From: Vaughan Pratt <pratt@cs.stanford.edu>
To: categories@mta.ca
Subject: Re: CATS Categorical model for Floyd-Hoare logic?
Date: Sat, 14 Feb 1998 20:41:25 +0000 [thread overview]
Message-ID: <199802142041.MAA21284@coraki.Stanford.EDU> (raw)
In-Reply-To: Your message of "Fri, 13 Feb 1998 17:40:06 -0800." <199802140140.RAA11783@blackhawk.kestrel.edu>
>Has there been work on a categorical model for "while programs" (or,
>equivalently, assembly language) and Floyd-Hoare logic?
The first such was developed by Arbib and Manes in the mid-70's. Manes
went on to develop the theory in great detail, writing a near-book-length
article on it a decade later, not sure where it appeared.
(1) What is the structure of this category?
As I recall it was an additive (semiadditive?) category, with sequential
composition represent by composition, and choice by sum within homsets.
The objects were predicates, the arrows were programs (aka predicate
transformers).
Does it have products, sums, etc? What program constructs do they
correspond to?
Not sure about products, but it certainly had sums. which was how
if-then-else was handled.
(2) What is the correct equality on arrows?
My recollection is that it was fully abstract: the correct equality is
equality.
Vaughan Pratt
prev parent reply other threads:[~1998-02-14 20:41 UTC|newest]
Thread overview: 2+ messages / expand[flat|nested] mbox.gz Atom feed top
1998-02-14 1:40 David Espinosa
1998-02-14 20:41 ` Vaughan Pratt [this message]
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