From mboxrd@z Thu Jan  1 00:00:00 1970
X-Spam-Checker-Version: SpamAssassin 3.4.4 (2020-01-24) on polar.synack.me
X-Spam-Level: 
X-Spam-Status: No, score=-1.9 required=5.0 tests=BAYES_00 autolearn=ham
	autolearn_force=no version=3.4.4
X-Google-Thread: a07f3367d7,39579ad87542da0e
X-Google-Attributes: gida07f3367d7,public,usenet
X-Google-NewGroupId: yes
X-Google-Language: ENGLISH,ASCII-7-bit
X-Received: by 10.180.11.232 with SMTP id t8mr726467wib.3.1369279638206;
        Wed, 22 May 2013 20:27:18 -0700 (PDT)
Path: 
 fw11ni1151wic.0!nntp.google.com!feeder1.cambriumusenet.nl!feed.tweaknews.nl!193.141.40.65.MISMATCH!npeer.de.kpn-eurorings.net!npeer-ng0.de.kpn-eurorings.net!border2.nntp.ams2.giganews.com!border4.nntp.ams.giganews.com!border2.nntp.ams.giganews.com!nntp.giganews.com!news.panservice.it!fu-berlin.de!uni-berlin.de!individual.net!not-for-mail
From: Niklas Holsti <niklas.holsti@tidorum.invalid>
Newsgroups: comp.lang.ada
Subject: Re: Seeking for papers about tagged types vs access to subprograms
Date: Fri, 17 May 2013 08:25:37 +0300
Organization: Tidorum Ltd
Message-ID: <avltafFbt13U1@mid.individual.net>
References: <op.wv8jh1c1ule2fv@cardamome> <kmh7d4$up3$1@loke.gir.dk>
 <1oy5rmprgawqs.1jz36okze0xju$.dlg@40tude.net> <kmk45u$v45$1@loke.gir.dk>
 <1q2ql1e4rcgko.diszzq1mhaq8$.dlg@40tude.net>
 <518dedd4$0$6581$9b4e6d93@newsspool3.arcor-online.net>
 <hxkln519n179.1kt13z7phxg2f.dlg@40tude.net> <kms7hs$8ur$1@loke.gir.dk>
 <1um7tijeo609b$.1gtdijp0acfmn$.dlg@40tude.net> <op.ww2nq7t6ule2fv@cardamome>
 <mk9m6fxa1jbr$.mm0kw7g3igma$.dlg@40tude.net>
 <alpine.DEB.2.02.1305150714300.2254@whirlwind>
 <1nkyb845dehcu.1sd90udwsrpdu.dlg@40tude.net>
 <alpine.DEB.2.02.1305151601340.7888@whirlwind>
 <1mg9eepp12ood$.14lj7s8a7eygd$.dlg@40tude.net>
 <alpine.DEB.2.02.1305160641330.2594@whirlwind>
 <1cj8b5amtua30.1foe0rdpldt2.dlg@40tude.net>
 <alpine.DEB.2.02.1305160829510.2501@whirlwind>
 <lnx0yaymncw7$.pqorucpcq8r3$.dlg@40tude.net>
 <5195144f$0$6558$9b4e6d93@newsspool4.arcor-online.net>
 <alpine.DEB.2.02.1305161404190.3294@whirlwind>
 <avl0tsF6g4nU1@mid.individual.net>
 <alpine.DEB.2.02.1305161850410.3928@whirlwind>
Mime-Version: 1.0
X-Trace: individual.net aNGKFigPsZNxj+5b1H6Mdg9din5LsZ7H//hvK+4KOaVg5bJt2f
Cancel-Lock: sha1:14w7EY7TRQjssiZ332rIr3wHisE=
User-Agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.6;
 rv:17.0) Gecko/20130328 Thunderbird/17.0.5
In-Reply-To: <alpine.DEB.2.02.1305161850410.3928@whirlwind>
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 7bit
Date: 2013-05-17T08:25:37+03:00
List-Id: <comp.lang.ada>

On 13-05-17 02:20 , Peter C. Chapin wrote:
> On Fri, 17 May 2013, Niklas Holsti wrote:
> 
>> A proof seems simple enough, assuming that the set of inputs is
>> infinite and enumerable: if you want to decide whether f1 and f2 are
>> equivalent, make a program P that iteratively generates (enumerates)
>> all possible inputs x; computes f1(x) and f2(x); and stops if f1(x) /=
>> f2(x). This program P halts if and only if f1 /= f2. Since halting is
>> undecidable, so therefore is function equality.
> 
> You've shown that the method of enumerating all possible argument values
> and testing f1(x) = f2(x) doesn't work.

Yes, my argument is wrong (the reduction should go the other way). I
tried to cancel my post, but too late.... sorry.

I should not try to write proofs of undecidability at one hour past
midnight.

-- 
Niklas Holsti
Tidorum Ltd
niklas holsti tidorum fi
      .      @       .