Re: OCaml et l'évaluation paresseuse

From: Pierre Weis (
Date: Mon Oct 11 1999 - 00:27:52 MET DST

From: Pierre Weis <>
Message-Id: <>
Subject: Re: OCaml et l'évaluation paresseuse
To: (Pierre Weis)
Date: Mon, 11 Oct 1999 00:27:52 +0200 (MET DST)
In-Reply-To: <> from "Pierre Weis" at Oct 4, 99 00:53:12 am

I add a post-scriptum to my long message on lazy evaluation, to
describe what have been and could be some lazy support in Caml.

Along the lines of mutable annotations for fields of records, we add a
``lazy annotation'' for fields of records and arguments of
constructors. This is pretty easy to use since the lazy annotation
appears only once, in the type definition. In programs using this
``lazy type'', calls to ``force'' and ``delay'' are automatically
inserted by the compiler. Also the call by need semantics is done by
the compiler, hence no assignments are needed in users programs. Also,
mutable and lazy are mutually exclusive annotations.

Examples of lazy programs:
Definition of delay and force, as constructor Freeze and function unfreeze:

type 'a frozen = lazy Freeze of 'a;;

let unfreeze (Freeze x) = x;;

Definition of lazy streams:

type 'a stream = {lazy hd : 'a ; lazy tl : 'a stream};;

let rec map_stream f = function
  | {hd = x; tl = t} -> {hd = f x; tl = map_stream f t};;

Lazy recursive defintions:

let rec nat = {hd = 0; tl = map_stream succ nat};;

(* Erathostenes sieve and prime numbers *)
let rec sieve p =
 let rec sieve_rec = function
 | {hd = x;tl = t} ->
    if x mod p = 0 then sieve_rec t
    else {hd = x; tl = sieve_rec t} in

let rec primes = function
 {hd = x; tl = t} -> {hd = x; tl = primes (sieve x t)};;

let rec (Freeze nat_from_2) =
    Freeze {hd = 2; tl = map_stream succ nat_from_2};;
let Primes = primes nat_from_2;;

Formal series:

Our aim is to define the function \verb"sinus" and \verb"cosinus" as
the streams of the coefficients of their serial developments.

let sf_uminus = map_stream (fun x -> (-x));;

let integrate l =
    let rec intrec n {hd = x; tl = l} =
        {hd = (x/(n+1)); tl = (intrec (n+1) l)} in
    intrec 0 l;;

let rec cosinus = {hd = 1; tl = integrate (sf_uminus sinus)}
and sinus = {hd = 0; tl = integrate (cosinus)};;

Static semantics:

-- This has no influence on the result of typechecking, except that
argument of lazy constructors of lazy fileds can be polymorphically
typechecked (no ``non expansivity rule'' applies).


-- Allocation : when allocating records or applying constructors,
lazy fields or constructors arguments are delayed (if not syntactically
a value), encapsulating their argument expression e under a thunk: fun
() -> e.

-- Record access: when accessing a lazy field, the thunk is
automatically forced if necessary and the value obtained replaces the
thunk (call by need semantics).

-- Pattern matching: When pattern matching, the pattern matching
algorithm also force lazy thunks in lazy fields or lazy constructors
arguments (in case of a constructor argument the result also replaces
the original unevaluated thunk).

This has been implemented in an old version of Caml, and is much more
convenient to use (but more complex to implement) than the simple Lazy
module facility of the current version of Objective Caml.

Pierre Weis

INRIA, Projet Cristal,,

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