Re: type recursifs et abreviations cyclique and Co

Jason Hickey
 Xavier Leroy
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Date:   (:) 
From:  Xavier Leroy <Xavier.Leroy@i...> 
Subject:  Re: recursive types 
Here is the straight dope (or my view of it, anyway) about recursive types, or more precisely, the fact that all recursive type expressions are no longer allowed in OCaml 1.06: 1 It is true that recursive (infinite) type expressions such as 'a where 'a = 'a list (standing for the infinite type ... list list list list can be added to the ML type system without causing major theoretical difficulties. In particular, unification and type inference work just as well on recursive types (infinite terms) than on regular types (finite terms). 2 "Classic" ML does not have recursive types, just finite terms as type expressions. Except some versions of Objective Caml, you won't find any implementation of ML that accepts them. 3 The reason Objective Caml supports recursive types is that they are absolutely needed by the object stuff. More precisely, recursive types naturally arise when doing type inference for objects (without prior declarations of object types). Hence, Objective Caml performs type inference using full recursive types (cyclic terms) internally. 4 Still (and now comes the language design issue), one may decide to impose extra restrictions on type expressions, such as "all cycles in a type must go through an object type", thus prohibiting recursive types that don't involve object types, such as ... list list list above. In OCaml, we have experimented with several such restrictions. I think early releases (up to 1.04) had restrictions, though I don't remember which; 1.05 had no restrictions at all, and was strongly criticized for that (see below); 1.06 has the "all cycles must go through an object type" restriction. 5 The main problem with unrestricted recursive types is that they allow type inference to give nonsensical types to clearly wrong code, instead of issuing a type error immediately. For instance, consider the function let f x y = if ... then x @ y else x Assume I make a typo and type "@" instead of "::" : let f x y = if ... then x :: y else x Any sane ML implementation reports a type error. But OCaml 1.05 (the one with unrestricted types) would accept the definition above, and infer the deeply obscure type: val f : ('a list as 'a) > ('b list as 'b) list > ('c list as 'c) Calls to the function f will probably be illtyped, so the error will eventually be caught, but possibly very far from the actual error (the definition of f). Some users of OCaml 1.05 loudly complained that unrestricted recursive types make the language much harder to use for beginners and intermediate programmers. We agreed that they had a strong point here. You don't want types such as the above for f. Really. Trust me. So we and decided to go back to recursive types restricted to objects only  the reasoning being that this does not reject any "classic" ML code (which typechecks without recursive types already), but still lets the right types for objects being inferred. 6 Of course, we forgot that users would exploit the "unrestricted recursive types" bug of OCaml 1.05, and come back at us claiming it's a useful feature. So, let's see how useful are recursive types that are not objects. I'm taking Jason Hickey's examples here. > type x = x option > the type "x" should probably be isomorphic to the natural numbers Such a type can be written more clearly as type x = Z  S of x (or even better type x = int, but that's a different story). > Consider an unlabeled abstract binary tree: > > type 'a t = ('a option) * ('a option) (* abstract *) > ... > type node = X of node t Again, I don't see the point of the 'a t type. A much clearer way to describe unlabeled binary trees is: type node = Empty  Node of node * node Notice: no extra boxing here. The point I'm trying to make here is that pretty much all the time, recursive types can be avoided ad clarity of the code can be improved by using the right concrete types (sums or records) to hide the recursion, rather than using generic sum or product types such as "option" and "*", then obtain the desired recursive structure by using recursive type expressions. I know of only one or two cool examples where recursive type expressions come in handy and avoid code duplication that the regular ML type system forces you to do otherwise. Now, in reply to Jason Hickey's points: > 1. The interpretation of the general recursive type has a > welldefined type theoretic meaning. Yes, but this doesn't imply it's a desirable feature in a programming language. > Why not issue a warning rather than forbidding the construction? That's one option, though issuing meaningful warnings is probably harder than just rejecting the program. Another option we discussed is a commandline flag that changes the behavior of the typechecker w.r.t. recursive types. > For instance, the following code is > not forbidden: > let flag = (match List.length [] with 0 > true) > even though constructions of this form are "prone to error," > and generate warning messages. Right. Some of us think all warnings should be errors, though. In this particular case, upward compatibility with the "classic ML" way leads to accepting the program and just issue a warning. For recursive types, the same argument argues in favor of rejecting the program. > 2. The policy imposes a needless efficiency penalty on type > abstraction. Only if you don't hide the recursion inside the abstraction, and insist on taking fixpoints outside the abstraction. As I've shown before, the penalty can almost always be avoided by writing your concrete types in a "natural" style. Anyway (warningsilly joke ahead), since when type theorists are worried about efficiency? (end of silly joke). > 3. If the type system can be bypassed with an extraneous boxing, > type x = x t > type x = X of x t > then what is the point? The programmers write the "X" constructor explicitely in the program, thus making their intentions clear. It's completely different from an inferred recursive type, which is more often than not an unintended consequence of a coding error. > 4. (Joke) All significant programs are "prone to error." Perhaps the > OCaml compiler should forbid them all! This is an old Usenetstyle argument. Another (joke) conclusion is that for the same reasons, we should turn off all typechecking and error checking in the compiler. > I use this construction extensively in Nuprl (theorem proving) > and Ensemble (communications) applications; do I really need > to change my code? We should have released 1.06 earlier; this would have left you less time to exploit 1.05's bugs so thoroughly... At any rate, I'd certainly encourage you to think about the data structures you use, and whether you couldn't rewrite them in a clearer way by getting rid of recursive types and using Caml's concrete datatypes (sums and records) instead. Of course, if you come up with convincing reallife examples (not just typetheoretic examples) of why recursive types are useful, we'll reconsider.  Xavier Leroy