[Camllist] Encoding existential types without modules
 Daniel_Bünzli
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Date:   (:) 
From:  Daniel_Bünzli <daniel.buenzli@e...> 
Subject:  [Camllist] Encoding existential types without modules 
Hello, I think this may be usefull to others (e.g. to port some clever haskell code). Below, I give two examples that show how to encode existential types in ocaml without using modules. This is done by adapting to ocaml the encoding given by Pierce in [1]. It uses polymorphic record fields. The examples are a little bit silly but their aim is to show the concept of the encoding. The first example is a counter abstract datatype. The second one is a datatype that can hold a list of composable function, that is a type that expresses something like type ('a, 'b) funlist = Nil of ('a >'b)  Cons of exists 'c. ('a > 'c) * ('c,'b) funlist I usually need three types to encode an existential type. Does anybody see a simpler way of doing that ? Daniel [1] Benjamin C. Pierce, Types and Programming Languages, section 24.3  Abstract counter datatype (* The type expressed by the three types below is : type packed_counter = exists 'x. { create : 'x; get : ('x > int); inc : ('x > 'x)} *) type 'x counter = { create : 'x; get : ('x > int); inc : ('x > 'x) } type 't counter_scope = { bind_counter : 'x. 'x counter > 't } type packed_counter = { open_counter : 't. 't counter_scope > 't } (* Creating a package from a counter implementation *) let pack_counter impl = { open_counter = fun scope > scope.bind_counter impl } (* Using a package with a scoped expression *) let with_packed_counter p e = p.open_counter e (* Two different implementations of the counter *) let int_impl = { create = 1 ; get = (function i > i) ; inc = (fun i > i+1) } let float_impl = { create = 1.0; get = (function i > (int_of_float i)) ; inc = (fun i > i +. 1.0) } let counter = pack_counter int_impl let counter' = pack_counter float_impl (* An expression using an abstract counter *) let expr = { bind_counter = fun counter > (* counter is bound to the << interface >> *) (counter.get (counter.inc counter.create)) } let result = with_packed_counter counter expr let result' = with_packed_counter counter' expr (* This doesn't type, the counter type is abstract ! let expr = { bind_counter = fun counter > (counter.get (counter.inc (counter.get counter.create))) } *) (* This doesn't type, the abstract type tries to escape its scope ! let expr = { bind_counter = fun counter > (counter.create) } *)  Lists of composable functions. module Funlist : sig (* The funlist datatype *) type ('a, 'b) t (* Constructors *) val nil : ('a, 'a) t val cons : ('a > 'b) > ('b, 'c) t > ('a, 'c) t (* Applying a value to a composition *) val apply : ('a, 'b) t > 'a > 'b end = struct (* The type expressed by the four types below is : type ('a, 'b) t = Nil of ('a > 'b)  Cons of exists 'c. ('a > 'c) * ('c, 'b) t *) type ('a, 'b) t = Nil of ('a > 'b)  Cons of ('a, 'b) packed_list and ('a, 'b, 'c) list_data = ('a > 'c) * ('c, 'b) t and ('a, 'b, 'z) list_scope = { bind_list : 'c. ('a, 'b, 'c) list_data > 'z} and ('a, 'b) packed_list = { open_list : 'z. ('a, 'b, 'z) list_scope > 'z } (* Packing and unpacking lists *) let pack_list h t = { open_list = fun scope > scope.bind_list (h,t) } let with_packed_list p e = p.open_list e (* Constructors *) let nil = Nil(fun x > x) let cons h t = Cons(pack_list h t) (* The following type is introduced to avoid the problem of polymorphic recursion that comes while attempting a naive implementation of the apply funtion. The idea was taken from Laufer, Odersky, Polymorphic Type Inference and Abstract Data Types, 1994. *) (* The type expressed by the three types below is : type 'b packed_apply = exists 'a. ('a, 'b) t * 'a *) type ('a, 'b) apply_data = ('a, 'b) t * 'a type ('b, 'z) apply_scope = { bind_apply : 'a. ('a, 'b) apply_data > 'z} type 'b packed_apply = { open_apply : 'z. ('b, 'z) apply_scope > 'z} (* Packing and unpacking applications *) let pack_apply l x = { open_apply = fun scope > scope.bind_apply (l,x) } let with_packed_apply p e = p.open_apply e let rec apply' a = with_packed_apply a { bind_apply = function  Nil id, x > id x  Cons l, x > with_packed_list l { bind_list = function h,t > apply' (pack_apply t (h x))}} let apply l x = apply' (pack_apply l x) end (* Example of use *) let twice x = 2*x let double x = (x, x) let list = Funlist.cons twice (Funlist.cons (( = ) 4) (Funlist.cons double Funlist.nil)) let a, b = Funlist.apply list 2  To unsubscribe, mail camllistrequest@inria.fr Archives: http://caml.inria.fr Bug reports: http://caml.inria.fr/bin/camlbugs FAQ: http://caml.inria.fr/FAQ/ Beginner's list: http://groups.yahoo.com/group/ocaml_beginners