the “longest match” rule: when a character sequence can be decomposed into two tokens in several different ways, the decomposition retained is the one with the longest first token.
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Preprocessors that generate OCaml source code can insert line number directives in their output so that error messages produced by the compiler contain line numbers and file names referring to the source file before preprocessing, instead of after preprocessing. A line number directive is composed of a # (sharp sign), followed by a positive integer (the source line number), optionally followed by a character string (the source file name). Line number directives are treated as blanks during lexical analysis.
This section describes the kinds of values that are manipulated by OCaml programs.
Integer values are integer numbers from −230 to 230−1, that is −1073741824 to 1073741823. The implementation may support a wider range of integer values: on 64-bit platforms, the current implementation supports integers ranging from −262 to 262−1.
Floating-point values are numbers in floating-point representation. The current implementation uses double-precision floating-point numbers conforming to the IEEE 754 standard, with 53 bits of mantissa and an exponent ranging from −1022 to 1023.
Character values are represented as 8-bit integers between 0 and 255. Character codes between 0 and 127 are interpreted following the ASCII standard. The current implementation interprets character codes between 128 and 255 following the ISO 8859-1 standard.
String values are finite sequences of characters. The current implementation supports strings containing up to 224 − 5 characters (16777211 characters); on 64-bit platforms, the limit is 257 − 9.
Tuples of values are written (v1, …, vn), standing for the n-tuple of values v1 to vn. The current implementation supports tuple of up to 222 − 1 elements (4194303 elements).
Record values are labeled tuples of values. The record value written { field1 = v1; …; fieldn = vn } associates the value vi to the record field fieldi, for i = 1 … n. The current implementation supports records with up to 222 − 1 fields (4194303 fields).
Arrays are finite, variable-sized sequences of values of the same type. The current implementation supports arrays containing up to 222 − 1 elements (4194303 elements) unless the elements are floating-point numbers (2097151 elements in this case); on 64-bit platforms, the limit is 254 − 1 for all arrays.
Variant values are either a constant constructor, or a non-constant constructor applied to a number of values. The former case is written constr; the latter case is written constr (v1, ... , vn ), where the vi are said to be the arguments of the non-constant constructor constr. The parentheses may be omitted if there is only one argument.
The following constants are treated like built-in constant constructors:
| Constant | Constructor |
| false | the boolean false |
| true | the boolean true |
| () | the “unit” value |
| [] | the empty list |
The current implementation limits each variant type to have at most 246 non-constant constructors and 230−1 constant constructors.
Polymorphic variants are an alternate form of variant values, not belonging explicitly to a predefined variant type, and following specific typing rules. They can be either constant, written `tag-name, or non-constant, written `tag-name(v).
Functional values are mappings from values to values.
Objects are composed of a hidden internal state which is a record of instance variables, and a set of methods for accessing and modifying these variables. The structure of an object is described by the toplevel class that created it.
Identifiers are used to give names to several classes of language objects and refer to these objects by name later:
These eleven name spaces are distinguished both by the context and by the capitalization of the identifier: whether the first letter of the identifier is in lowercase (written lowercase-ident below) or in uppercase (written capitalized-ident). Underscore is considered a lowercase letter for this purpose.
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See also the following language extension: extended indexing operators.
As shown above, prefix and infix symbols as well as some keywords can be used as value names, provided they are written between parentheses. The capitalization rules are summarized in the table below.
| Name space | Case of first letter |
| Values | lowercase |
| Constructors | uppercase |
| Labels | lowercase |
| Polymorphic variant tags | uppercase |
| Exceptions | uppercase |
| Type constructors | lowercase |
| Record fields | lowercase |
| Classes | lowercase |
| Instance variables | lowercase |
| Methods | lowercase |
| Modules | uppercase |
| Module types | any |
Note on polymorphic variant tags: the current implementation accepts lowercase variant tags in addition to capitalized variant tags, but we suggest you avoid lowercase variant tags for portability and compatibility with future OCaml versions.
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A named object can be referred to either by its name (following the usual static scoping rules for names) or by an access path prefix . name, where prefix designates a module and name is the name of an object defined in that module. The first component of the path, prefix, is either a simple module name or an access path name1 . name2 …, in case the defining module is itself nested inside other modules. For referring to type constructors, module types, or class types, the prefix can also contain simple functor applications (as in the syntactic class extended-module-path above) in case the defining module is the result of a functor application.
Label names, tag names, method names and instance variable names need not be qualified: the former three are global labels, while the latter are local to a class.
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See also the following language extensions: first-class modules, attributes and extension nodes.
The table below shows the relative precedences and associativity of operators and non-closed type constructions. The constructions with higher precedences come first.
| Operator | Associativity |
| Type constructor application | – |
| # | – |
| * | – |
| -> | right |
| as | – |
Type expressions denote types in definitions of data types as well as in type constraints over patterns and expressions.
The type expression ' ident stands for the type variable named ident. The type expression _ stands for either an anonymous type variable or anonymous type parameters. In data type definitions, type variables are names for the data type parameters. In type constraints, they represent unspecified types that can be instantiated by any type to satisfy the type constraint. In general the scope of a named type variable is the whole top-level phrase where it appears, and it can only be generalized when leaving this scope. Anonymous variables have no such restriction. In the following cases, the scope of named type variables is restricted to the type expression where they appear: 1) for universal (explicitly polymorphic) type variables; 2) for type variables that only appear in public method specifications (as those variables will be made universal, as described in section 7.9.1); 3) for variables used as aliases, when the type they are aliased to would be invalid in the scope of the enclosing definition (i.e. when it contains free universal type variables, or locally defined types.)
The type expression ( typexpr ) denotes the same type as typexpr.
The type expression typexpr1 -> typexpr2 denotes the type of functions mapping arguments of type typexpr1 to results of type typexpr2.
label-name : typexpr1 -> typexpr2 denotes the same function type, but the argument is labeled label.
? label-name : typexpr1 -> typexpr2 denotes the type of functions mapping an optional labeled argument of type typexpr1 to results of type typexpr2. That is, the physical type of the function will be typexpr1 option -> typexpr2.
The type expression typexpr1 * … * typexprn denotes the type of tuples whose elements belong to types typexpr1, … typexprn respectively.
Type constructors with no parameter, as in typeconstr, are type expressions.
The type expression typexpr typeconstr, where typeconstr is a type constructor with one parameter, denotes the application of the unary type constructor typeconstr to the type typexpr.
The type expression (typexpr1,…, typexprn) typeconstr, where typeconstr is a type constructor with n parameters, denotes the application of the n-ary type constructor typeconstr to the types typexpr1 through typexprn.
In the type expression _ typeconstr , the anonymous type expression _ stands in for anonymous type parameters and is equivalent to (_, …,_) with as many repetitions of _ as the arity of typeconstr.
The type expression typexpr as ' ident denotes the same type as typexpr, and also binds the type variable ident to type typexpr both in typexpr and in other types. In general the scope of an alias is the same as for a named type variable, and covers the whole enclosing definition. If the type variable ident actually occurs in typexpr, a recursive type is created. Recursive types for which there exists a recursive path that does not contain an object or polymorphic variant type constructor are rejected, except when the -rectypes mode is selected.
If ' ident denotes an explicit polymorphic variable, and typexpr denotes either an object or polymorphic variant type, the row variable of typexpr is captured by ' ident, and quantified upon.
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Polymorphic variant types describe the values a polymorphic variant may take.
The first case is an exact variant type: all possible tags are known, with their associated types, and they can all be present. Its structure is fully known.
The second case is an open variant type, describing a polymorphic variant value: it gives the list of all tags the value could take, with their associated types. This type is still compatible with a variant type containing more tags. A special case is the unknown type, which does not define any tag, and is compatible with any variant type.
The third case is a closed variant type. It gives information about all the possible tags and their associated types, and which tags are known to potentially appear in values. The exact variant type (first case) is just an abbreviation for a closed variant type where all possible tags are also potentially present.
In all three cases, tags may be either specified directly in the `tag-name [of typexpr] form, or indirectly through a type expression, which must expand to an exact variant type, whose tag specifications are inserted in its place.
Full specifications of variant tags are only used for non-exact closed types. They can be understood as a conjunctive type for the argument: it is intended to have all the types enumerated in the specification.
Such conjunctive constraints may be unsatisfiable. In such a case the corresponding tag may not be used in a value of this type. This does not mean that the whole type is not valid: one can still use other available tags. Conjunctive constraints are mainly intended as output from the type checker. When they are used in source programs, unsolvable constraints may cause early failures.
An object type < [method-type { ; method-type }] > is a record of method types.
Each method may have an explicit polymorphic type: { ' ident }+ . typexpr. Explicit polymorphic variables have a local scope, and an explicit polymorphic type can only be unified to an equivalent one, where only the order and names of polymorphic variables may change.
The type < {method-type ;} .. > is the type of an object whose method names and types are described by method-type1, …, method-typen, and possibly some other methods represented by the ellipsis. This ellipsis actually is a special kind of type variable (called row variable in the literature) that stands for any number of extra method types.
The type # class-path is a special kind of abbreviation. This abbreviation unifies with the type of any object belonging to a subclass of class class-path. It is handled in a special way as it usually hides a type variable (an ellipsis, representing the methods that may be added in a subclass). In particular, it vanishes when the ellipsis gets instantiated. Each type expression # class-path defines a new type variable, so type # class-path -> # class-path is usually not the same as type (# class-path as ' ident) -> ' ident.
Use of #-types to abbreviate polymorphic variant types is deprecated. If t is an exact variant type then #t translates to [< t], and #t[> `tag1 …` tagk] translates to [< t > `tag1 …` tagk]
There are no type expressions describing (defined) variant types nor record types, since those are always named, i.e. defined before use and referred to by name. Type definitions are described in section 7.8.1.
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See also the following language extensions: integer literals for types int32, int64 and nativeint, quoted strings and extension literals.
The syntactic class of constants comprises literals from the four base types (integers, floating-point numbers, characters, character strings), and constant constructors from both normal and polymorphic variants, as well as the special constants false, true, (), [], and [||], which behave like constant constructors, and begin end, which is equivalent to ().
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See also the following language extensions: lazy patterns, local opens, first-class modules, attributes, extension nodes and exception cases in pattern matching.
The table below shows the relative precedences and associativity of operators and non-closed pattern constructions. The constructions with higher precedences come first.
| Operator | Associativity |
| .. | – |
| lazy (see section 8.3) | – |
| Constructor application, Tag application | right |
| :: | right |
| , | – |
| | | left |
| as | – |
Patterns are templates that allow selecting data structures of a given shape, and binding identifiers to components of the data structure. This selection operation is called pattern matching; its outcome is either “this value does not match this pattern”, or “this value matches this pattern, resulting in the following bindings of names to values”.
A pattern that consists in a value name matches any value, binding the name to the value. The pattern _ also matches any value, but does not bind any name.
Patterns are linear: a variable cannot be bound several times by a given pattern. In particular, there is no way to test for equality between two parts of a data structure using only a pattern (but when guards can be used for this purpose).
A pattern consisting in a constant matches the values that are equal to this constant.
The pattern pattern1 as value-name matches the same values as pattern1. If the matching against pattern1 is successful, the name value-name is bound to the matched value, in addition to the bindings performed by the matching against pattern1.
The pattern ( pattern1 ) matches the same values as pattern1. A type constraint can appear in a parenthesized pattern, as in ( pattern1 : typexpr ). This constraint forces the type of pattern1 to be compatible with typexpr.
The pattern pattern1 | pattern2 represents the logical “or” of the two patterns pattern1 and pattern2. A value matches pattern1 | pattern2 if it matches pattern1 or pattern2. The two sub-patterns pattern1 and pattern2 must bind exactly the same identifiers to values having the same types. Matching is performed from left to right. More precisely, in case some value v matches pattern1 | pattern2, the bindings performed are those of pattern1 when v matches pattern1. Otherwise, value v matches pattern2 whose bindings are performed.
The pattern constr ( pattern1 , … , patternn ) matches all variants whose constructor is equal to constr, and whose arguments match pattern1 … patternn. It is a type error if n is not the number of arguments expected by the constructor.
The pattern constr _ matches all variants whose constructor is constr.
The pattern pattern1 :: pattern2 matches non-empty lists whose heads match pattern1, and whose tails match pattern2.
The pattern [ pattern1 ; … ; patternn ] matches lists of length n whose elements match pattern1 …patternn, respectively. This pattern behaves like pattern1 :: … :: patternn :: [].
The pattern `tag-name pattern1 matches all polymorphic variants whose tag is equal to tag-name, and whose argument matches pattern1.
If the type [('a,'b,…)] typeconstr = [ ` tag-name1 typexpr1 | … | ` tag-namen typexprn] is defined, then the pattern #typeconstr is a shorthand for the following or-pattern: ( `tag-name1(_ : typexpr1) | … | ` tag-namen(_ : typexprn)). It matches all values of type [< typeconstr ].
The pattern pattern1 , … , patternn matches n-tuples whose components match the patterns pattern1 through patternn. That is, the pattern matches the tuple values (v1, …, vn) such that patterni matches vi for i = 1,… , n.
The pattern { field1 [= pattern1] ; … ; fieldn [= patternn] } matches records that define at least the fields field1 through fieldn, and such that the value associated to fieldi matches the pattern patterni, for i = 1,… , n. A single identifier fieldk stands for fieldk = fieldk , and a single qualified identifier module-path . fieldk stands for module-path . fieldk = fieldk . The record value can define more fields than field1 …fieldn; the values associated to these extra fields are not taken into account for matching. Optionally, a record pattern can be terminated by ; _ to convey the fact that not all fields of the record type are listed in the record pattern and that it is intentional. Optional type constraints can be added field by field with { field1 : typexpr1 = pattern1 ;… ; fieldn : typexprn = patternn } to force the type of fieldk to be compatible with typexprk.
The pattern [| pattern1 ; … ; patternn |] matches arrays of length n such that the i-th array element matches the pattern patterni, for i = 1,… , n.
The pattern ' c ' .. ' d ' is a shorthand for the pattern
where c1, c2, …, cn are the characters that occur between c and d in the ASCII character set. For instance, the pattern '0'..'9' matches all characters that are digits.
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See also the following language extensions: object notations, first-class modules, overriding in open statements, syntax for Bigarray access, attributes, extension nodes, local exceptions extended indexing operators.
The table below shows the relative precedences and associativity of operators and non-closed constructions. The constructions with higher precedence come first. For infix and prefix symbols, we write “*…” to mean “any symbol starting with *”.
| Construction or operator | Associativity |
| prefix-symbol | – |
| . .( .[ .{ (see section 8.15) | – |
| #… | – |
| function application, constructor application, tag application, assert, lazy | left |
| - -. (prefix) | – |
| **… lsl lsr asr | right |
| *… /… %… mod land lor lxor | left |
| +… -… | left |
| :: | right |
| @… ^… | right |
| =… <… >… |… &… $… != | left |
| & && | right |
| or || | right |
| , | – |
| <- := | right |
| if | – |
| ; | right |
| let match fun function try | – |
An expression consisting in a constant evaluates to this constant.
An expression consisting in an access path evaluates to the value bound to this path in the current evaluation environment. The path can be either a value name or an access path to a value component of a module.
The expressions ( expr ) and begin expr end have the same value as expr. The two constructs are semantically equivalent, but it is good style to use begin … end inside control structures:
if … then begin … ; … end else begin … ; … end
and ( … ) for the other grouping situations.
Parenthesized expressions can contain a type constraint, as in ( expr : typexpr ). This constraint forces the type of expr to be compatible with typexpr.
Parenthesized expressions can also contain coercions ( expr [: typexpr] :> typexpr) (see subsection 7.7.6 below).
Function application is denoted by juxtaposition of (possibly labeled) expressions. The expression expr argument1 … argumentn evaluates the expression expr and those appearing in argument1 to argumentn. The expression expr must evaluate to a functional value f, which is then applied to the values of argument1, …, argumentn.
The order in which the expressions expr, argument1, …, argumentn are evaluated is not specified.
Arguments and parameters are matched according to their respective labels. Argument order is irrelevant, except among arguments with the same label, or no label.
If a parameter is specified as optional (label prefixed by ?) in the type of expr, the corresponding argument will be automatically wrapped with the constructor Some, except if the argument itself is also prefixed by ?, in which case it is passed as is. If a non-labeled argument is passed, and its corresponding parameter is preceded by one or several optional parameters, then these parameters are defaulted, i.e. the value None will be passed for them. All other missing parameters (without corresponding argument), both optional and non-optional, will be kept, and the result of the function will still be a function of these missing parameters to the body of f.
As a special case, if the function has a known arity, all the arguments are unlabeled, and their number matches the number of non-optional parameters, then labels are ignored and non-optional parameters are matched in their definition order. Optional arguments are defaulted.
In all cases but exact match of order and labels, without optional parameters, the function type should be known at the application point. This can be ensured by adding a type constraint. Principality of the derivation can be checked in the -principal mode.
Two syntactic forms are provided to define functions. The first form is introduced by the keyword function:
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This expression evaluates to a functional value with one argument. When this function is applied to a value v, this value is matched against each pattern pattern1 to patternn. If one of these matchings succeeds, that is, if the value v matches the pattern patterni for some i, then the expression expri associated to the selected pattern is evaluated, and its value becomes the value of the function application. The evaluation of expri takes place in an environment enriched by the bindings performed during the matching.
If several patterns match the argument v, the one that occurs first in the function definition is selected. If none of the patterns matches the argument, the exception Match_failure is raised.
The other form of function definition is introduced by the keyword fun:
This expression is equivalent to:
An optional type constraint typexpr can be added before -> to enforce the type of the result to be compatible with the constraint typexpr:
is equivalent to
Beware of the small syntactic difference between a type constraint on the last parameter
and one on the result
The parameter patterns ~lab and ~(lab [: typ]) are shorthands for respectively ~lab: lab and ~lab:( lab [: typ]), and similarly for their optional counterparts.
A function of the form fun ? lab :( pattern = expr0 ) -> expr is equivalent to
where ident is a fresh variable, except that it is unspecified when expr0 is evaluated.
After these two transformations, expressions are of the form
If we ignore labels, which will only be meaningful at function application, this is equivalent to
That is, the fun expression above evaluates to a curried function with n arguments: after applying this function n times to the values v1 … vn, the values will be matched in parallel against the patterns pattern1 … patternn. If the matching succeeds, the function returns the value of expr in an environment enriched by the bindings performed during the matchings. If the matching fails, the exception Match_failure is raised.
The cases of a pattern matching (in the function, match and try constructs) can include guard expressions, which are arbitrary boolean expressions that must evaluate to true for the match case to be selected. Guards occur just before the -> token and are introduced by the when keyword:
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Matching proceeds as described before, except that if the value matches some pattern patterni which has a guard condi, then the expression condi is evaluated (in an environment enriched by the bindings performed during matching). If condi evaluates to true, then expri is evaluated and its value returned as the result of the matching, as usual. But if condi evaluates to false, the matching is resumed against the patterns following patterni.
The let and let rec constructs bind value names locally. The construct
evaluates expr1 … exprn in some unspecified order and matches their values against the patterns pattern1 … patternn. If the matchings succeed, expr is evaluated in the environment enriched by the bindings performed during matching, and the value of expr is returned as the value of the whole let expression. If one of the matchings fails, the exception Match_failure is raised.
An alternate syntax is provided to bind variables to functional values: instead of writing
in a let expression, one may instead write
Recursive definitions of names are introduced by let rec:
The only difference with the let construct described above is that the bindings of names to values performed by the pattern-matching are considered already performed when the expressions expr1 to exprn are evaluated. That is, the expressions expr1 to exprn can reference identifiers that are bound by one of the patterns pattern1, …, patternn, and expect them to have the same value as in expr, the body of the let rec construct.
The recursive definition is guaranteed to behave as described above if the expressions expr1 to exprn are function definitions (fun … or function …), and the patterns pattern1 … patternn are just value names, as in:
This defines name1 … namen as mutually recursive functions local to expr.
The behavior of other forms of let rec definitions is implementation-dependent. The current implementation also supports a certain class of recursive definitions of non-functional values, as explained in section 8.2.
(Introduced in OCaml 3.12)
Polymorphic type annotations in let-definitions behave in a way similar to polymorphic methods:
These annotations explicitly require the defined value to be polymorphic, and allow one to use this polymorphism in recursive occurrences (when using let rec). Note however that this is a normal polymorphic type, unifiable with any instance of itself.
The expression expr1 ; expr2 evaluates expr1 first, then expr2, and returns the value of expr2.
The expression if expr1 then expr2 else expr3 evaluates to the value of expr2 if expr1 evaluates to the boolean true, and to the value of expr3 if expr1 evaluates to the boolean false.
The else expr3 part can be omitted, in which case it defaults to else ().
The expression
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matches the value of expr against the patterns pattern1 to patternn. If the matching against patterni succeeds, the associated expression expri is evaluated, and its value becomes the value of the whole match expression. The evaluation of expri takes place in an environment enriched by the bindings performed during matching. If several patterns match the value of expr, the one that occurs first in the match expression is selected. If none of the patterns match the value of expr, the exception Match_failure is raised.
The expression expr1 && expr2 evaluates to true if both expr1 and expr2 evaluate to true; otherwise, it evaluates to false. The first component, expr1, is evaluated first. The second component, expr2, is not evaluated if the first component evaluates to false. Hence, the expression expr1 && expr2 behaves exactly as
The expression expr1 || expr2 evaluates to true if one of the expressions expr1 and expr2 evaluates to true; otherwise, it evaluates to false. The first component, expr1, is evaluated first. The second component, expr2, is not evaluated if the first component evaluates to true. Hence, the expression expr1 || expr2 behaves exactly as
The boolean operators & and or are deprecated synonyms for (respectively) && and ||.
The expression while expr1 do expr2 done repeatedly evaluates expr2 while expr1 evaluates to true. The loop condition expr1 is evaluated and tested at the beginning of each iteration. The whole while … done expression evaluates to the unit value ().
The expression for name = expr1 to expr2 do expr3 done first evaluates the expressions expr1 and expr2 (the boundaries) into integer values n and p. Then, the loop body expr3 is repeatedly evaluated in an environment where name is successively bound to the values n, n+1, …, p−1, p. The loop body is never evaluated if n > p.
The expression for name = expr1 downto expr2 do expr3 done evaluates similarly, except that name is successively bound to the values n, n−1, …, p+1, p. The loop body is never evaluated if n < p.
In both cases, the whole for expression evaluates to the unit value ().
The expression
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evaluates the expression expr and returns its value if the evaluation of expr does not raise any exception. If the evaluation of expr raises an exception, the exception value is matched against the patterns pattern1 to patternn. If the matching against patterni succeeds, the associated expression expri is evaluated, and its value becomes the value of the whole try expression. The evaluation of expri takes place in an environment enriched by the bindings performed during matching. If several patterns match the value of expr, the one that occurs first in the try expression is selected. If none of the patterns matches the value of expr, the exception value is raised again, thereby transparently “passing through” the try construct.
The expression expr1 , … , exprn evaluates to the n-tuple of the values of expressions expr1 to exprn. The evaluation order of the subexpressions is not specified.
The expression constr expr evaluates to the unary variant value whose constructor is constr, and whose argument is the value of expr. Similarly, the expression constr ( expr1 , … , exprn ) evaluates to the n-ary variant value whose constructor is constr and whose arguments are the values of expr1, …, exprn.
The expression constr ( expr1, …, exprn) evaluates to the variant value whose constructor is constr, and whose arguments are the values of expr1 … exprn.
For lists, some syntactic sugar is provided. The expression expr1 :: expr2 stands for the constructor ( :: ) applied to the arguments ( expr1 , expr2 ), and therefore evaluates to the list whose head is the value of expr1 and whose tail is the value of expr2. The expression [ expr1 ; … ; exprn ] is equivalent to expr1 :: … :: exprn :: [], and therefore evaluates to the list whose elements are the values of expr1 to exprn.
The expression `tag-name expr evaluates to the polymorphic variant value whose tag is tag-name, and whose argument is the value of expr.
The expression { field1 [= expr1] ; … ; fieldn [= exprn ]} evaluates to the record value { field1 = v1; …; fieldn = vn } where vi is the value of expri for i = 1,… , n. A single identifier fieldk stands for fieldk = fieldk, and a qualified identifier module-path . fieldk stands for module-path . fieldk = fieldk. The fields field1 to fieldn must all belong to the same record type; each field of this record type must appear exactly once in the record expression, though they can appear in any order. The order in which expr1 to exprn are evaluated is not specified. Optional type constraints can be added after each field { field1 : typexpr1 = expr1 ;… ; fieldn : typexprn = exprn } to force the type of fieldk to be compatible with typexprk.
The expression { expr with field1 [= expr1] ; … ; fieldn [= exprn] } builds a fresh record with fields field1 … fieldn equal to expr1 … exprn, and all other fields having the same value as in the record expr. In other terms, it returns a shallow copy of the record expr, except for the fields field1 … fieldn, which are initialized to expr1 … exprn. As previously, single identifier fieldk stands for fieldk = fieldk, a qualified identifier module-path . fieldk stands for module-path . fieldk = fieldk and it is possible to add an optional type constraint on each field being updated with { expr with field1 : typexpr1 = expr1 ; … ; fieldn : typexprn = exprn }.
The expression expr1 . field evaluates expr1 to a record value, and returns the value associated to field in this record value.
The expression expr1 . field <- expr2 evaluates expr1 to a record value, which is then modified in-place by replacing the value associated to field in this record by the value of expr2. This operation is permitted only if field has been declared mutable in the definition of the record type. The whole expression expr1 . field <- expr2 evaluates to the unit value ().
The expression [| expr1 ; … ; exprn |] evaluates to a n-element array, whose elements are initialized with the values of expr1 to exprn respectively. The order in which these expressions are evaluated is unspecified.
The expression expr1 .( expr2 ) returns the value of element number expr2 in the array denoted by expr1. The first element has number 0; the last element has number n−1, where n is the size of the array. The exception Invalid_argument is raised if the access is out of bounds.
The expression expr1 .( expr2 ) <- expr3 modifies in-place the array denoted by expr1, replacing element number expr2 by the value of expr3. The exception Invalid_argument is raised if the access is out of bounds. The value of the whole expression is ().
The expression expr1 .[ expr2 ] returns the value of character number expr2 in the string denoted by expr1. The first character has number 0; the last character has number n−1, where n is the length of the string. The exception Invalid_argument is raised if the access is out of bounds.
The expression expr1 .[ expr2 ] <- expr3 modifies in-place the string denoted by expr1, replacing character number expr2 by the value of expr3. The exception Invalid_argument is raised if the access is out of bounds. The value of the whole expression is ().
Note: this possibility is offered only for backward compatibility with older versions of OCaml and will be removed in a future version. New code should use byte sequences and the Bytes.set function.
Symbols from the class infix-symbol, as well as the keywords *, +, -, -., =, !=, <, >, or, ||, &, &&, :=, mod, land, lor, lxor, lsl, lsr, and asr can appear in infix position (between two expressions). Symbols from the class prefix-symbol, as well as the keywords - and -. can appear in prefix position (in front of an expression).
Infix and prefix symbols do not have a fixed meaning: they are simply interpreted as applications of functions bound to the names corresponding to the symbols. The expression prefix-symbol expr is interpreted as the application ( prefix-symbol ) expr. Similarly, the expression expr1 infix-symbol expr2 is interpreted as the application ( infix-symbol ) expr1 expr2.
The table below lists the symbols defined in the initial environment and their initial meaning. (See the description of the core library module Pervasives in chapter 25 for more details). Their meaning may be changed at any time using let ( infix-op ) name1 name2 = …
Note: the operators &&, ||, and ~- are handled specially and it is not advisable to change their meaning.
The keywords - and -. can appear both as infix and prefix operators. When they appear as prefix operators, they are interpreted respectively as the functions (~-) and (~-.).
| Operator | Initial meaning |
| + | Integer addition. |
| - (infix) | Integer subtraction. |
| ~- - (prefix) | Integer negation. |
| * | Integer multiplication. |
| / | Integer division. Raise Division_by_zero if second argument is zero. |
| mod | Integer modulus. Raise Division_by_zero if second argument is zero. |
| land | Bitwise logical “and” on integers. |
| lor | Bitwise logical “or” on integers. |
| lxor | Bitwise logical “exclusive or” on integers. |
| lsl | Bitwise logical shift left on integers. |
| lsr | Bitwise logical shift right on integers. |
| asr | Bitwise arithmetic shift right on integers. |
| +. | Floating-point addition. |
| -. (infix) | Floating-point subtraction. |
| ~-. -. (prefix) | Floating-point negation. |
| *. | Floating-point multiplication. |
| /. | Floating-point division. |
| ** | Floating-point exponentiation. |
| @ | List concatenation. |
| ^ | String concatenation. |
| ! | Dereferencing (return the current contents of a reference). |
| := | Reference assignment (update the reference given as first argument with the value of the second argument). |
| = | Structural equality test. |
| <> | Structural inequality test. |
| == | Physical equality test. |
| != | Physical inequality test. |
| < | Test “less than”. |
| <= | Test “less than or equal”. |
| > | Test “greater than”. |
| >= | Test “greater than or equal”. |
| && & | Boolean conjunction. |
| || or | Boolean disjunction. |
When class-path evaluates to a class body, new class-path evaluates to a new object containing the instance variables and methods of this class.
When class-path evaluates to a class function, new class-path evaluates to a function expecting the same number of arguments and returning a new object of this class.
Creating directly an object through the object class-body end construct is operationally equivalent to defining locally a class class-name = object class-body end —see sections 7.9.2 and following for the syntax of class-body— and immediately creating a single object from it by new class-name.
The typing of immediate objects is slightly different from explicitly defining a class in two respects. First, the inferred object type may contain free type variables. Second, since the class body of an immediate object will never be extended, its self type can be unified with a closed object type.
The expression expr # method-name invokes the method method-name of the object denoted by expr.
If method-name is a polymorphic method, its type should be known at the invocation site. This is true for instance if expr is the name of a fresh object (let ident = new class-path … ) or if there is a type constraint. Principality of the derivation can be checked in the -principal mode.
The instance variables of a class are visible only in the body of the methods defined in the same class or a class that inherits from the class defining the instance variables. The expression inst-var-name evaluates to the value of the given instance variable. The expression inst-var-name <- expr assigns the value of expr to the instance variable inst-var-name, which must be mutable. The whole expression inst-var-name <- expr evaluates to ().
An object can be duplicated using the library function Oo.copy (see Module Oo). Inside a method, the expression {< inst-var-name = expr { ; inst-var-name = expr } >} returns a copy of self with the given instance variables replaced by the values of the associated expressions; other instance variables have the same value in the returned object as in self.
Expressions whose type contains object or polymorphic variant types can be explicitly coerced (weakened) to a supertype. The expression (expr :> typexpr) coerces the expression expr to type typexpr. The expression (expr : typexpr1 :> typexpr2) coerces the expression expr from type typexpr1 to type typexpr2.
The former operator will sometimes fail to coerce an expression expr from a type typ1 to a type typ2 even if type typ1 is a subtype of type typ2: in the current implementation it only expands two levels of type abbreviations containing objects and/or polymorphic variants, keeping only recursion when it is explicit in the class type (for objects). As an exception to the above algorithm, if both the inferred type of expr and typ are ground (i.e. do not contain type variables), the former operator behaves as the latter one, taking the inferred type of expr as typ1. In case of failure with the former operator, the latter one should be used.
It is only possible to coerce an expression expr from type typ1 to type typ2, if the type of expr is an instance of typ1 (like for a type annotation), and typ1 is a subtype of typ2. The type of the coerced expression is an instance of typ2. If the types contain variables, they may be instantiated by the subtyping algorithm, but this is only done after determining whether typ1 is a potential subtype of typ2. This means that typing may fail during this latter unification step, even if some instance of typ1 is a subtype of some instance of typ2. In the following paragraphs we describe the subtyping relation used.
A fixed object type admits as subtype any object type that includes all its methods. The types of the methods shall be subtypes of those in the supertype. Namely,
is a supertype of
which may contain an ellipsis .. if every typi is a supertype of the corresponding typ′i.
A monomorphic method type can be a supertype of a polymorphic method type. Namely, if typ is an instance of typ′, then 'a1 … 'an . typ′ is a subtype of typ.
Inside a class definition, newly defined types are not available for subtyping, as the type abbreviations are not yet completely defined. There is an exception for coercing self to the (exact) type of its class: this is allowed if the type of self does not appear in a contravariant position in the class type, i.e. if there are no binary methods.
A polymorphic variant type typ is a subtype of another polymorphic variant type typ′ if the upper bound of typ (i.e. the maximum set of constructors that may appear in an instance of typ) is included in the lower bound of typ′, and the types of arguments for the constructors of typ are subtypes of those in typ′. Namely,
which may be a shrinkable type, is a subtype of
which may be an extensible type, if every typi is a subtype of typ′i.
Other types do not introduce new subtyping, but they may propagate the subtyping of their arguments. For instance, typ1 * typ2 is a subtype of typ′1 * typ′2 when typ1 and typ2 are respectively subtypes of typ′1 and typ′2. For function types, the relation is more subtle: typ1 -> typ2 is a subtype of typ′1 -> typ′2 if typ1 is a supertype of typ′1 and typ2 is a subtype of typ′2. For this reason, function types are covariant in their second argument (like tuples), but contravariant in their first argument. Mutable types, like array or ref are neither covariant nor contravariant, they are nonvariant, that is they do not propagate subtyping.
For user-defined types, the variance is automatically inferred: a parameter is covariant if it has only covariant occurrences, contravariant if it has only contravariant occurrences, variance-free if it has no occurrences, and nonvariant otherwise. A variance-free parameter may change freely through subtyping, it does not have to be a subtype or a supertype. For abstract and private types, the variance must be given explicitly (see section 7.8.1), otherwise the default is nonvariant. This is also the case for constrained arguments in type definitions.
OCaml supports the assert construct to check debugging assertions. The expression assert expr evaluates the expression expr and returns () if expr evaluates to true. If it evaluates to false the exception Assert_failure is raised with the source file name and the location of expr as arguments. Assertion checking can be turned off with the -noassert compiler option. In this case, expr is not evaluated at all.
As a special case, assert false is reduced to raise (Assert_failure ...), which gives it a polymorphic type. This means that it can be used in place of any expression (for example as a branch of any pattern-matching). It also means that the assert false “assertions” cannot be turned off by the -noassert option.
The expression lazy expr returns a value v of type Lazy.t that encapsulates the computation of expr. The argument expr is not evaluated at this point in the program. Instead, its evaluation will be performed the first time the function Lazy.force is applied to the value v, returning the actual value of expr. Subsequent applications of Lazy.force to v do not evaluate expr again. Applications of Lazy.force may be implicit through pattern matching (see 8.3).
The expression let module module-name = module-expr in expr locally binds the module expression module-expr to the identifier module-name during the evaluation of the expression expr. It then returns the value of expr. For example:
let remove_duplicates comparison_fun string_list =
let module StringSet =
Set.Make(struct type t = string
let compare = comparison_fun end) in
StringSet.elements
(List.fold_right StringSet.add string_list StringSet.empty)
The expressions let open module-path in expr and module-path.( expr) are strictly equivalent. These constructions locally open the module referred to by the module path module-path in the respective scope of the expression expr.
When the body of a local open expression is delimited by [ ], [| |], or { }, the parentheses can be omitted. For expression, parentheses can also be omitted for {< >}. For example, module-path.[ expr] is equivalent to module-path.([ expr]), and module-path.[| expr |] is equivalent to module-path.([| expr |]).
Type definitions bind type constructors to data types: either variant types, record types, type abbreviations, or abstract data types. They also bind the value constructors and record fields associated with the definition.
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See also the following language extensions: private types, generalized algebraic datatypes, attributes, extension nodes, extensible variant types and inline records.
Type definitions are introduced by the type keyword, and consist in one or several simple definitions, possibly mutually recursive, separated by the and keyword. Each simple definition defines one type constructor.
A simple definition consists in a lowercase identifier, possibly preceded by one or several type parameters, and followed by an optional type equation, then an optional type representation, and then a constraint clause. The identifier is the name of the type constructor being defined.
In the right-hand side of type definitions, references to one of the type constructor name being defined are considered as recursive, unless type is followed by nonrec. The nonrec keyword was introduced in OCaml 4.02.2.
The optional type parameters are either one type variable ' ident, for type constructors with one parameter, or a list of type variables ('ident1,…,' identn), for type constructors with several parameters. Each type parameter may be prefixed by a variance constraint + (resp. -) indicating that the parameter is covariant (resp. contravariant). These type parameters can appear in the type expressions of the right-hand side of the definition, optionally restricted by a variance constraint ; i.e. a covariant parameter may only appear on the right side of a functional arrow (more precisely, follow the left branch of an even number of arrows), and a contravariant parameter only the left side (left branch of an odd number of arrows). If the type has a representation or an equation, and the parameter is free (i.e. not bound via a type constraint to a constructed type), its variance constraint is checked but subtyping etc. will use the inferred variance of the parameter, which may be less restrictive; otherwise (i.e. for abstract types or non-free parameters), the variance must be given explicitly, and the parameter is invariant if no variance is given.
The optional type equation = typexpr makes the defined type equivalent to the type expression typexpr: one can be substituted for the other during typing. If no type equation is given, a new type is generated: the defined type is incompatible with any other type.
The optional type representation describes the data structure representing the defined type, by giving the list of associated constructors (if it is a variant type) or associated fields (if it is a record type). If no type representation is given, nothing is assumed on the structure of the type besides what is stated in the optional type equation.
The type representation = [|] constr-decl { | constr-decl } describes a variant type. The constructor declarations constr-decl1, …, constr-decln describe the constructors associated to this variant type. The constructor declaration constr-name of typexpr1 * … * typexprn declares the name constr-name as a non-constant constructor, whose arguments have types typexpr1 …typexprn. The constructor declaration constr-name declares the name constr-name as a constant constructor. Constructor names must be capitalized.
The type representation = { field-decl { ; field-decl } [;] } describes a record type. The field declarations field-decl1, …, field-decln describe the fields associated to this record type. The field declaration field-name : poly-typexpr declares field-name as a field whose argument has type poly-typexpr. The field declaration mutable field-name : poly-typexpr behaves similarly; in addition, it allows physical modification of this field. Immutable fields are covariant, mutable fields are non-variant. Both mutable and immutable fields may have explicitly polymorphic types. The polymorphism of the contents is statically checked whenever a record value is created or modified. Extracted values may have their types instantiated.
The two components of a type definition, the optional equation and the optional representation, can be combined independently, giving rise to four typical situations:
The type variables appearing as type parameters can optionally be prefixed by + or - to indicate that the type constructor is covariant or contravariant with respect to this parameter. This variance information is used to decide subtyping relations when checking the validity of :> coercions (see section 7.7.6).
For instance, type +'a t declares t as an abstract type that is covariant in its parameter; this means that if the type τ is a subtype of the type σ, then τ t is a subtype of σ t. Similarly, type -'a t declares that the abstract type t is contravariant in its parameter: if τ is a subtype of σ, then σ t is a subtype of τ t. If no + or - variance annotation is given, the type constructor is assumed non-variant in the corresponding parameter. For instance, the abstract type declaration type 'a t means that τ t is neither a subtype nor a supertype of σ t if τ is subtype of σ.
The variance indicated by the + and - annotations on parameters is enforced only for abstract and private types, or when there are type constraints. Otherwise, for abbreviations, variant and record types without type constraints, the variance properties of the type constructor are inferred from its definition, and the variance annotations are only checked for conformance with the definition.
The construct constraint ' ident = typexpr allows the specification of type parameters. Any actual type argument corresponding to the type parameter ident has to be an instance of typexpr (more precisely, ident and typexpr are unified). Type variables of typexpr can appear in the type equation and the type declaration.
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Exception definitions add new constructors to the built-in variant
type exn of exception values. The constructors are declared as
for a definition of a variant type.
The form exception constr-decl generates a new exception, distinct from all other exceptions in the system. The form exception constr-name = constr gives an alternate name to an existing exception.
Classes are defined using a small language, similar to the module language.
Class types are the class-level equivalent of type expressions: they specify the general shape and type properties of classes.
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See also the following language extensions: attributes and extension nodes.
The expression classtype-path is equivalent to the class type bound to the name classtype-path. Similarly, the expression [ typexpr1 , … typexprn ] classtype-path is equivalent to the parametric class type bound to the name classtype-path, in which type parameters have been instantiated to respectively typexpr1, …typexprn.
The class type expression typexpr -> class-type is the type of class functions (functions from values to classes) that take as argument a value of type typexpr and return as result a class of type class-type.
The class type expression object [( typexpr )] {class-field-spec} end is the type of a class body. It specifies its instance variables and methods. In this type, typexpr is matched against the self type, therefore providing a name for the self type.
A class body will match a class body type if it provides definitions for all the components specified in the class body type, and these definitions meet the type requirements given in the class body type. Furthermore, all methods either virtual or public present in the class body must also be present in the class body type (on the other hand, some instance variables and concrete private methods may be omitted). A virtual method will match a concrete method, which makes it possible to forget its implementation. An immutable instance variable will match a mutable instance variable.
Local opens are supported in class types since OCaml 4.06.
The inheritance construct inherit class-body-type provides for inclusion of methods and instance variables from other class types. The instance variable and method types from class-body-type are added into the current class type.
A specification of an instance variable is written val [mutable] [virtual] inst-var-name : typexpr, where inst-var-name is the name of the instance variable and typexpr its expected type. The flag mutable indicates whether this instance variable can be physically modified. The flag virtual indicates that this instance variable is not initialized. It can be initialized later through inheritance.
An instance variable specification will hide any previous specification of an instance variable of the same name.
The specification of a method is written method [private] method-name : poly-typexpr, where method-name is the name of the method and poly-typexpr its expected type, possibly polymorphic. The flag private indicates that the method cannot be accessed from outside the object.
The polymorphism may be left implicit in public method specifications: any type variable which is not bound to a class parameter and does not appear elsewhere inside the class specification will be assumed to be universal, and made polymorphic in the resulting method type. Writing an explicit polymorphic type will disable this behaviour.
If several specifications are present for the same method, they must have compatible types. Any non-private specification of a method forces it to be public.
A virtual method specification is written method [private] virtual method-name : poly-typexpr, where method-name is the name of the method and poly-typexpr its expected type.
The construct constraint typexpr1 = typexpr2 forces the two type expressions to be equal. This is typically used to specify type parameters: in this way, they can be bound to specific type expressions.
Class expressions are the class-level equivalent of value expressions: they evaluate to classes, thus providing implementations for the specifications expressed in class types.
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See also the following language extensions: locally abstract types, attributes and extension nodes.
The expression class-path evaluates to the class bound to the name class-path. Similarly, the expression [ typexpr1 , … typexprn ] class-path evaluates to the parametric class bound to the name class-path, in which type parameters have been instantiated respectively to typexpr1, …typexprn.
The expression ( class-expr ) evaluates to the same module as class-expr.
The expression ( class-expr : class-type ) checks that class-type matches the type of class-expr (that is, that the implementation class-expr meets the type specification class-type). The whole expression evaluates to the same class as class-expr, except that all components not specified in class-type are hidden and can no longer be accessed.
Class application is denoted by juxtaposition of (possibly labeled) expressions. It denotes the class whose constructor is the first expression applied to the given arguments. The arguments are evaluated as for expression application, but the constructor itself will only be evaluated when objects are created. In particular, side-effects caused by the application of the constructor will only occur at object creation time.
The expression fun [[?]label-name:] pattern -> class-expr evaluates to a function from values to classes. When this function is applied to a value v, this value is matched against the pattern pattern and the result is the result of the evaluation of class-expr in the extended environment.
Conversion from functions with default values to functions with patterns only works identically for class functions as for normal functions.
The expression
is a short form for
The let and let rec constructs bind value names locally, as for the core language expressions.
If a local definition occurs at the very beginning of a class definition, it will be evaluated when the class is created (just as if the definition was outside of the class). Otherwise, it will be evaluated when the object constructor is called.
Local opens are supported in class expressions since OCaml 4.06.
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The expression object class-body end denotes a class body. This is the prototype for an object : it lists the instance variables and methods of an objet of this class.
A class body is a class value: it is not evaluated at once. Rather, its components are evaluated each time an object is created.
In a class body, the pattern ( pattern [: typexpr] ) is matched against self, therefore providing a binding for self and self type. Self can only be used in method and initializers.
Self type cannot be a closed object type, so that the class remains extensible.
Since OCaml 4.01, it is an error if the same method or instance variable name is defined several times in the same class body.
The inheritance construct inherit class-expr allows reusing methods and instance variables from other classes. The class expression class-expr must evaluate to a class body. The instance variables, methods and initializers from this class body are added into the current class. The addition of a method will override any previously defined method of the same name.
An ancestor can be bound by appending as lowercase-ident to the inheritance construct. lowercase-ident is not a true variable and can only be used to select a method, i.e. in an expression lowercase-ident # method-name. This gives access to the method method-name as it was defined in the parent class even if it is redefined in the current class. The scope of this ancestor binding is limited to the current class. The ancestor method may be called from a subclass but only indirectly.
The definition val [mutable] inst-var-name = expr adds an instance variable inst-var-name whose initial value is the value of expression expr. The flag mutable allows physical modification of this variable by methods.
An instance variable can only be used in the methods and initializers that follow its definition.
Since version 3.10, redefinitions of a visible instance variable with the same name do not create a new variable, but are merged, using the last value for initialization. They must have identical types and mutability. However, if an instance variable is hidden by omitting it from an interface, it will be kept distinct from other instance variables with the same name.
A variable specification is written val [mutable] virtual inst-var-name : typexpr. It specifies whether the variable is modifiable, and gives its type.
Virtual instance variables were added in version 3.10.
A method definition is written method method-name = expr. The definition of a method overrides any previous definition of this method. The method will be public (that is, not private) if any of the definition states so.
A private method, method private method-name = expr, is a method that can only be invoked on self (from other methods of the same object, defined in this class or one of its subclasses). This invocation is performed using the expression value-name # method-name, where value-name is directly bound to self at the beginning of the class definition. Private methods do not appear in object types. A method may have both public and private definitions, but as soon as there is a public one, all subsequent definitions will be made public.
Methods may have an explicitly polymorphic type, allowing them to be used polymorphically in programs (even for the same object). The explicit declaration may be done in one of three ways: (1) by giving an explicit polymorphic type in the method definition, immediately after the method name, i.e. method [private] method-name : {' ident}+ . typexpr = expr; (2) by a forward declaration of the explicit polymorphic type through a virtual method definition; (3) by importing such a declaration through inheritance and/or constraining the type of self.
Some special expressions are available in method bodies for manipulating instance variables and duplicating self:
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The expression inst-var-name <- expr modifies in-place the current object by replacing the value associated to inst-var-name by the value of expr. Of course, this instance variable must have been declared mutable.
The expression {< inst-var-name1 = expr1 ; … ; inst-var-namen = exprn >} evaluates to a copy of the current object in which the values of instance variables inst-var-name1, …, inst-var-namen have been replaced by the values of the corresponding expressions expr1, …, exprn.
A method specification is written method [private] virtual method-name : poly-typexpr. It specifies whether the method is public or private, and gives its type. If the method is intended to be polymorphic, the type must be explicitly polymorphic.
Since Ocaml 3.12, the keywords inherit!, val! and method! have the same semantics as inherit, val and method, but they additionally require the definition they introduce to be overriding. Namely, method! requires method-name to be already defined in this class, val! requires inst-var-name to be already defined in this class, and inherit! requires class-expr to override some definitions. If no such overriding occurs, an error is signaled.
As a side-effect, these 3 keywords avoid the warnings 7 (method override) and 13 (instance variable override). Note that warning 7 is disabled by default.
The construct constraint typexpr1 = typexpr2 forces the two type expressions to be equals. This is typically used to specify type parameters: in that way they can be bound to specific type expressions.
A class initializer initializer expr specifies an expression that will be evaluated whenever an object is created from the class, once all its instance variables have been initialized.
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A class definition class class-binding { and class-binding } is recursive. Each class-binding defines a class-name that can be used in the whole expression except for inheritance. It can also be used for inheritance, but only in the definitions that follow its own.
A class binding binds the class name class-name to the value of expression class-expr. It also binds the class type class-name to the type of the class, and defines two type abbreviations : class-name and # class-name. The first one is the type of objects of this class, while the second is more general as it unifies with the type of any object belonging to a subclass (see section 7.4).
A class must be flagged virtual if one of its methods is virtual (that is, appears in the class type, but is not actually defined). Objects cannot be created from a virtual class.
The class type parameters correspond to the ones of the class type and of the two type abbreviations defined by the class binding. They must be bound to actual types in the class definition using type constraints. So that the abbreviations are well-formed, type variables of the inferred type of the class must either be type parameters or be bound in the constraint clause.
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This is the counterpart in signatures of class definitions. A class specification matches a class definition if they have the same type parameters and their types match.
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A class type definition class class-name = class-body-type defines an abbreviation class-name for the class body type class-body-type. As for class definitions, two type abbreviations class-name and # class-name are also defined. The definition can be parameterized by some type parameters. If any method in the class type body is virtual, the definition must be flagged virtual.
Two class type definitions match if they have the same type parameters and they expand to matching types.
Module types are the module-level equivalent of type expressions: they specify the general shape and type properties of modules.
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See also the following language extensions: recovering the type of a module, substitution inside a signature, type-level module aliases, attributes, extension nodes and generative functors.
The expression modtype-path is equivalent to the module type bound to the name modtype-path. The expression ( module-type ) denotes the same type as module-type.
Signatures are type specifications for structures. Signatures sig … end are collections of type specifications for value names, type names, exceptions, module names and module type names. A structure will match a signature if the structure provides definitions (implementations) for all the names specified in the signature (and possibly more), and these definitions meet the type requirements given in the signature.
An optional ;; is allowed after each specification in a signature. It serves as a syntactic separator with no semantic meaning.
A specification of a value component in a signature is written val value-name : typexpr, where value-name is the name of the value and typexpr its expected type.
The form external value-name : typexpr = external-declaration is similar, except that it requires in addition the name to be implemented as the external function specified in external-declaration (see chapter 20).
A specification of one or several type components in a signature is written type typedef { and typedef } and consists of a sequence of mutually recursive definitions of type names.
Each type definition in the signature specifies an optional type equation = typexpr and an optional type representation = constr-decl … or = { field-decl … }. The implementation of the type name in a matching structure must be compatible with the type expression specified in the equation (if given), and have the specified representation (if given). Conversely, users of that signature will be able to rely on the type equation or type representation, if given. More precisely, we have the following four situations:
The specification exception constr-decl in a signature requires the matching structure to provide an exception with the name and arguments specified in the definition, and makes the exception available to all users of the structure.
A specification of one or several classes in a signature is written class class-spec { and class-spec } and consists of a sequence of mutually recursive definitions of class names.
Class specifications are described more precisely in section 7.9.4.
A specification of one or several classe types in a signature is written class type classtype-def { and classtype-def } and consists of a sequence of mutually recursive definitions of class type names. Class type specifications are described more precisely in section 7.9.5.
A specification of a module component in a signature is written module module-name : module-type, where module-name is the name of the module component and module-type its expected type. Modules can be nested arbitrarily; in particular, functors can appear as components of structures and functor types as components of signatures.
For specifying a module component that is a functor, one may write
instead of
A module type component of a signature can be specified either as a manifest module type or as an abstract module type.
An abstract module type specification module type modtype-name allows the name modtype-name to be implemented by any module type in a matching signature, but hides the implementation of the module type to all users of the signature.
A manifest module type specification module type modtype-name = module-type requires the name modtype-name to be implemented by the module type module-type in a matching signature, but makes the equality between modtype-name and module-type apparent to all users of the signature.
The expression open module-path in a signature does not specify any components. It simply affects the parsing of the following items of the signature, allowing components of the module denoted by module-path to be referred to by their simple names name instead of path accesses module-path . name. The scope of the open stops at the end of the signature expression.
The expression include module-type in a signature performs textual inclusion of the components of the signature denoted by module-type. It behaves as if the components of the included signature were copied at the location of the include. The module-type argument must refer to a module type that is a signature, not a functor type.
The module type expression functor ( module-name : module-type1 ) -> module-type2 is the type of functors (functions from modules to modules) that take as argument a module of type module-type1 and return as result a module of type module-type2. The module type module-type2 can use the name module-name to refer to type components of the actual argument of the functor. If the type module-type2 does not depend on type components of module-name, the module type expression can be simplified with the alternative short syntax module-type1 -> module-type2 . No restrictions are placed on the type of the functor argument; in particular, a functor may take another functor as argument (“higher-order” functor).
Assuming module-type denotes a signature, the expression module-type with mod-constraint { and mod-constraint } denotes the same signature where type equations have been added to some of the type specifications, as described by the constraints following the with keyword. The constraint type [type-parameters] typeconstr = typexpr adds the type equation = typexpr to the specification of the type component named typeconstr of the constrained signature. The constraint module module-path = extended-module-path adds type equations to all type components of the sub-structure denoted by module-path, making them equivalent to the corresponding type components of the structure denoted by extended-module-path.
For instance, if the module type name S is bound to the signature
sig type t module M: (sig type u end) end
then S with type t=int denotes the signature
sig type t=int module M: (sig type u end) end
and S with module M = N denotes the signature
sig type t module M: (sig type u=N.u end) end
A functor taking two arguments of type S that share their t component is written
functor (A: S) (B: S with type t = A.t) ...
Constraints are added left to right. After each constraint has been applied, the resulting signature must be a subtype of the signature before the constraint was applied. Thus, the with operator can only add information on the type components of a signature, but never remove information.
Module expressions are the module-level equivalent of value expressions: they evaluate to modules, thus providing implementations for the specifications expressed in module types.
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See also the following language extensions: recursive modules, first-class modules, overriding in open statements, attributes, extension nodes and generative functors.
The expression module-path evaluates to the module bound to the name module-path.
The expression ( module-expr ) evaluates to the same module as module-expr.
The expression ( module-expr : module-type ) checks that the type of module-expr is a subtype of module-type, that is, that all components specified in module-type are implemented in module-expr, and their implementation meets the requirements given in module-type. In other terms, it checks that the implementation module-expr meets the type specification module-type. The whole expression evaluates to the same module as module-expr, except that all components not specified in module-type are hidden and can no longer be accessed.
Structures struct … end are collections of definitions for value names, type names, exceptions, module names and module type names. The definitions are evaluated in the order in which they appear in the structure. The scopes of the bindings performed by the definitions extend to the end of the structure. As a consequence, a definition may refer to names bound by earlier definitions in the same structure.
For compatibility with toplevel phrases (chapter 10), optional ;; are allowed after and before each definition in a structure. These ;; have no semantic meanings. Similarly, an expr preceded by ;; is allowed as a component of a structure. It is equivalent to let _ = expr, i.e. expr is evaluated for its side-effects but is not bound to any identifier. If expr is the first component of a structure, the preceding ;; can be omitted.
A value definition let [rec] let-binding { and let-binding } bind value names in the same way as a let … in … expression (see section 7.7.1). The value names appearing in the left-hand sides of the bindings are bound to the corresponding values in the right-hand sides.
A value definition external value-name : typexpr = external-declaration implements value-name as the external function specified in external-declaration (see chapter 20).
A definition of one or several type components is written type typedef { and typedef } and consists of a sequence of mutually recursive definitions of type names.
Exceptions are defined with the syntax exception constr-decl or exception constr-name = constr.
A definition of one or several classes is written class class-binding { and class-binding } and consists of a sequence of mutually recursive definitions of class names. Class definitions are described more precisely in section 7.9.3.
A definition of one or several classes is written class type classtype-def { and classtype-def } and consists of a sequence of mutually recursive definitions of class type names. Class type definitions are described more precisely in section 7.9.5.
The basic form for defining a module component is module module-name = module-expr, which evaluates module-expr and binds the result to the name module-name.
One can write
instead of
Another derived form is
which is equivalent to
A definition for a module type is written module type modtype-name = module-type. It binds the name modtype-name to the module type denoted by the expression module-type.
The expression open module-path in a structure does not define any components nor perform any bindings. It simply affects the parsing of the following items of the structure, allowing components of the module denoted by module-path to be referred to by their simple names name instead of path accesses module-path . name. The scope of the open stops at the end of the structure expression.
The expression include module-expr in a structure re-exports in the current structure all definitions of the structure denoted by module-expr. For instance, if the identifier S is bound to the module
struct type t = int let x = 2 end
the module expression
struct include S let y = (x + 1 : t) end
is equivalent to the module expression
struct type t = S.t let x = S.x let y = (x + 1 : t) end
The difference between open and include is that open simply provides short names for the components of the opened structure, without defining any components of the current structure, while include also adds definitions for the components of the included structure.
The expression functor ( module-name : module-type ) -> module-expr evaluates to a functor that takes as argument modules of the type module-type1, binds module-name to these modules, evaluates module-expr in the extended environment, and returns the resulting modules as results. No restrictions are placed on the type of the functor argument; in particular, a functor may take another functor as argument (“higher-order” functor).
The expression module-expr1 ( module-expr2 ) evaluates module-expr1 to a functor and module-expr2 to a module, and applies the former to the latter. The type of module-expr2 must match the type expected for the arguments of the functor module-expr1.
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Compilation units bridge the module system and the separate compilation system. A compilation unit is composed of two parts: an interface and an implementation. The interface contains a sequence of specifications, just as the inside of a sig … end signature expression. The implementation contains a sequence of definitions and expressions, just as the inside of a struct … end module expression. A compilation unit also has a name unit-name, derived from the names of the files containing the interface and the implementation (see chapter 9 for more details). A compilation unit behaves roughly as the module definition
A compilation unit can refer to other compilation units by their names, as if they were regular modules. For instance, if U is a compilation unit that defines a type t, other compilation units can refer to that type under the name U.t; they can also refer to U as a whole structure. Except for names of other compilation units, a unit interface or unit implementation must not have any other free variables. In other terms, the type-checking and compilation of an interface or implementation proceeds in the initial environment
where name1 … namen are the names of the other compilation units available in the search path (see chapter 9 for more details) and specification1 … specificationn are their respective interfaces.
This chapter describes language extensions and convenience features that are implemented in OCaml, but not described in the OCaml reference manual.
(Introduced in Objective Caml 3.07)
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An integer literal can be followed by one of the letters l, L or n to indicate that this integer has type int32, int64 or nativeint respectively, instead of the default type int for integer literals. The library modules Int32[Int32], Int64[Int64] and Nativeint[Nativeint] provide operations on these integer types.
(Introduced in Objective Caml 1.00)
As mentioned in section 7.7.1, the let rec binding construct, in addition to the definition of recursive functions, also supports a certain class of recursive definitions of non-functional values, such as
which binds name1 to the cyclic list 1::2::1::2::…, and name2 to the cyclic list 2::1::2::1::…Informally, the class of accepted definitions consists of those definitions where the defined names occur only inside function bodies or as argument to a data constructor.
More precisely, consider the expression:
It will be accepted if each one of expr1 … exprn is statically constructive with respect to name1 … namen, is not immediately linked to any of name1 … namen, and is not an array constructor whose arguments have abstract type.
An expression e is said to be statically constructive with respect to the variables name1 … namen if at least one of the following conditions is true:
An expression e is said to be immediately linked to the variable name in the following cases:
(Introduced in Objective Caml 3.11)
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The pattern lazy pattern matches a value v of type Lazy.t, provided pattern matches the result of forcing v with Lazy.force. A successful match of a pattern containing lazy sub-patterns forces the corresponding parts of the value being matched, even those that imply no test such as lazy value-name or lazy _. Matching a value with a pattern-matching where some patterns contain lazy sub-patterns may imply forcing parts of the value, even when the pattern selected in the end has no lazy sub-pattern.
For more information, see the description of module Lazy in the standard library ( Module Lazy).
(Introduced in Objective Caml 3.07)
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Recursive module definitions, introduced by the module rec …and … construction, generalize regular module definitions module module-name = module-expr and module specifications module module-name : module-type by allowing the defining module-expr and the module-type to refer recursively to the module identifiers being defined. A typical example of a recursive module definition is:
module rec A : sig
type t = Leaf of string | Node of ASet.t
val compare: t -> t -> int
end
= struct
type t = Leaf of string | Node of ASet.t
let compare t1 t2 =
match (t1, t2) with
(Leaf s1, Leaf s2) -> Pervasives.compare s1 s2
| (Leaf _, Node _) -> 1
| (Node _, Leaf _) -> -1
| (Node n1, Node n2) -> ASet.compare n1 n2
end
and ASet : Set.S with type elt = A.t
= Set.Make(A)
It can be given the following specification:
module rec A : sig
type t = Leaf of string | Node of ASet.t
val compare: t -> t -> int
end
and ASet : Set.S with type elt = A.t
This is an experimental extension of OCaml: the class of recursive definitions accepted, as well as its dynamic semantics are not final and subject to change in future releases.
Currently, the compiler requires that all dependency cycles between the recursively-defined module identifiers go through at least one “safe” module. A module is “safe” if all value definitions that it contains have function types typexpr1 -> typexpr2. Evaluation of a recursive module definition proceeds by building initial values for the safe modules involved, binding all (functional) values to fun _ -> raise Undefined_recursive_module. The defining module expressions are then evaluated, and the initial values for the safe modules are replaced by the values thus computed. If a function component of a safe module is applied during this computation (which corresponds to an ill-founded recursive definition), the Undefined_recursive_module exception is raised.
Note that, in the specification case, the module-types must be parenthesized if they use the with mod-constraint construct.
Private type declarations in module signatures, of the form type t = private ..., enable libraries to reveal some, but not all aspects of the implementation of a type to clients of the library. In this respect, they strike a middle ground between abstract type declarations, where no information is revealed on the type implementation, and data type definitions and type abbreviations, where all aspects of the type implementation are publicized. Private type declarations come in three flavors: for variant and record types (section 8.5.1), for type abbreviations (section 8.5.2), and for row types (section 8.5.3).
(Introduced in Objective Caml 3.07)
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Values of a variant or record type declared private can be de-structured normally in pattern-matching or via the expr . field notation for record accesses. However, values of these types cannot be constructed directly by constructor application or record construction. Moreover, assignment on a mutable field of a private record type is not allowed.
The typical use of private types is in the export signature of a module, to ensure that construction of values of the private type always go through the functions provided by the module, while still allowing pattern-matching outside the defining module. For example:
module M : sig
type t = private A | B of int
val a : t
val b : int -> t
end
= struct
type t = A | B of int
let a = A
let b n = assert (n > 0); B n
end
Here, the private declaration ensures that in any value of type M.t, the argument to the B constructor is always a positive integer.
With respect to the variance of their parameters, private types are handled like abstract types. That is, if a private type has parameters, their variance is the one explicitly given by prefixing the parameter by a ‘+’ or a ‘-’, it is invariant otherwise.
(Introduced in Objective Caml 3.11)
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Unlike a regular type abbreviation, a private type abbreviation declares a type that is distinct from its implementation type typexpr. However, coercions from the type to typexpr are permitted. Moreover, the compiler “knows” the implementation type and can take advantage of this knowledge to perform type-directed optimizations.
The following example uses a private type abbreviation to define a module of nonnegative integers:
module N : sig
type t = private int
val of_int: int -> t
val to_int: t -> int
end
= struct
type t = int
let of_int n = assert (n >= 0); n
let to_int n = n
end
The type N.t is incompatible with int, ensuring that nonnegative integers and regular integers are not confused. However, if x has type N.t, the coercion (x :> int) is legal and returns the underlying integer, just like N.to_int x. Deep coercions are also supported: if l has type N.t list, the coercion (l :> int list) returns the list of underlying integers, like List.map N.to_int l but without copying the list l.
Note that the coercion ( expr :> typexpr ) is actually an abbreviated form, and will only work in presence of private abbreviations if neither the type of expr nor typexpr contain any type variables. If they do, you must use the full form ( expr : typexpr1 :> typexpr2 ) where typexpr1 is the expected type of expr. Concretely, this would be (x : N.t :> int) and (l : N.t list :> int list) for the above examples.
(Introduced in Objective Caml 3.09)
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Private row types are type abbreviations where part of the structure of the type is left abstract. Concretely typexpr in the above should denote either an object type or a polymorphic variant type, with some possibility of refinement left. If the private declaration is used in an interface, the corresponding implementation may either provide a ground instance, or a refined private type.
module M : sig type c = private < x : int; .. > val o : c end =
struct
class c = object method x = 3 method y = 2 end
let o = new c
end
This declaration does more than hiding the y method, it also makes the type c incompatible with any other closed object type, meaning that only o will be of type c. In that respect it behaves similarly to private record types. But private row types are more flexible with respect to incremental refinement. This feature can be used in combination with functors.
module F(X : sig type c = private < x : int; .. > end) =
struct
let get_x (o : X.c) = o#x
end
module G(X : sig type c = private < x : int; y : int; .. > end) =
struct
include F(X)
let get_y (o : X.c) = o#y
end
A polymorphic variant type [t], for example
type t = [ `A of int | `B of bool ]
can be refined in two ways. A definition [u] may add new field to [t], and the declaration
type u = private [> t]
will keep those new fields abstract. Construction of values of type [u] is possible using the known variants of [t], but any pattern-matching will require a default case to handle the potential extra fields. Dually, a declaration [u] may restrict the fields of [t] through abstraction: the declaration
type v = private [< t > `A]
corresponds to private variant types. One cannot create a value of the private type [v], except using the constructors that are explicitly listed as present, (`A n) in this example; yet, when patter-matching on a [v], one should assume that any of the constructors of [t] could be present.
Similarly to abstract types, the variance of type parameters is not inferred, and must be given explicitly.
(Introduced in OCaml 4.04)
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For patterns, local opens are limited to the module-path.( pattern) construction. This construction locally open the module referred to by the module path module-path in the scope of the pattern pattern.
When the body of a local open pattern is delimited by [ ], [| |], or { }, the parentheses can be omitted. For example, module-path.[ pattern] is equivalent to module-path.([ pattern]), and module-path.[| pattern |] is equivalent to module-path.([| pattern |]).
(Introduced in OCaml 4.03)
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In an object copy expression, a single identifier id stands for id = id, and a qualified identifier module-path . id stands for module-path . id = id. For example, all following methods are equivalent:
object
val x=0. val y=0. val z=0.
method f_0 x y = {< x; y >}
method f_1 x y = {< x = x; y >}
method f_2 x y = {< x=x ; y = y >}
end
(Introduced in OCaml 3.12, short syntax added in 4.03)
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The expression fun ( type typeconstr-name ) -> expr introduces a type constructor named typeconstr-name which is considered abstract in the scope of the sub-expression, but then replaced by a fresh type variable. Note that contrary to what the syntax could suggest, the expression fun ( type typeconstr-name ) -> expr itself does not suspend the evaluation of expr as a regular abstraction would. The syntax has been chosen to fit nicely in the context of function declarations, where it is generally used. It is possible to freely mix regular function parameters with pseudo type parameters, as in:
let f = fun (type t) (foo : t list) -> ...
and even use the alternative syntax for declaring functions:
let f (type t) (foo : t list) = ...
If several locally abstract types need to be introduced, it is possible to use the syntax fun ( type typeconstr-name1 … typeconstr-namen ) -> expr as syntactic sugar for fun ( type typeconstr-name1 ) -> … -> fun ( type typeconstr-namen ) -> expr. For instance,
let f = fun (type t u v) -> fun (foo : (t * u * v) list) -> ...
let f' (type t u v) (foo : (t * u * v) list) = ...
This construction is useful because the type constructors it introduces can be used in places where a type variable is not allowed. For instance, one can use it to define an exception in a local module within a polymorphic function.
let f (type t) () =
let module M = struct exception E of t end in
(fun x -> M.E x), (function M.E x -> Some x | _ -> None)
Here is another example:
let sort_uniq (type s) (cmp : s -> s -> int) =
let module S = Set.Make(struct type t = s let compare = cmp end) in
fun l ->
S.elements (List.fold_right S.add l S.empty)
It is also extremely useful for first-class modules (see section 8.9) and generalized algebraic datatypes (GADTs: see section 8.14).
(Introduced in OCaml 4.00)
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The (type typeconstr-name) syntax construction by itself does not make polymorphic the type variable it introduces, but it can be combined with explicit polymorphic annotations where needed. The above rule is provided as syntactic sugar to make this easier:
let rec f : type t1 t2. t1 * t2 list -> t1 = ...
is automatically expanded into
let rec f : 't1 't2. 't1 * 't2 list -> 't1 =
fun (type t1) (type t2) -> (... : t1 * t2 list -> t1)
This syntax can be very useful when defining recursive functions involving GADTs, see the section 8.14 for a more detailed explanation.
The same feature is provided for method definitions.
(Introduced in OCaml 3.12; pattern syntax and package type inference introduced in 4.00; structural comparison of package types introduced in 4.02.; fewer parens required starting from 4.05)
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Modules are typically thought of as static components. This extension makes it possible to pack a module as a first-class value, which can later be dynamically unpacked into a module.
The expression ( module module-expr : package-type ) converts the module (structure or functor) denoted by module expression module-expr to a value of the core language that encapsulates this module. The type of this core language value is ( module package-type ). The package-type annotation can be omitted if it can be inferred from the context.
Conversely, the module expression ( val expr : package-type ) evaluates the core language expression expr to a value, which must have type module package-type, and extracts the module that was encapsulated in this value. Again package-type can be omitted if the type of expr is known. If the module expression is already parenthesized, like the arguments of functors are, no additional parens are needed: Map.Make(val key).
The pattern ( module module-name : package-type ) matches a package with type package-type and binds it to module-name. It is not allowed in toplevel let bindings. Again package-type can be omitted if it can be inferred from the enclosing pattern.
The package-type syntactic class appearing in the ( module package-type ) type expression and in the annotated forms represents a subset of module types. This subset consists of named module types with optional constraints of a limited form: only non-parametrized types can be specified.
For type-checking purposes (and starting from OCaml 4.02), package types are compared using the structural comparison of module types.
In general, the module expression ( val expr : package-type ) cannot be used in the body of a functor, because this could cause unsoundness in conjunction with applicative functors. Since OCaml 4.02, this is relaxed in two ways: if package-type does not contain nominal type declarations (i.e. types that are created with a proper identity), then this expression can be used anywhere, and even if it contains such types it can be used inside the body of a generative functor, described in section 8.21. It can also be used anywhere in the context of a local module binding let module module-name = ( val expr1 : package-type ) in expr2.
A typical use of first-class modules is to select at run-time among several implementations of a signature. Each implementation is a structure that we can encapsulate as a first-class module, then store in a data structure such as a hash table:
module type DEVICE = sig ... end
let devices : (string, (module DEVICE)) Hashtbl.t = Hashtbl.create 17
module SVG = struct ... end
let _ = Hashtbl.add devices "SVG" (module SVG : DEVICE)
module PDF = struct ... end
let _ = Hashtbl.add devices "PDF" (module PDF: DEVICE)
We can then select one implementation based on command-line arguments, for instance:
module Device =
(val (try Hashtbl.find devices (parse_cmdline())
with Not_found -> eprintf "Unknown device %s\n"; exit 2)
: DEVICE)
Alternatively, the selection can be performed within a function:
let draw_using_device device_name picture =
let module Device =
(val (Hashtbl.find_devices device_name) : DEVICE)
in
Device.draw picture
With first-class modules, it is possible to parametrize some code over the implementation of a module without using a functor.
let sort (type s) (module Set : Set.S with type elt = s) l =
Set.elements (List.fold_right Set.add l Set.empty)
val sort : (module Set.S with type elt = 'a) -> 'a list -> 'a list
To use this function, one can wrap the Set.Make functor:
let make_set (type s) cmp =
let module S = Set.Make(struct
type t = s
let compare = cmp
end) in
(module S : Set.S with type elt = s)
val make_set : ('a -> 'a -> int) -> (module Set.S with type elt = 'a)
(Introduced in OCaml 3.12)
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The construction module type of module-expr expands to the module type (signature or functor type) inferred for the module expression module-expr. To make this module type reusable in many situations, it is intentionally not strengthened: abstract types and datatypes are not explicitly related with the types of the original module. For the same reason, module aliases in the inferred type are expanded.
A typical use, in conjunction with the signature-level include construct, is to extend the signature of an existing structure. In that case, one wants to keep the types equal to types in the original module. This can done using the following idiom.
module type MYHASH = sig
include module type of struct include Hashtbl end
val replace: ('a, 'b) t -> 'a -> 'b -> unit
end
The signature MYHASH then contains all the fields of the signature of the module Hashtbl (with strengthened type definitions), plus the new field replace. An implementation of this signature can be obtained easily by using the include construct again, but this time at the structure level:
module MyHash : MYHASH = struct
include Hashtbl
let replace t k v = remove t k; add t k v
end
Another application where the absence of strengthening comes handy, is to provide an alternative implementation for an existing module.
module MySet : module type of Set = struct
...
end
This idiom guarantees that Myset is compatible with Set, but allows it to represent sets internally in a different way.
(Introduced in OCaml 3.12, generalized in 4.06)
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A “destructive” substitution (with ... := ...) behaves essentially like normal signature constraints (with ... = ...), but it additionally removes the redefined type or module from the signature.
Prior to OCaml 4.06, there were a number of restrictions: one could only remove types and modules at the outermost level (not inside submodules), and in the case of with type the definition had to be another type constructor with the same type parameters.
A natural application of destructive substitution is merging two signatures sharing a type name.
module type Printable = sig type t val print : Format.formatter -> t -> unit end module type Comparable = sig type t val compare : t -> t -> int end module type PrintableComparable = sig include Printable include Comparable with type t := t end
One can also use this to completely remove a field:
module type S = Comparable with type t := intmodule type S = sig val compare : int -> int -> int end
or to rename one:
module type S = sig type u include Comparable with type t := u endmodule type S = sig type u val compare : u -> u -> int end
Note that you can also remove manifest types, by substituting with the same type.
module type ComparableInt = Comparable with type t = int ;;module type ComparableInt = sig type t = int val compare : t -> t -> int end
module type CompareInt = ComparableInt with type t := intmodule type CompareInt = sig val compare : int -> int -> int end
(Introduced in OCaml 4.02)
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The above specification, inside a signature, only matches a module definition equal to module-path. Conversely, a type-level module alias can be matched by itself, or by any supertype of the type of the module it references.
There are several restrictions on module-path:
Such specifications are also inferred. Namely, when P is a path satisfying the above constraints,
module N = P
has type
module N = P
Type-level module aliases are used when checking module path equalities. That is, in a context where module name N is known to be an alias for P, not only these two module paths check as equal, but F (N) and F (P) are also recognized as equal. In the default compilation mode, this is the only difference with the previous approach of module aliases having just the same module type as the module they reference.
When the compiler flag -no-alias-deps is enabled, type-level module aliases are also exploited to avoid introducing dependencies between compilation units. Namely, a module alias referring to a module inside another compilation unit does not introduce a link-time dependency on that compilation unit, as long as it is not dereferenced; it still introduces a compile-time dependency if the interface needs to be read, i.e. if the module is a submodule of the compilation unit, or if some type components are referred to. Additionally, accessing a module alias introduces a link-time dependency on the compilation unit containing the module referenced by the alias, rather than the compilation unit containing the alias. Note that these differences in link-time behavior may be incompatible with the previous behavior, as some compilation units might not be extracted from libraries, and their side-effects ignored.
These weakened dependencies make possible to use module aliases in place of the -pack mechanism. Suppose that you have a library Mylib composed of modules A and B. Using -pack, one would issue the command line
ocamlc -pack a.cmo b.cmo -o mylib.cmo
and as a result obtain a Mylib compilation unit, containing physically A and B as submodules, and with no dependencies on their respective compilation units. Here is a concrete example of a possible alternative approach:
module A = Mylib_A
module B = Mylib_B
ocamlc -c -no-alias-deps Mylib.ml
ocamlc -c -no-alias-deps -open Mylib Mylib_*.mli Mylib_*.ml
ocamlc -a Mylib*.cmo -o Mylib.cma
This approach lets you access A and B directly inside the library, and as Mylib.A and Mylib.B from outside. It also has the advantage that Mylib is no longer monolithic: if you use Mylib.A, only Mylib_A will be linked in, not Mylib_B.
(Introduced in OCaml 4.01)
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Since OCaml 4.01, open statements shadowing an existing identifier (which is later used) trigger the warning 44. Adding a ! character after the open keyword indicates that such a shadowing is intentional and should not trigger the warning.
This is also available (since OCaml 4.06) for local opens in class expressions and class type expressions.
(Introduced in OCaml 4.00)
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Generalized algebraic datatypes, or GADTs, extend usual sum types in two ways: constraints on type parameters may change depending on the value constructor, and some type variables may be existentially quantified. Adding constraints is done by giving an explicit return type (the rightmost typexpr in the above syntax), where type parameters are instantiated. This return type must use the same type constructor as the type being defined, and have the same number of parameters. Variables are made existential when they appear inside a constructor’s argument, but not in its return type.
Since the use of a return type often eliminates the need to name type parameters in the left-hand side of a type definition, one can replace them with anonymous types _ in that case.
The constraints associated to each constructor can be recovered through pattern-matching. Namely, if the type of the scrutinee of a pattern-matching contains a locally abstract type, this type can be refined according to the constructor used. These extra constraints are only valid inside the corresponding branch of the pattern-matching. If a constructor has some existential variables, fresh locally abstract types are generated, and they must not escape the scope of this branch.
Here is a concrete example:
type _ term =
| Int : int -> int term
| Add : (int -> int -> int) term
| App : ('b -> 'a) term * 'b term -> 'a term
let rec eval : type a. a term -> a = function
| Int n -> n (* a = int *)
| Add -> (fun x y -> x+y) (* a = int -> int -> int *)
| App(f,x) -> (eval f) (eval x)
(* eval called at types (b->a) and b for fresh b *)
let two = eval (App (App (Add, Int 1), Int 1))
val two : int = 2
It is important to remark that the function eval is using the polymorphic syntax for locally abstract types. When defining a recursive function that manipulates a GADT, explicit polymorphic recursion should generally be used. For instance, the following definition fails with a type error:
let rec eval (type a) : a term -> a = function
| Int n -> n
| Add -> (fun x y -> x+y)
| App(f,x) -> (eval f) (eval x)
(* ^
Error: This expression has type ($App_'b -> a) term but an expression was
expected of type 'a
The type constructor $App_'b would escape its scope
*)
In absence of an explicit polymorphic annotation, a monomorphic type is inferred for the recursive function. If a recursive call occurs inside the function definition at a type that involves an existential GADT type variable, this variable flows to the type of the recursive function, and thus escapes its scope. In the above example, this happens in the branch App(f,x) when eval is called with f as an argument. In this branch, the type of f is ($App_ 'b-> a). The prefix $ in $App_ 'b denotes an existential type named by the compiler (see 8.14). Since the type of eval is 'a term -> 'a, the call eval f makes the existential type $App_'b flow to the type variable 'a and escape its scope. This triggers the above error.
Type inference for GADTs is notoriously hard. This is due to the fact some types may become ambiguous when escaping from a branch. For instance, in the Int case above, n could have either type int or a, and they are not equivalent outside of that branch. As a first approximation, type inference will always work if a pattern-matching is annotated with types containing no free type variables (both on the scrutinee and the return type). This is the case in the above example, thanks to the type annotation containing only locally abstract types.
In practice, type inference is a bit more clever than that: type annotations do not need to be immediately on the pattern-matching, and the types do not have to be always closed. As a result, it is usually enough to only annotate functions, as in the example above. Type annotations are propagated in two ways: for the scrutinee, they follow the flow of type inference, in a way similar to polymorphic methods; for the return type, they follow the structure of the program, they are split on functions, propagated to all branches of a pattern matching, and go through tuples, records, and sum types. Moreover, the notion of ambiguity used is stronger: a type is only seen as ambiguous if it was mixed with incompatible types (equated by constraints), without type annotations between them. For instance, the following program types correctly.
let rec sum : type a. a term -> _ = fun x ->
let y =
match x with
| Int n -> n
| Add -> 0
| App(f,x) -> sum f + sum x
in y + 1
val sum : 'a term -> int = <fun>
Here the return type int is never mixed with a, so it is seen as non-ambiguous, and can be inferred. When using such partial type annotations we strongly suggest specifying the -principal mode, to check that inference is principal.
The exhaustiveness check is aware of GADT constraints, and can automatically infer that some cases cannot happen. For instance, the following pattern matching is correctly seen as exhaustive (the Add case cannot happen).
let get_int : int term -> int = function
| Int n -> n
| App(_,_) -> 0
(Introduced in OCaml 4.03)
Usually, the exhaustiveness check only tries to check whether the cases omitted from the pattern matching are typable or not. However, you can force it to try harder by adding refutation cases:
|
In presence of a refutation case, the exhaustiveness check will first compute the intersection of the pattern with the complement of the cases preceding it. It then checks whether the resulting patterns can really match any concrete values by trying to type-check them. Wild cards in the generated patterns are handled in a special way: if their type is a variant type with only GADT constructors, then the pattern is split into the different constructors, in order to check whether any of them is possible (this splitting is not done for arguments of these constructors, to avoid non-termination.) We also split tuples and variant types with only one case, since they may contain GADTs inside. For instance, the following code is deemed exhaustive:
type _ t =
| Int : int t
| Bool : bool t
let deep : (char t * int) option -> char = function
| None -> 'c'
| _ -> .
Namely, the inferred remaining case is Some _, which is split into Some (Int, _) and Some (Bool, _), which are both untypable. Note that the refutation case could be omitted here, because it is automatically added when there is only one case in the pattern matching.
Another addition is that the redundancy check is now aware of GADTs: a case will be detected as redundant if it could be replaced by a refutation case using the same pattern.
The term type we have defined above is an indexed type, where a type parameter reflects a property of the value contents. Another use of GADTs is singleton types, where a GADT value represents exactly one type. This value can be used as runtime representation for this type, and a function receiving it can have a polytypic behavior.
Here is an example of a polymorphic function that takes the runtime representation of some type t and a value of the same type, then pretty-prints the value as a string:
type _ typ =
| Int : int typ
| String : string typ
| Pair : 'a typ * 'b typ -> ('a * 'b) typ
let rec to_string: type t. t typ -> t -> string =
fun t x ->
match t with
| Int -> string_of_int x
| String -> Printf.sprintf "%S" x
| Pair(t1,t2) ->
let (x1, x2) = x in
Printf.sprintf "(%s,%s)" (to_string t1 x1) (to_string t2 x2)
Another frequent application of GADTs is equality witnesses.
type (_,_) eq = Eq : ('a,'a) eq
let cast : type a b. (a,b) eq -> a -> b = fun Eq x -> x
Here type eq has only one constructor, and by matching on it one adds a local constraint allowing the conversion between a and b. By building such equality witnesses, one can make equal types which are syntactically different.
Here is an example using both singleton types and equality witnesses to implement dynamic types.
let rec eq_type : type a b. a typ -> b typ -> (a,b) eq option =
fun a b ->
match a, b with
| Int, Int -> Some Eq
| String, String -> Some Eq
| Pair(a1,a2), Pair(b1,b2) ->
begin match eq_type a1 b1, eq_type a2 b2 with
| Some Eq, Some Eq -> Some Eq
| _ -> None
end
| _ -> None
type dyn = Dyn : 'a typ * 'a -> dyn
let get_dyn : type a. a typ -> dyn -> a option =
fun a (Dyn(b,x)) ->
match eq_type a b with
| None -> None
| Some Eq -> Some x
The typing of pattern matching in presence of GADT can generate many existential types. When necessary, error messages refer to these existential types using compiler-generated names. Currently, the compiler generates these names according to the following nomenclature:
type any = Any : 'name -> any let escape (Any x) = xError: This expression has type $Any_'name but an expression was expected of type 'a The type constructor $Any_'name would escape its scope
type any = Any : _ -> any let escape (Any x) = xError: This expression has type $Any but an expression was expected of type 'a The type constructor $Any would escape its scope
type ('arg,'result,'aux) fn = | Fun: ('a ->'b) -> ('a,'b,unit) fn | Mem1: ('a ->'b) * 'a * 'b -> ('a, 'b, 'a * 'b) fn let apply: ('arg,'result, _ ) fn -> 'arg -> 'result = fun f x -> match f with | Fun f -> f x | Mem1 (f,y,fy) -> if x = y then fy else f xError: This pattern matches values of type ($'arg, 'result, $'arg * 'result) fn but a pattern was expected which matches values of type ($'arg, 'result, unit) fn The type constructor $'arg would escape its scope
As shown by the last item, the current behavior is imperfect and may be improved in future versions.
(Introduced in OCaml 4.04)
GADT pattern-matching may also add type equations to non-local abstract types. The behaviour is the same as with local abstract types. Reusing the above eq type, one can write:
module M : sig type t val x : t val e : (t,int) eq end = struct
type t = int
let x = 33
let e = Eq
end
let x : int = let Eq = M.e in M.x
Of course, not all abstract types can be refined, as this would contradict the exhaustiveness check. Namely, builtin types (those defined by the compiler itself, such as int or array), and abstract types defined by the local module, are non-instantiable, and as such cause a type error rather than introduce an equation.
(Introduced in Objective Caml 3.00)
|
This extension provides syntactic sugar for getting and setting elements in the arrays provided by the Bigarray[Bigarray] library.
The short expressions are translated into calls to functions of the Bigarray module as described in the following table.
| expression | translation |
| expr0.{ expr1} | Bigarray.Array1.get expr0 expr1 |
| expr0.{ expr1} <- expr | Bigarray.Array1.set expr0 expr1 expr |
| expr0.{ expr1, expr2} | Bigarray.Array2.get expr0 expr1 expr2 |
| expr0.{ expr1, expr2} <- expr | Bigarray.Array2.set expr0 expr1 expr2 expr |
| expr0.{ expr1, expr2, expr3} | Bigarray.Array3.get expr0 expr1 expr2 expr3 |
| expr0.{ expr1, expr2, expr3} <- expr | Bigarray.Array3.set expr0 expr1 expr2 expr3 expr |
| expr0.{ expr1, …, exprn} | Bigarray.Genarray.get expr0 [| expr1, … , exprn |] |
| expr0.{ expr1, …, exprn} <- expr | Bigarray.Genarray.set expr0 [| expr1, … , exprn |] expr |
The last two entries are valid for any n > 3.
(Introduced in OCaml 4.02, infix notations for constructs other than expressions added in 4.03)
Attributes are “decorations” of the syntax tree which are mostly ignored by the type-checker but can be used by external tools. An attribute is made of an identifier and a payload, which can be a structure, a type expression (prefixed with :), a signature (prefixed with :) or a pattern (prefixed with ?) optionally followed by a when clause:
|
The first form of attributes is attached with a postfix notation on “algebraic” categories:
|
This form of attributes can also be inserted after the `tag-name in polymorphic variant type expressions (tag-spec-first, tag-spec, tag-spec-full) or after the method-name in method-type.
The same syntactic form is also used to attach attributes to labels and constructors in type declarations:
|
Note: when a label declaration is followed by a semi-colon, attributes can also be put after the semi-colon (in which case they are merged to those specified before).
The second form of attributes are attached to “blocks” such as type declarations, class fields, etc:
|
A third form of attributes appears as stand-alone structure or signature items in the module or class sub-languages. They are not attached to any specific node in the syntax tree:
|
(Note: contrary to what the grammar above describes, item-attributes cannot be attached to these floating attributes in class-field-spec and class-field.)
It is also possible to specify attributes using an infix syntax. For instance:
let[@foo] x = 2 in x + 1 === (let x = 2 [@@foo] in x + 1) begin[@foo][@bar x] ... end === (begin ... end)[@foo][@@bar x] module[@foo] M = ... === module M = ... [@@foo] type[@foo] t = T === type t = T [@@foo] method[@foo] m = ... === method m = ... [@@foo]
For let, the attributes are applied to each bindings:
let[@foo] x = 2 and y = 3 in x + y === (let x = 2 [@@foo] and y = 3 in x + y) let[@foo] x = 2 and[@bar] y = 3 in x + y === (let x = 2 [@@foo] and y = 3 [@bar] in x + y)
Some attributes are understood by the type-checker:
module X = struct [@@@warning "+9"] (* locally enable warning 9 in this structure *) ... end [@@deprecated "Please use module 'Y' instead."] let x = begin[@warning "+9"] ... end in .... type t = A | B [@@deprecated "Please use type 's' instead."] let f x = assert (x >= 0) [@ppwarning "TODO: remove this later"]; let rec no_op = function | [] -> () | _ :: q -> (no_op[@tailcall]) q;; let f x = x [@@inline] let () = (f[@inlined]) () type fragile = | Int of int [@warn_on_literal_pattern] | String of string [@warn_on_literal_pattern] let f = function | Int 0 | String "constant" -> () (* trigger warning 52 *) | _ -> () module Immediate: sig type t [@@immediate] val x: t ref end = struct type t = A | B let x = ref 0 end ....
(Introduced in OCaml 4.02, infix notations for constructs other than expressions added in 4.03, infix notation (e1 ;%ext e2) added in 4.04. )
Extension nodes are generic placeholders in the syntax tree. They are rejected by the type-checker and are intended to be “expanded” by external tools such as -ppx rewriters.
Extension nodes share the same notion of identifier and payload as attributes 8.16.
The first form of extension node is used for “algebraic” categories:
|
A second form of extension node can be used in structures and signatures, both in the module and object languages:
|
An infix form is available for extension nodes when the payload is of the same kind (expression with expression, pattern with pattern ...).
Examples:
let%foo x = 2 in x + 1 === [%foo let x = 2 in x + 1] begin%foo ... end === [%foo begin ... end] x ;%foo 2 === [%foo x; 2] module%foo M = .. === [%%foo module M = ... ] val%foo x : t === [%%foo: val x : t]
When this form is used together with the infix syntax for attributes, the attributes are considered to apply to the payload:
fun%foo[@bar] x -> x + 1 === [%foo (fun x -> x + 1)[@foo ] ];
(Introduced in OCaml 4.03)
Some extension nodes are understood by the compiler itself:
type t = .. type t += X of int | Y of string let x = [%extension_constructor X] let y = [%extension_constructor Y]
x <> y;;- : bool = true
(Introduced in OCaml 4.02)
Quoted strings {foo|...|foo} provide a different lexical syntax to write string literals in OCaml code. They are useful to represent strings of arbitrary content without escaping – as long as the delimiter you chose (here |foo}) does not occur in the string itself.
|
The opening delimiter has the form {id| where id is a (possibly empty) sequence of lowercase letters and underscores. The corresponding closing delimiter is |id} (with the same identifier). Unlike regular OCaml string literals, quoted strings do not interpret any character in a special way.
Example:
String.length {|\"|} (* returns 2 *)
String.length {foo|\"|foo} (* returns 2 *)
Quoted strings are interesting in particular in conjunction to extension nodes [%foo ...] (see 8.17) to embed foreign syntax fragments to be interpreted by a preprocessor and turned into OCaml code: you can use [%sql {|...|}] for example to represent arbitrary SQL statements – assuming you have a ppx-rewriter that recognizes the %sql extension – without requiring escaping quotes.
Note that the non-extension form, for example {sql|...|sql}, should not be used for this purpose, as the user cannot see in the code that this string literal has a different semantics than they expect, and giving a semantics to a specific delimiter limits the freedom to change the delimiter to avoid escaping issues.
(Introduced in OCaml 4.02)
A new form of exception patterns is allowed, only as a toplevel pattern under a match...with pattern-matching (other occurrences are rejected by the type-checker).
|
Cases with such a toplevel pattern are called “exception cases”, as opposed to regular “value cases”. Exception cases are applied when the evaluation of the matched expression raises an exception. The exception value is then matched against all the exception cases and re-raised if none of them accept the exception (as for a try...with block). Since the bodies of all exception and value cases is outside the scope of the exception handler, they are all considered to be in tail-position: if the match...with block itself is in tail position in the current function, any function call in tail position in one of the case bodies results in an actual tail call.
It is an error if all cases are exception cases in a given pattern matching.
(Introduced in OCaml 4.02)
|
Extensible variant types are variant types which can be extended with new variant constructors. Extensible variant types are defined using ... New variant constructors are added using +=.
type attr = ..
type attr += Str of string
type attr +=
| Int of int
| Float of float
Pattern matching on an extensible variant type requires a default case to handle unknown variant constructors:
let to_string = function
| Str s -> s
| Int i -> string_of_int i
| Float f -> string_of_float f
| _ -> "?"
A preexisting example of an extensible variant type is the built-in exn type used for exceptions. Indeed, exception constructors can be declared using the type extension syntax:
type exn += Exc of int
Extensible variant constructors can be rebound to a different name. This allows exporting variants from another module.
type Expr.attr += Str = Expr.Str
Extensible variant constructors can be declared private. As with regular variants, this prevents them from being constructed directly by constructor application while still allowing them to be de-structured in pattern-matching.
module Bool : sig
type attr += private Bool of int
val bool : bool -> attr
end = struct
type attr += Bool of int
let bool p = if p then Bool 1 else Bool 0
end
(Introduced in OCaml 4.06)
|
Extensible variant types can be declared private. This prevents new constructors from being declared directly, but allows extension constructors to be referred to in interfaces.
module Msg : sig
type t = private ..
module MkConstr (X : sig type t end) : sig
type t += C of X.t
end
end = struct
type t = ..
module MkConstr (X : sig type t end) = struct
type t += C of X.t
end
end
(Introduced in OCaml 4.02)
|
A generative functor takes a unit () argument. In order to use it, one must necessarily apply it to this unit argument, ensuring that all type components in the result of the functor behave in a generative way, i.e. they are different from types obtained by other applications of the same functor. This is equivalent to taking an argument of signature sig end, and always applying to struct end, but not to some defined module (in the latter case, applying twice to the same module would return identical types).
As a side-effect of this generativity, one is allowed to unpack first-class modules in the body of generative functors.
(Introduced in OCaml 4.02.2, extended in 4.03)
Some syntactic constructions are accepted during parsing and rejected during type checking. These syntactic constructions can therefore not be used directly in vanilla OCaml. However, -ppx rewriters and other external tools can exploit this parser leniency to extend the language with these new syntactic constructions by rewriting them to vanilla constructions.
|
Operator names starting with a # character and containing more than one # character are reserved for extensions.
|
Int and float literals followed by an one-letter identifier in the range [g..z∣ G..Z] are extension-only literals.
|
The arguments of a sum-type constructors can now be defined using the same syntax as records. Mutable and polymorphic fields are allowed. GADT syntax is supported. Attributes can be specified on individual fields.
Syntactically, building or matching constructors with such an inline record argument is similar to working with a unary constructor whose unique argument is a declared record type. A pattern can bind the inline record as a pseudo-value, but the record cannot escape the scope of the binding and can only be used with the dot-notation to extract or modify fields or to build new constructor values.
type t =
| Point of {width: int; mutable x: float; mutable y: float}
| ...
let v = Point {width = 10; x = 0.; y = 0.}
let scale l = function
| Point p -> Point {p with x = l *. p.x; y = l *. p.y}
| ....
let print = function
| Point {x; y; _} -> Printf.printf "%f/%f" x y
| ....
let reset = function
| Point p -> p.x <- 0.; p.y <- 0.
| ...
let invalid = function
| Point p -> p (* INVALID *)
| ...
(Introduced in OCaml 4.04)
It is possible to define local exceptions in expressions:
|
The syntactic scope of the exception constructor is the inner expression, but nothing prevents exception values created with this constructor from escaping this scope. Two executions of the definition above result in two incompatible exception constructors (as for any exception definition).
(Introduced in OCaml 4.03)
Comments which start with ** are treated specially by the compiler. They are automatically converted during parsing into attributes (see 8.16) to allow tools to process them as documentation.
Such comments can take three forms: floating comments, item comments and label comments. Any comment starting with ** which does not match one of these forms will cause the compiler to emit warning 50.
Comments which start with ** are also used by the ocamldoc documentation generator (see 16). The three comment forms recognised by the compiler are a subset of the forms accepted by ocamldoc (see 16.2).
Comments surrounded by blank lines that appear within structures, signatures, classes or class types are converted into floating-attributes. For example:
type t = T (** Now some definitions for [t] *) let mkT = T
will be converted to:
type t = T [@@@ocaml.text " Now some definitions for [t] "] let mkT = T
Comments which appear immediately before or immediately after a structure item, signature item, class item or class type item are converted into item-attributes. Immediately before or immediately after means that there must be no blank lines, ;;, or other documentation comments between them. For example:
type t = T (** A description of [t] *)
or
(** A description of [t] *) type t = T
will be converted to:
type t = T [@@ocaml.doc " A description of [t] "]
Note that, if a comment appears immediately next to multiple items, as in:
type t = T (** An ambiguous comment *) type s = S
then it will be attached to both items:
type t = T [@@ocaml.doc " An ambiguous comment "] type s = S [@@ocaml.doc " An ambiguous comment "]
and the compiler will emit warning 50.
Comments which appear immediately after a labelled argument, record field, variant constructor, object method or polymorphic variant constructor are are converted into attributes. Immediately after means that there must be no blank lines or other documentation comments between them. For example:
type t1 = lbl:int (** Labelled argument *) -> unit
type t2 = {
fld: int; (** Record field *)
fld2: float;
}
type t3 =
| Cstr of string (** Variant constructor *)
| Cstr2 of string
type t4 = < meth: int * int; (** Object method *) >
type t5 = [
`PCstr (** Polymorphic variant constructor *)
]
will be converted to:
type t1 = lbl:(int [@ocaml.doc " Labelled argument "]) -> unit
type t2 = {
fld: int [@ocaml.doc " Record field "];
fld2: float;
}
type t3 =
| Cstr of string [@ocaml.doc " Variant constructor "]
| Cstr2 of string
type t4 = < meth : int * int [@ocaml.doc " Object method "] >
type t5 = [
`PCstr [@ocaml.doc " Polymorphic variant constructor "]
]
Note that label comments take precedence over item comments, so:
type t = T of string (** Attaches to T not t *)
will be converted to:
type t = T of string [@ocaml.doc " Attaches to T not t "]
whilst:
type t = T of string (** Attaches to T not t *) (** Attaches to t *)
will be converted to:
type t = T of string [@ocaml.doc " Attaches to T not t "] [@@ocaml.doc " Attaches to t "]
In the absence of meaningful comment on the last constructor of a type, an empty comment (**) can be used instead:
type t = T of string (**) (** Attaches to t *)
will be converted directly to
type t = T of string [@@ocaml.doc " Attaches to t "]
(Introduced in 4.06)
|
This extension provides syntactic sugar for getting and setting elements for user-defined indexed types. For instance, we can define python-like dictionaries with
module Dict = struct include Hashtbl let ( .%{} ) tabl index = find tabl index let ( .%{}<- ) tabl index value = add tabl index value end let dict = let dict = Dict.create 10 in let () = dict.Dict.%{"one"} <- 1; let open Dict in dict.%{"two"} <- 2 in dict
dict.Dict.%{"one"};;- : int = 1
let open Dict in dict.%{"two"};;- : int = 2
Part III |
This chapter describes the OCaml batch compiler ocamlc, which compiles OCaml source files to bytecode object files and links these object files to produce standalone bytecode executable files. These executable files are then run by the bytecode interpreter ocamlrun.
The ocamlc command has a command-line interface similar to the one of most C compilers. It accepts several types of arguments and processes them sequentially, after all options have been processed:
If the interface file x.mli exists, the implementation x.ml is checked against the corresponding compiled interface x.cmi, which is assumed to exist. If no interface x.mli is provided, the compilation of x.ml produces a compiled interface file x.cmi in addition to the compiled object code file x.cmo. The file x.cmi produced corresponds to an interface that exports everything that is defined in the implementation x.ml.
The output of the linking phase is a file containing compiled bytecode that can be executed by the OCaml bytecode interpreter: the command named ocamlrun. If a.out is the name of the file produced by the linking phase, the command
ocamlrun a.out arg1 arg2 … argn
executes the compiled code contained in a.out, passing it as arguments the character strings arg1 to argn. (See chapter 11 for more details.)
On most systems, the file produced by the linking phase can be run directly, as in:
./a.out arg1 arg2 … argn
The produced file has the executable bit set, and it manages to launch the bytecode interpreter by itself.
The following command-line options are recognized by ocamlc. The options -pack, -a, -c and -output-obj are mutually exclusive.
If -custom, -cclib or -ccopt options are passed on the command line, these options are stored in the resulting .cmalibrary. Then, linking with this library automatically adds back the -custom, -cclib and -ccopt options as if they had been provided on the command line, unless the -noautolink option is given.
The environment variable OCAML_COLOR is considered if -color is not provided. Its values are auto/always/never as above.
Unix: Never use the strip command on executables produced by ocamlc -custom, this would remove the bytecode part of the executable.
Unix: Security warning: never set the “setuid” or “setgid” bits on executables produced by ocamlc -custom, this would make them vulnerable to attacks.
If the given directory starts with +, it is taken relative to the standard library directory. For instance, -I +unix adds the subdirectory unix of the standard library to the search path.
The -opaque option, available since 4.04, disables cross-module optimization information for the currently compiled unit. When compiling .mli interface, using -opaque marks the compiled .cmi interface so that subsequent compilations of modules that depend on it will not rely on the corresponding .cmx file, nor warn if it is absent. When the native compiler compiles a .ml implementation, using -opaque generates a .cmx that does not contain any cross-module optimization information.
Using this option may degrade the quality of generated code, but it reduces compilation time, both on clean and incremental builds. Indeed, with the native compiler, when the implementation of a compilation unit changes, all the units that depend on it may need to be recompiled – because the cross-module information may have changed. If the compilation unit whose implementation changed was compiled with -opaque, no such recompilation needs to occur. This option can thus be used, for example, to get faster edit-compile-test feedback loops.
ocamlc -pack -o p.cmo a.cmo b.cmo c.cmogenerates compiled files p.cmo and p.cmi describing a compilation unit having three sub-modules A, B and C, corresponding to the contents of the object files a.cmo, b.cmo and c.cmo. These contents can be referenced as P.A, P.B and P.C in the remainder of the program.
The warning-list argument is a sequence of warning specifiers, with no separators between them. A warning specifier is one of the following:
Warning numbers and letters which are out of the range of warnings that are currently defined are ignored. The warnings are as follows.
The default setting is -w +a-4-6-7-9-27-29-32..42-44-45-48-50-60. It is displayed by ocamlc -help. Note that warnings 5 and 10 are not always triggered, depending on the internals of the type checker.
Note: it is not recommended to use warning sets (i.e. letters) as arguments to -warn-error in production code, because this can break your build when future versions of OCaml add some new warnings.
The default setting is -warn-error -a+31 (only warning 31 is fatal).
The compiler command line can be modified “from the outside” with the following mechanisms. These are experimental and subject to change. They should be used only for experimental and development work, not in released packages.
This short section is intended to clarify the relationship between the names of the modules corresponding to compilation units and the names of the files that contain their compiled interface and compiled implementation.
The compiler always derives the module name by taking the capitalized base name of the source file (.ml or .mli file). That is, it strips the leading directory name, if any, as well as the .ml or .mli suffix; then, it set the first letter to uppercase, in order to comply with the requirement that module names must be capitalized. For instance, compiling the file mylib/misc.ml provides an implementation for the module named Misc. Other compilation units may refer to components defined in mylib/misc.ml under the names Misc.name; they can also do open Misc, then use unqualified names name.
The .cmi and .cmo files produced by the compiler have the same base name as the source file. Hence, the compiled files always have their base name equal (modulo capitalization of the first letter) to the name of the module they describe (for .cmi files) or implement (for .cmo files).
When the compiler encounters a reference to a free module identifier Mod, it looks in the search path for a file named Mod.cmi or mod.cmi and loads the compiled interface contained in that file. As a consequence, renaming .cmi files is not advised: the name of a .cmi file must always correspond to the name of the compilation unit it implements. It is admissible to move them to another directory, if their base name is preserved, and the correct -I options are given to the compiler. The compiler will flag an error if it loads a .cmi file that has been renamed.
Compiled bytecode files (.cmo files), on the other hand, can be freely renamed once created. That’s because the linker never attempts to find by itself the .cmo file that implements a module with a given name: it relies instead on the user providing the list of .cmo files by hand.
This section describes and explains the most frequently encountered error messages.
If filename has the format mod.cmo, this means you are trying to link a bytecode object file that does not exist yet. Fix: compile mod.ml first.
If your program spans several directories, this error can also appear because you haven’t specified the directories to look into. Fix: add the correct -I options to the command line.
In some cases, it is hard to understand why the two types t1 and t2 are incompatible. For instance, the compiler can report that “expression of type foo cannot be used with type foo”, and it really seems that the two types foo are compatible. This is not always true. Two type constructors can have the same name, but actually represent different types. This can happen if a type constructor is redefined. Example:
type foo = A | B
let f = function A -> 0 | B -> 1
type foo = C | D
f C
This result in the error message “expression C of type foo cannot be used with type foo”.
Non-generalized type variables in a type cause no difficulties inside a given structure or compilation unit (the contents of a .ml file, or an interactive session), but they cannot be allowed inside signatures nor in compiled interfaces (.cmi file), because they could be used inconsistently later. Therefore, the compiler flags an error when a structure or compilation unit defines a value name whose type contains non-generalized type variables. There are two ways to fix this error:
let sort_int_list = Sort.list (<)
(* inferred type 'a list -> 'a list, with 'a not generalized *)
write
let sort_int_list = (Sort.list (<) : int list -> int list);;
let map_length = List.map Array.length
(* inferred type 'a array list -> int list, with 'a not generalized *)
write
let map_length lv = List.map Array.length lv
Of course, you will always encounter this error if you have mutually recursive functions across modules. That is, function Mod1.f calls function Mod2.g, and function Mod2.g calls function Mod1.f. In this case, no matter what permutations you perform on the command line, the program will be rejected at link-time. Fixes:
mod1.ml: let f x = ... Mod2.g ... mod2.ml: let g y = ... Mod1.f ...define
mod1.ml: let f g x = ... g ... mod2.ml: let rec g y = ... Mod1.f g ...and link mod1.cmo before mod2.cmo.
mod1.ml: let forward_g =
ref((fun x -> failwith "forward_g") : <type>)
let f x = ... !forward_g ...
mod2.ml: let g y = ... Mod1.f ...
let _ = Mod1.forward_g := g
This section describes and explains in detail some warnings:
When pattern matching on records, it can be useful to match only few fields of a record. Eliding fields can be done either implicitly or explicitly by ending the record pattern with ; _. However, implicit field elision is at odd with pattern matching exhaustiveness checks. Enabling warning 9 prioritizes exhaustiveness checks over the convenience of implicit field elision and will warn on implicit field elision in record patterns. In particular, this warning can help to spot exhaustive record pattern that may need to be updated after the addition of new fields to a record type.
type 'a point = {x='a ;y='a}
let dx { x } = x (* implicit field elision: trigger warning 9 *)
let dy { y; _ } = y (* explicit field elision: do not trigger warning 9 *)
Some constructors, such as the exception constructors Failure and Invalid_argument, take as parameter a string value holding a text message intended for the user.
These text messages are usually not stable over time: call sites building these constructors may refine the message in a future version to make it more explicit, etc. Therefore, it is dangerous to match over the precise value of the message. For example, until OCaml 4.02, Array.iter2 would raise the exception
Invalid_argument "arrays must have the same length"
Since 4.03 it raises the more helpful message
Invalid_argument "Array.iter2: arrays must have the same length"
but this means that any code of the form
try ... with Invalid_argument "arrays must have the same length" -> ...
is now broken and may suffer from uncaught exceptions.
Warning 52 is there to prevent users from writing such fragile code in the first place. It does not occur on every matching on a literal string, but only in the case in which library authors expressed their intent to possibly change the constructor parameter value in the future, by using the attribute ocaml.warn_on_literal_pattern (see the manual section on builtin attributes in 8.16.1):
type t =
| Foo of string [@ocaml.warn_on_literal_pattern]
| Bar of string
let no_warning = function
| Bar "specific value" -> 0
| _ -> 1
let warning = function
| Foo "specific value" -> 0
| _ -> 1
> | Foo "specific value" -> 0
> ^^^^^^^^^^^^^^^^
> Warning 52: Code should not depend on the actual values of
> this constructor's arguments. They are only for information
> and may change in future versions. (See manual section 8.5)
In particular, all built-in exceptions with a string argument have this attribute set: Invalid_argument, Failure, Sys_error will all raise this warning if you match for a specific string argument.
If your code raises this warning, you should not change the way you test for the specific string to avoid the warning (for example using a string equality inside the right-hand-side instead of a literal pattern), as your code would remain fragile. You should instead enlarge the scope of the pattern by matching on all possible values.
let warning = function | Foo _ -> 0 | _ -> 1
This may require some care: if the scrutinee may return several different cases of the same pattern, or raise distinct instances of the same exception, you may need to modify your code to separate those several cases.
For example,
try (int_of_string count_str, bool_of_string choice_str) with | Failure "int_of_string" -> (0, true) | Failure "bool_of_string" -> (-1, false)
should be rewritten into more atomic tests. For example, using the exception patterns documented in Section 8.19, one can write:
match int_of_string count_str with
| exception (Failure _) -> (0, true)
| count ->
begin match bool_of_string choice_str with
| exception (Failure _) -> (-1, false)
| choice -> (count, choice)
end
The only case where that transformation is not possible is if a given function call may raise distinct exceptions with the same constructor but different string values. In this case, you will have to check for specific string values. This is dangerous API design and it should be discouraged: it’s better to define more precise exception constructors than store useful information in strings.
The semantics of or-patterns in OCaml is specified with a left-to-right bias: a value v matches the pattern p | q if it matches p or q, but if it matches both, the environment captured by the match is the environment captured by p, never the one captured by q.
While this property is generally intuitive, there is at least one specific case where a different semantics might be expected. Consider a pattern followed by a when-guard: | p when g -> e, for example:
| ((Const x, _) | (_, Const x)) when is_neutral x -> branch
The semantics is clear: match the scrutinee against the pattern, if it matches, test the guard, and if the guard passes, take the branch. In particular, consider the input (Const a, Const b), where a fails the test is_neutral a, while b passes the test is_neutral b. With the left-to-right semantics, the clause above is not taken by its input: matching (Const a, Const b) against the or-pattern succeeds in the left branch, it returns the environment x -> a, and then the guard is_neutral a is tested and fails, the branch is not taken.
However, another semantics may be considered more natural here: any pair that has one side passing the test will take the branch. With this semantics the previous code fragment would be equivalent to
| (Const x, _) when is_neutral x -> branch
| (_, Const x) when is_neutral x -> branch
This is not the semantics adopted by OCaml.
Warning 57 is dedicated to these confusing cases where the specified left-to-right semantics is not equivalent to a non-deterministic semantics (any branch can be taken) relatively to a specific guard. More precisely, it warns when guard uses “ambiguous” variables, that are bound to different parts of the scrutinees by different sides of a or-pattern.
This chapter describes the toplevel system for OCaml, that permits interactive use of the OCaml system through a read-eval-print loop (REPL). In this mode, the system repeatedly reads OCaml phrases from the input, then typechecks, compile and evaluate them, then prints the inferred type and result value, if any. The system prints a # (sharp) prompt before reading each phrase.
Input to the toplevel can span several lines. It is terminated by ;; (a double-semicolon). The toplevel input consists in one or several toplevel phrases, with the following syntax:
|
A phrase can consist of a definition, like those found in implementations of compilation units or in struct … end module expressions. The definition can bind value names, type names, an exception, a module name, or a module type name. The toplevel system performs the bindings, then prints the types and values (if any) for the names thus defined.
A phrase may also consist in a value expression (section 7.7). It is simply evaluated without performing any bindings, and its value is printed.
Finally, a phrase can also consist in a toplevel directive, starting with # (the sharp sign). These directives control the behavior of the toplevel; they are listed below in section 10.2.
Unix: The toplevel system is started by the command ocaml, as follows:ocaml options objects # interactive mode ocaml options objects scriptfile # script modeoptions are described below. objects are filenames ending in .cmo or .cma; they are loaded into the interpreter immediately after options are set. scriptfile is any file name not ending in .cmo or .cma.If no scriptfile is given on the command line, the toplevel system enters interactive mode: phrases are read on standard input, results are printed on standard output, errors on standard error. End-of-file on standard input terminates ocaml (see also the #quit directive in section 10.2).
On start-up (before the first phrase is read), if the file .ocamlinit exists in the current directory, its contents are read as a sequence of OCaml phrases and executed as per the #use directive described in section 10.2. The evaluation outcode for each phrase are not displayed. If the current directory does not contain an .ocamlinit file, but the user’s home directory (environment variable HOME) does, the latter is read and executed as described below.
The toplevel system does not perform line editing, but it can easily be used in conjunction with an external line editor such as ledit, ocaml2 or rlwrap (see the Caml Hump). Another option is to use ocaml under Gnu Emacs, which gives the full editing power of Emacs (command run-caml from library inf-caml).
At any point, the parsing, compilation or evaluation of the current phrase can be interrupted by pressing ctrl-C (or, more precisely, by sending the INTR signal to the ocaml process). The toplevel then immediately returns to the # prompt.
If scriptfile is given on the command-line to ocaml, the toplevel system enters script mode: the contents of the file are read as a sequence of OCaml phrases and executed, as per the #use directive (section 10.2). The outcome of the evaluation is not printed. On reaching the end of file, the ocaml command exits immediately. No commands are read from standard input. Sys.argv is transformed, ignoring all OCaml parameters, and starting with the script file name in Sys.argv.(0).
In script mode, the first line of the script is ignored if it starts with #!. Thus, it should be possible to make the script itself executable and put as first line #!/usr/local/bin/ocaml, thus calling the toplevel system automatically when the script is run. However, ocaml itself is a #! script on most installations of OCaml, and Unix kernels usually do not handle nested #! scripts. A better solution is to put the following as the first line of the script:
#!/usr/local/bin/ocamlrun /usr/local/bin/ocaml
The following command-line options are recognized by the ocaml command.
If the given directory starts with +, it is taken relative to the standard library directory. For instance, -I +unix adds the subdirectory unix of the standard library to the search path.
Directories can also be added to the list once the toplevel is running with the #directory directive (section 10.2).
The warning-list argument is a sequence of warning specifiers, with no separators between them. A warning specifier is one of the following:
Warning numbers and letters which are out of the range of warnings that are currently defined are ignored. The warnings are as follows.
The default setting is -w +a-4-6-7-9-27-29-32..42-44-45-48-50-60. It is displayed by -help. Note that warnings 5 and 10 are not always triggered, depending on the internals of the type checker.
Note: it is not recommended to use warning sets (i.e. letters) as arguments to -warn-error in production code, because this can break your build when future versions of OCaml add some new warnings.
The default setting is -warn-error -a+31 (only warning 31 is fatal).
Unix: The following environment variables are also consulted:
- OCAMLTOP_UTF_8
- When printing string values, non-ascii bytes ( > \0x7E ) are printed as decimal escape sequence if OCAMLTOP_UTF_8 is set to false. Otherwise, they are printed unescaped.
- TERM
- When printing error messages, the toplevel system attempts to underline visually the location of the error. It consults the TERM variable to determines the type of output terminal and look up its capabilities in the terminal database.
- HOME
- Directory where the .ocamlinit file is searched.
The following directives control the toplevel behavior, load files in memory, and trace program execution.
Note: all directives start with a # (sharp) symbol. This # must be typed before the directive, and must not be confused with the # prompt displayed by the interactive loop. For instance, typing #quit;; will exit the toplevel loop, but typing quit;; will result in an “unbound value quit” error.
For directives that take file names as arguments, if the given file name specifies no directory, the file is searched in the following directories:
The printing function printer-name should have type Format.formatter -> t -> unit, where t is the type for the values to be printed, and should output its textual representation for the value of type t on the given formatter, using the functions provided by the Format library. For backward compatibility, printer-name can also have type t -> unit and should then output on the standard formatter, but this usage is deprecated.
Toplevel phrases can refer to identifiers defined in compilation units with the same mechanisms as for separately compiled units: either by using qualified names (Modulename.localname), or by using the open construct and unqualified names (see section 7.3).
However, before referencing another compilation unit, an implementation of that unit must be present in memory. At start-up, the toplevel system contains implementations for all the modules in the the standard library. Implementations for user modules can be entered with the #load directive described above. Referencing a unit for which no implementation has been provided results in the error Reference to undefined global `...'.
Note that entering open Mod merely accesses the compiled interface (.cmi file) for Mod, but does not load the implementation of Mod, and does not cause any error if no implementation of Mod has been loaded. The error “reference to undefined global Mod” will occur only when executing a value or module definition that refers to Mod.
This section describes and explains the most frequently encountered error messages.
If filename has the format mod.cmi, this means you have referenced the compilation unit mod, but its compiled interface could not be found. Fix: compile mod.mli or mod.ml first, to create the compiled interface mod.cmi.
If filename has the format mod.cmo, this means you are trying to load with #load a bytecode object file that does not exist yet. Fix: compile mod.ml first.
If your program spans several directories, this error can also appear because you haven’t specified the directories to look into. Fix: use the #directory directive to add the correct directories to the search path.
The ocamlmktop command builds OCaml toplevels that contain user code preloaded at start-up.
The ocamlmktop command takes as argument a set of .cmo and .cma files, and links them with the object files that implement the OCaml toplevel. The typical use is:
ocamlmktop -o mytoplevel foo.cmo bar.cmo gee.cmo
This creates the bytecode file mytoplevel, containing the OCaml toplevel system, plus the code from the three .cmo files. This toplevel is directly executable and is started by:
./mytoplevel
This enters a regular toplevel loop, except that the code from foo.cmo, bar.cmo and gee.cmo is already loaded in memory, just as if you had typed:
#load "foo.cmo";;
#load "bar.cmo";;
#load "gee.cmo";;
on entrance to the toplevel. The modules Foo, Bar and Gee are not opened, though; you still have to do
open Foo;;
yourself, if this is what you wish.
The following command-line options are recognized by ocamlmktop.
This section describes a tool that is not yet officially supported but may be found useful.
OCaml code executing in the traditional toplevel system uses the bytecode interpreter. When increased performance is required, or for testing programs that will only execute correctly when compiled to native code, the native toplevel may be used instead.
For the majority of installations the native toplevel will not have been installed along with the rest of the OCaml toolchain. In such circumstances it will be necessary to build the OCaml distribution from source. From the built source tree of the distribution you may use make natruntop to build and execute a native toplevel. (Alternatively make ocamlnat can be used, which just performs the build step.)
If the make install command is run after having built the native toplevel then the ocamlnat program (either from the source or the installation directory) may be invoked directly rather than using make natruntop.
The ocamlrun command executes bytecode files produced by the linking phase of the ocamlc command.
The ocamlrun command comprises three main parts: the bytecode interpreter, that actually executes bytecode files; the memory allocator and garbage collector; and a set of C functions that implement primitive operations such as input/output.
The usage for ocamlrun is:
ocamlrun options bytecode-executable arg1 ... argn
The first non-option argument is taken to be the name of the file containing the executable bytecode. (That file is searched in the executable path as well as in the current directory.) The remaining arguments are passed to the OCaml program, in the string array Sys.argv. Element 0 of this array is the name of the bytecode executable file; elements 1 to n are the remaining arguments arg1 to argn.
As mentioned in chapter 9, the bytecode executable files produced by the ocamlc command are self-executable, and manage to launch the ocamlrun command on themselves automatically. That is, assuming a.out is a bytecode executable file,
a.out arg1 ... argn
works exactly as
ocamlrun a.out arg1 ... argn
Notice that it is not possible to pass options to ocamlrun when invoking a.out directly.
Windows: Under several versions of Windows, bytecode executable files are self-executable only if their name ends in .exe. It is recommended to always give .exe names to bytecode executables, e.g. compile with ocamlc -o myprog.exe ... rather than ocamlc -o myprog ....
The following command-line options are recognized by ocamlrun.
The following environment variables are also consulted:
If the option letter is not recognized, the whole parameter is ignored; if the equal sign or the number is missing, the value is taken as 1; if the multiplier is not recognized, it is ignored.
For example, on a 32-bit machine, under bash the command
export OCAMLRUNPARAM='b,s=256k,v=0x015'
tells a subsequent ocamlrun to print backtraces for uncaught exceptions, set its initial minor heap size to 1 megabyte and print a message at the start of each major GC cycle, when the heap size changes, and when compaction is triggered.
On platforms that support dynamic loading, ocamlrun can link dynamically with C shared libraries (DLLs) providing additional C primitives beyond those provided by the standard runtime system. The names for these libraries are provided at link time as described in section 20.1.4), and recorded in the bytecode executable file; ocamlrun, then, locates these libraries and resolves references to their primitives when the bytecode executable program starts.
The ocamlrun command searches shared libraries in the following directories, in the order indicated:
This section describes and explains the most frequently encountered error messages.
To help you diagnose this error, run your program with the -v option to ocamlrun, or with the OCAMLRUNPARAM environment variable set to v=63. If it displays lots of “Growing stack…” messages, this is probably a looping recursive function. If it displays lots of “Growing heap…” messages, with the heap size growing slowly, this is probably an attempt to construct a data structure with too many (infinitely many?) cells. If it displays few “Growing heap…” messages, but with a huge increment in the heap size, this is probably an attempt to build an excessively large array, string or byte sequence.
This chapter describes the OCaml high-performance native-code compiler ocamlopt, which compiles OCaml source files to native code object files and links these object files to produce standalone executables.
The native-code compiler is only available on certain platforms. It produces code that runs faster than the bytecode produced by ocamlc, at the cost of increased compilation time and executable code size. Compatibility with the bytecode compiler is extremely high: the same source code should run identically when compiled with ocamlc and ocamlopt.
It is not possible to mix native-code object files produced by ocamlopt with bytecode object files produced by ocamlc: a program must be compiled entirely with ocamlopt or entirely with ocamlc. Native-code object files produced by ocamlopt cannot be loaded in the toplevel system ocaml.
The ocamlopt command has a command-line interface very close to that of ocamlc. It accepts the same types of arguments, and processes them sequentially, after all options have been processed:
The implementation is checked against the interface file x.mli (if it exists) as described in the manual for ocamlc (chapter 9).
The output of the linking phase is a regular Unix or Windows executable file. It does not need ocamlrun to run.
The following command-line options are recognized by ocamlopt. The options -pack, -a, -shared, -c and -output-obj are mutually exclusive.
If -cclib or -ccopt options are passed on the command line, these options are stored in the resulting .cmxalibrary. Then, linking with this library automatically adds back the -cclib and -ccopt options as if they had been provided on the command line, unless the -noautolink option is given.
The environment variable OCAML_COLOR is considered if -color is not provided. Its values are auto/always/never as above.
If the given directory starts with +, it is taken relative to the standard library directory. For instance, -I +unix adds the subdirectory unix of the standard library to the search path.
The -opaque option, available since 4.04, disables cross-module optimization information for the currently compiled unit. When compiling .mli interface, using -opaque marks the compiled .cmi interface so that subsequent compilations of modules that depend on it will not rely on the corresponding .cmx file, nor warn if it is absent. When the native compiler compiles a .ml implementation, using -opaque generates a .cmx that does not contain any cross-module optimization information.
Using this option may degrade the quality of generated code, but it reduces compilation time, both on clean and incremental builds. Indeed, with the native compiler, when the implementation of a compilation unit changes, all the units that depend on it may need to be recompiled – because the cross-module information may have changed. If the compilation unit whose implementation changed was compiled with -opaque, no such recompilation needs to occur. This option can thus be used, for example, to get faster edit-compile-test feedback loops.
Unix: See the Unix manual page for gprof(1) for more information about the profiles.Full support for gprof is only available for certain platforms (currently: Intel x86 32 and 64 bits under Linux, BSD and MacOS X). On other platforms, the -p option will result in a less precise profile (no call graph information, only a time profile).
Windows: The -p option does not work under Windows.
ocamlopt -pack -o P.cmx A.cmx B.cmx C.cmxgenerates compiled files P.cmx, P.o and P.cmi describing a compilation unit having three sub-modules A, B and C, corresponding to the contents of the object files A.cmx, B.cmx and C.cmx. These contents can be referenced as P.A, P.B and P.C in the remainder of the program.
The .cmx object files being combined must have been compiled with the appropriate -for-pack option. In the example above, A.cmx, B.cmx and C.cmx must have been compiled with ocamlopt -for-pack P.
Multiple levels of packing can be achieved by combining -pack with -for-pack. Consider the following example:
ocamlopt -for-pack P.Q -c A.ml
ocamlopt -pack -o Q.cmx -for-pack P A.cmx
ocamlopt -for-pack P -c B.ml
ocamlopt -pack -o P.cmx Q.cmx B.cmx
The resulting P.cmx object file has sub-modules P.Q, P.Q.A and P.B.
The warning-list argument is a sequence of warning specifiers, with no separators between them. A warning specifier is one of the following:
Warning numbers and letters which are out of the range of warnings that are currently defined are ignored. The warnings are as follows.
The default setting is -w +a-4-6-7-9-27-29-32..42-44-45-48-50-60. It is displayed by ocamlopt -help. Note that warnings 5 and 10 are not always triggered, depending on the internals of the type checker.
Note: it is not recommended to use warning sets (i.e. letters) as arguments to -warn-error in production code, because this can break your build when future versions of OCaml add some new warnings.
The default setting is -warn-error -a+31 (only warning 31 is fatal).
The IA32 code generator (Intel Pentium, AMD Athlon) supports the following additional option:
The AMD64 code generator (64-bit versions of Intel Pentium and AMD Athlon) supports the following additional options:
The compiler command line can be modified “from the outside” with the following mechanisms. These are experimental and subject to change. They should be used only for experimental and development work, not in released packages.
The error messages are almost identical to those of ocamlc. See section 9.4.
Executables generated by ocamlopt are native, stand-alone executable files that can be invoked directly. They do not depend on the ocamlrun bytecode runtime system nor on dynamically-loaded C/OCaml stub libraries.
During execution of an ocamlopt-generated executable, the following environment variables are also consulted:
This section lists the known incompatibilities between the bytecode compiler and the native-code compiler. Except on those points, the two compilers should generate code that behave identically.
let _ = ignore M.fcontains a reference to compilation unit M when compiled to bytecode. This reference forces M to be linked and its initialization code to be executed. The native-code compiler eliminates the reference to M, hence the compilation unit M may not be linked and executed. A workaround is to compile M with the -linkall flag so that it will always be linked and executed, even if not referenced. See also the Sys.opaque_identity function from the Sys standard library module.
This chapter describes two program generators: ocamllex, that produces a lexical analyzer from a set of regular expressions with associated semantic actions, and ocamlyacc, that produces a parser from a grammar with associated semantic actions.
These program generators are very close to the well-known lex and yacc commands that can be found in most C programming environments. This chapter assumes a working knowledge of lex and yacc: while it describes the input syntax for ocamllex and ocamlyacc and the main differences with lex and yacc, it does not explain the basics of writing a lexer or parser description in lex and yacc. Readers unfamiliar with lex and yacc are referred to “Compilers: principles, techniques, and tools” by Aho, Sethi and Ullman (Addison-Wesley, 1986), or “Lex & Yacc”, by Levine, Mason and Brown (O’Reilly, 1992).
The ocamllex command produces a lexical analyzer from a set of regular expressions with attached semantic actions, in the style of lex. Assuming the input file is lexer.mll, executing
ocamllex lexer.mll
produces OCaml code for a lexical analyzer in file lexer.ml. This file defines one lexing function per entry point in the lexer definition. These functions have the same names as the entry points. Lexing functions take as argument a lexer buffer, and return the semantic attribute of the corresponding entry point.
Lexer buffers are an abstract data type implemented in the standard library module Lexing. The functions Lexing.from_channel, Lexing.from_string and Lexing.from_function create lexer buffers that read from an input channel, a character string, or any reading function, respectively. (See the description of module Lexing in chapter 26.)
When used in conjunction with a parser generated by ocamlyacc, the semantic actions compute a value belonging to the type token defined by the generated parsing module. (See the description of ocamlyacc below.)
The following command-line options are recognized by ocamllex.
The format of lexer definitions is as follows:
{ header }
let ident = regexp …
[refill { refill-handler }]
rule entrypoint [arg1… argn] =
parse regexp { action }
| …
| regexp { action }
and entrypoint [arg1… argn] =
parse …
and …
{ trailer }
Comments are delimited by (* and *), as in OCaml. The parse keyword, can be replaced by the shortest keyword, with the semantic consequences explained below.
Refill handlers are a recent (optional) feature introduced in 4.02, documented below in subsection 13.2.7.
The header and trailer sections are arbitrary OCaml text enclosed in curly braces. Either or both can be omitted. If present, the header text is copied as is at the beginning of the output file and the trailer text at the end. Typically, the header section contains the open directives required by the actions, and possibly some auxiliary functions used in the actions.
Between the header and the entry points, one can give names to frequently-occurring regular expressions. This is written let ident = regexp. In regular expressions that follow this declaration, the identifier ident can be used as shorthand for regexp.
The names of the entry points must be valid identifiers for OCaml values (starting with a lowercase letter). Similarily, the arguments arg1… argn must be valid identifiers for OCaml. Each entry point becomes an OCaml function that takes n+1 arguments, the extra implicit last argument being of type Lexing.lexbuf. Characters are read from the Lexing.lexbuf argument and matched against the regular expressions provided in the rule, until a prefix of the input matches one of the rule. The corresponding action is then evaluated and returned as the result of the function.
If several regular expressions match a prefix of the input, the “longest match” rule applies: the regular expression that matches the longest prefix of the input is selected. In case of tie, the regular expression that occurs earlier in the rule is selected.
However, if lexer rules are introduced with the shortest keyword in place of the parse keyword, then the “shortest match” rule applies: the shortest prefix of the input is selected. In case of tie, the regular expression that occurs earlier in the rule is still selected. This feature is not intended for use in ordinary lexical analyzers, it may facilitate the use of ocamllex as a simple text processing tool.
The regular expressions are in the style of lex, with a more OCaml-like syntax.
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Concerning the precedences of operators, # has the highest precedence, followed by *, + and ?, then concatenation, then | (alternation), then as.
The actions are arbitrary OCaml expressions. They are evaluated in a context where the identifiers defined by using the as construct are bound to subparts of the matched string. Additionally, lexbuf is bound to the current lexer buffer. Some typical uses for lexbuf, in conjunction with the operations on lexer buffers provided by the Lexing standard library module, are listed below.
The as construct is similar to “groups” as provided by numerous regular expression packages. The type of these variables can be string, char, string option or char option.
We first consider the case of linear patterns, that is the case when all as bound variables are distinct. In regexp as ident, the type of ident normally is string (or string option) except when regexp is a character constant, an underscore, a string constant of length one, a character set specification, or an alternation of those. Then, the type of ident is char (or char option). Option types are introduced when overall rule matching does not imply matching of the bound sub-pattern. This is in particular the case of (