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From: | Ralf Hemmecke |
Subject: | Re: [Axiom-math] Type equivalence of domains in Axiom and Aldor |
Date: | Sat, 27 Oct 2007 22:53:42 +0200 |
User-agent: | Thunderbird 2.0.0.6 (X11/20070728) |
Def: Two domains P and Q are equivalent if and only if both domains satisfy exactly the same set of categories: (P has x) = (Q has x) for all Category expressions x *and* neither P nor Q has any explicit exports that are not provided by some named category.
Let's see... Cat: Category == with { coerce: Integer -> %; coerce: % -> Integer; bar: (%, %) -> %; } P: Cat == add { Rep == Integer; import from Rep coerce(x: Integer): % == per x; coerce(x: %): Integer == rep x; bar(x: %, y: %): % == per(rep x + rep y); } ----------------------------------^ Q: Cat == add { Rep == Integer; import from Rep coerce(x: Integer): % == per x; coerce(x: %): Integer == rep x; bar(x: %, y: %): % == per(rep x - rep y); } ----------------------------------^ You are saying that P and Q are equivalent. Ralf
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