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Edit detail for SandboxTypeDefinitions revision 3 of 15

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Editor: Bill Page
Time: 2008/07/08 06:53:30 GMT-7
Note: Each value belongs to ... its domain

added:

From BillPage Tue Jul 8 06:53:30 -0700 2008
From: Bill Page
Date: Tue, 08 Jul 2008 06:53:30 -0700
Subject: Each value belongs to ... its domain
Message-ID: <20080708065330-0700@axiom-wiki.newsynthesis.org>

In

 - http://www.csd.uwo.ca/~watt/pub/reprints/2003-cahand-aldor.pdf

*Stephen Watt wrote:* --
Each value belongs to some unique type, known as its domain, and the
domains of expressions can be inferred statically. Each domain is
itself a value belonging to the domain Type. Domains may additionally
belong to some number of subtypes (of Type), known as categories.



There seems to be different understandings of Type, domain, category, Category, etc. around. Here is an attempt to collect all these different opinions in order to make discussion about them clearer.

Definitions of Ralf Hemmecke

A category is an L-type whose type is the language-defined constant Category.

A domain is an L-type whose type is a category.

An L-type is either a category, a domain or the language-defined constants Category and Type.

Any L-type is of type Type.

I wrote L-type to mean type in the language, either Aldor or SPAD.

Each value belongs to ... its domain --Bill Page, Tue, 08 Jul 2008 06:53:30 -0700 reply
In

Stephen Watt wrote:
Each value belongs to some unique type, known as its domain, and the domains of expressions can be inferred statically. Each domain is itself a value belonging to the domain Type. Domains may additionally belong to some number of subtypes (of Type), known as categories.