From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/6667 Path: news.gmane.org!not-for-mail From: Philip Scott Newsgroups: gmane.science.mathematics.categories Subject: Re: the Church-Howard Correspondence Date: Thu, 5 May 2011 14:47:53 +0100 Message-ID: References: Reply-To: Philip Scott NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 (Apple Message framework v1084) Content-Type: text/plain; charset=us-ascii Content-Transfer-Encoding: quoted-printable X-Trace: dough.gmane.org 1304685296 29867 80.91.229.12 (6 May 2011 12:34:56 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Fri, 6 May 2011 12:34:56 +0000 (UTC) Cc: Categories mailing list To: "Vasili I. Galchin" Original-X-From: majordomo@mlist.mta.ca Fri May 06 14:34:52 2011 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtpx.mta.ca ([138.73.1.4]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1QIKFA-00086g-2L for gsmc-categories@m.gmane.org; Fri, 06 May 2011 14:34:52 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:42870) by smtpx.mta.ca with esmtp (Exim 4.71) (envelope-from ) id 1QIKA2-0000l7-HC; Fri, 06 May 2011 09:29:34 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1QIK9z-0004vr-WE for categories-list@mlist.mta.ca; Fri, 06 May 2011 09:29:32 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:6667 Archived-At: Dear Vasili: The author doesn't refer to, nor even seem to know about, = my book with J. Lambek, Introduction to Higher-Order Categorical Logic, J. Lambek and P. J. = Scott,=20 Cambridge Univ. Press, 1986, where all this was done in great detail.=20= In fact, the three way correspondence between categories of deductive = systems, of cartesian closed categories, and of typed lambda calculi (which the = author wishes to explain) was first done there, with many applications. Best, Phil Scott On 2011-05-04, at 4:27 PM, Vasili I. Galchin wrote: > After thinking about my English, please let me add to my previous = posting. I > believe the author of the paper is proving an equivalence of an = informal > notion (Curry-Howard "Isomorphism) with a formal mathematical notion = (the > equivalence of categories). >=20 > Regards, >=20 > Vasili >=20 > On Tue, May 3, 2011 at 4:18 PM, Vasili I. Galchin = wrote: >> Hello, >>=20 >> I started reading a paper >> www.math.uchicago.edu/~may/VIGRE/VIGRE2010/REUPapers/Berger.pdf >> entitled "A Categorical Approach to Proofs-As-Programs" by Carson >> Berger. He seems to be giving a formal equivalence of the various >> sides of this famous Correspondence using equivalence of categories. >> Have any members of this forum read this paper and if so, what >> significance do you give this paper? >>=20 >> Thank you, >>=20 >> Vasili >>=20 >=20 >=20 > [For admin and other information see: http://www.mta.ca/~cat-dist/ ] [For admin and other information see: http://www.mta.ca/~cat-dist/ ]