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From: Hendrik Tews <tews@tcs.inf.tu-dresden.de>
To: categories@mta.ca
Subject: Re: topos logic arising nicely
Date: Fri, 6 Jun 2003 11:29:15 +0200	[thread overview]
Message-ID: <16096.24299.686053.329698@ithif51.inf.tu-dresden.de> (raw)
In-Reply-To: <200306051108.NAA00738@fb04209.mathematik.tu-darmstadt.de>

Hi,

Thomas Streicher writes:
   Date: Thu, 5 Jun 2003 13:08:14 +0200 (CEST)
   Subject: categories: Re: topos logic arising nicely

   But I would be surprised if HOL has subtype formation as from a logical
   point of view subtypes are neither necessary nor convenient. Adding subtypes
   is only necessary for getting a topos out of a model of HOL.

I don't know, if I miss the point here. However, PVS has a HOL
system with predicate subtypes. And it is _very very_ convenient
(because of the predicate subtypes).

I don't know if it is a necessity, but the absence of subtypes in
Isabelle/HOL leads to a representation of partial functions, that
allows you to prove unexpected results. Despite what the Isabelle
tutorial says at page 187, you _can_ prove

  hd [] = last []

(saying that the head of the empy list equals its last element)


Bye,

Hendrik





  reply	other threads:[~2003-06-06  9:29 UTC|newest]

Thread overview: 9+ messages / expand[flat|nested]  mbox.gz  Atom feed  top
2003-06-05 11:08 Thomas Streicher
2003-06-06  9:29 ` Hendrik Tews [this message]
2003-06-08 11:39   ` Thomas Streicher
  -- strict thread matches above, loose matches on Subject: below --
2003-06-09 20:03 Thomas Streicher
2003-06-05 19:46 Thomas Streicher
2003-06-09  9:18 ` Paul B Levy
2003-06-03 20:14 Thomas Streicher
2003-06-04 15:20 ` Toby Bartels
2003-06-04 15:42 ` Paul B Levy

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