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[Axiom-developer] [#187 trouble with tuples] functions are objects of ty

From: Bill Page
Subject: [Axiom-developer] [#187 trouble with tuples] functions are objects of type Mapping
Date: Sun, 03 Jul 2005 22:48:32 -0500

Bill Page wrote:

> I think such tuples should be Products ... 

>From page 246 of the Axiom book:

"The type of a function is always a mapping of the form
 Source -> Target where Source and Target are types."

and from page 1085:

"Domains Mapping, Record, and Union are primitive domains. All
other domains are written in the Axiom programming language ..."

)show Mapping

>From a mathematical point of view clearly the idea that
Mapping(T, A, B) denotes the class of mappings from (A, B)
into T implies that (A,B) denotes some kind of set, i.e.
the Product(A,B).

William Sit wrote:

> I don't agree. When one wraps up something into a single object,
> it is inconvenient to look at the parts without unwrapping.

But [Cartesian Product] is implemented as a Record and the
domain Record is a primative in Axiom. So my proposal above
amounts to stating, for example, that:

should be viewed as equivalent to

And in fact after a simple optimization, the compiler should
be able to produce equivalent internal lisp code.
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