From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8281 Path: news.gmane.org!not-for-mail From: "Vasili I. Galchin" Newsgroups: gmane.science.mathematics.categories Subject: Functional programming and William Lawvere's notion of "variable sets"(vs topos of "static sets") in a Topos ... Date: Mon, 4 Aug 2014 02:03:43 -0500 Message-ID: Reply-To: "Vasili I. Galchin" NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8 X-Trace: ger.gmane.org 1407156998 6617 80.91.229.3 (4 Aug 2014 12:56:38 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Mon, 4 Aug 2014 12:56:38 +0000 (UTC) To: Categories mailing list Original-X-From: majordomo@mlist.mta.ca Mon Aug 04 14:56:32 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1XEHoP-0006uJ-Uf for gsmc-categories@m.gmane.org; Mon, 04 Aug 2014 14:56:26 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:50097) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1XEHo0-0008SO-Kv; Mon, 04 Aug 2014 09:56:00 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1XEHnz-000318-Ds for categories-list@mlist.mta.ca; Mon, 04 Aug 2014 09:55:59 -0300 Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8281 Archived-At: Dear Cat People ... I have been re-reading William Lawvere's description of "variable sets" (a functor category) in "a elementary topoi" on a discrete poset/preset vs a "abstract sets" in the topos of abstract sets . In Haskell( and other FPLs .. ) aren't "pure" computations just over the topos of abstract sets and "mutable" /"time-varying/stateful" computations aren't just "variable sets" (i.e. a functor over a discrete preset-poset)?? Please forgive my germ of an idea Kind regards, Vasya P.S. Yes I am familiar with Eugenio Moggi's papers on using monads for stateful computations .. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]