Subject: categories: Re: computation in CPS

From: Sjoerd CRANS <[email-masked]>
Date: Mon, 9 Nov 1998 16:31:58 -0500 (EST)

Philippe Gaucher <[email-masked]> asked:

> for a CPS, is there a way to compute 
> the source and target of a R({x}) using only compositions of elements 
> like R({y}) ?

Yes and no.

Yes in the sense that because the source and the target are pasting
schemes themselves, Johnson's pasting theorem gives that 1. they
are compositions of R({y})'s and 2. *any* way you do this gives the
same result.
No in two senses: although Johnson's proof actually gives an algorithm,
I don't think this algorithm has ever been implemented (in AXIOM for
example); and secondly, there is (as far as I know) no *general*
expression which works for cubes of all dimensions.

Sjoerd Crans