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[Axiom-developer] Re: FW: data structure vs. mathematical structure

From: Gabriel Dos Reis
Subject: [Axiom-developer] Re: FW: data structure vs. mathematical structure
Date: 15 Nov 2006 02:29:39 +0100

Ralf Hemmecke <address@hidden> writes:


| ++ A set over a domain D models the usual mathematical notion of a
| ++ finite set of elements from D.
| Although
| i: Integer
| and
| s: FinitePowerSet T
| would be in perfect analogy if one read ":" as "element of", then to
| go on "l: List T" would mean "List" is the container of all finite
| sequences (with some information about their representation (linked
| list)).

And that would match the usual definition of List as the least fixed
point of the functor

     X |-> 1 + X

in CPO.

However, the existence of 1.. in Axiom would suggest that actually
some people think of List as the greatest fixed point.

-- Gaby

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