From mboxrd@z Thu Jan 1 00:00:00 1970 Received: (from majordomo@localhost) by pauillac.inria.fr (8.7.6/8.7.3) id LAA06171; Fri, 27 Aug 2004 11:03:37 +0200 (MET DST) X-Authentication-Warning: pauillac.inria.fr: majordomo set sender to owner-caml-list@pauillac.inria.fr using -f Received: from concorde.inria.fr (concorde.inria.fr [192.93.2.39]) by pauillac.inria.fr (8.7.6/8.7.3) with ESMTP id LAA04244 for ; Fri, 27 Aug 2004 11:03:36 +0200 (MET DST) Received: from kurims.kurims.kyoto-u.ac.jp (kurims.kurims.kyoto-u.ac.jp [130.54.16.1]) by concorde.inria.fr (8.13.0/8.13.0) with ESMTP id i7R93YIO019491 for ; Fri, 27 Aug 2004 11:03:35 +0200 Received: from localhost (suiren.kurims.kyoto-u.ac.jp [130.54.16.25]) by kurims.kurims.kyoto-u.ac.jp (8.9.3p2-20030924/3.7W) with ESMTP id SAA11077; Fri, 27 Aug 2004 18:03:28 +0900 (JST) Date: Fri, 27 Aug 2004 18:03:28 +0900 (JST) Message-Id: <20040827.180328.128873320.garrigue@kurims.kyoto-u.ac.jp> To: jon@jdh30.plus.com Cc: caml-list@inria.fr Subject: Re: [Caml-list] Phantom types From: Jacques GARRIGUE In-Reply-To: <200408231616.58139.jon@jdh30.plus.com> References: <20040731163143.GB15775@fichte.ai.univie.ac.at> <200408231049.59342.jon@jdh30.plus.com> <200408231616.58139.jon@jdh30.plus.com> X-Mailer: Mew version 4.0.64 on Emacs 21.2 / Mule 5.0 (SAKAKI) Mime-Version: 1.0 Content-Type: Text/Plain; charset=us-ascii Content-Transfer-Encoding: 7bit X-Miltered: at concorde with ID 412EF8E6.000 by Joe's j-chkmail (http://j-chkmail.ensmp.fr)! X-Loop: caml-list@inria.fr X-Spam: no; 0.00; caml-list:01 jacques:01 val:01 val:01 abstr:01 abstr:01 superset:01 variance:01 covariance:01 jacques:01 phantom:01 garrigue:01 garrigue:01 polymorphic:01 subset:03 Sender: owner-caml-list@pauillac.inria.fr Precedence: bulk From: Jon Harrop > I should add, using: > > val add_even_even : [> `Even ] t -> [> `Even ] t -> [> `Even ] t > val add_even_odd : [> `Even ] t -> [> `Odd ] t -> [> `Odd ] t > > allows: > > # PhantomInt.add_even_odd i j;; > val k : _[> `Odd ] PhantomInt.t = This part is OK. > which can then be misused: > > # PhantomInt.add_even_even i k;; > - : [ `Even ] PhantomInt.t = But this one is wrong. > I think this is because [> `Even] means any superset of [ `Even ] whereas [< > `Even], which was probably intended, means any subset of [ `Even ]. Indeed, > the latter appears to work. Indeed, one must be careful about variance. So the right signature would be: type +'a t type any = [`Even|`Odd] val add_even_even : [ `Even ] t -> [ `Even ] t -> [> `Even ] t val add_even_odd : [ `Even ] t -> [ `Odd ] t -> [> `Odd ] t val add_unknown_unknown : any t -> any t -> any t (Note the + indicating covariance) Then you have # let k = PhantomInt.add_even_odd i j;; val k : [> `Odd ] PhantomInt.t = (polymorphic result!) # PhantomInt.add_even_even i k;; ** type error # PhantomInt.add_unknown_unknown i k;; - : any t = Jacques Garrigue ------------------- To unsubscribe, mail caml-list-request@inria.fr Archives: http://caml.inria.fr Bug reports: http://caml.inria.fr/bin/caml-bugs FAQ: http://caml.inria.fr/FAQ/ Beginner's list: http://groups.yahoo.com/group/ocaml_beginners