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SUO: 13 Jun 2002 -- Categories & Lattices




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CL = Cathy Legg

CL: Could you explain what you mean by 'parametric'
    and also what you mean by 'morphism'?  (I went
    and read the SUO message of 11 May which you
    suggested as background re 'morphism' but
    I could not understand that either).

CL: I don't suppose it would be possible to construct a toy example,
    an ontological fragment, and use it to demonstrate how these
    formal concepts operate in practice?

Cathy,

You may find the selections below, outlining the application of
category theory to programming language semantics, of some use.
Basic material on posets and lattices is also given in this book,
but their full application to so-called "order semantics" is not.

Jon Awbrey

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Program Semantics

Preface

01.  http://suo.ieee.org/ontology/msg03884.html

1.  An Introduction to Denotational Semantics

1.1.  Syntax and Semantics

02.  http://suo.ieee.org/ontology/msg03885.html
03.  http://suo.ieee.org/ontology/msg03886.html
04.  http://suo.ieee.org/ontology/msg03887.html

1.2.  A Simple Fragment of Pascal

05.  http://suo.ieee.org/ontology/msg03890.html
06.  http://suo.ieee.org/ontology/msg03895.html
07.  http://suo.ieee.org/ontology/msg03896.html
08.  http://suo.ieee.org/ontology/msg03898.html
09.  http://suo.ieee.org/ontology/msg03904.html
10.  http://suo.ieee.org/ontology/msg03905.html

1.3.  A Functional Programming Fragment

11.  http://suo.ieee.org/ontology/msg03906.html
12.  http://suo.ieee.org/ontology/msg03909.html
13.  http://suo.ieee.org/ontology/msg03910.html
14.  http://suo.ieee.org/ontology/msg03911.html
15.  http://suo.ieee.org/ontology/msg03912.html
16.  http://suo.ieee.org/ontology/msg03915.html
17.  http://suo.ieee.org/ontology/msg03919.html

1.4.  Multifunctions

18.  http://suo.ieee.org/ontology/msg03926.html
19.  http://suo.ieee.org/ontology/msg03927.html
20.  http://suo.ieee.org/ontology/msg03929.html

1.5.  A Preview of Partially Additive Semantics

21.  http://suo.ieee.org/ontology/msg03930.html
22.  http://suo.ieee.org/ontology/msg03932.html
23.  http://suo.ieee.org/ontology/msg03933.html
24.  http://suo.ieee.org/ontology/msg03934.html
25.  http://suo.ieee.org/ontology/msg03935.html
26.  http://suo.ieee.org/ontology/msg03938.html
27.  http://suo.ieee.org/ontology/msg03939.html
28.  http://suo.ieee.org/ontology/msg03942.html
29.  http://suo.ieee.org/ontology/msg03944.html
30.  http://suo.ieee.org/ontology/msg03945.html

2.  An Introduction to Category Theory

31.  http://suo.ieee.org/ontology/msg03946.html

2.1.  The Definition of a Category

32.  http://suo.ieee.org/ontology/msg03947.html
33.  http://suo.ieee.org/ontology/msg03949.html
34.  http://suo.ieee.org/ontology/msg03950.html
35.  http://suo.ieee.org/ontology/msg03953.html
36.  http://suo.ieee.org/ontology/msg03954.html

2.2.  Isomorphism, Duality, and Zero Objects

37.  http://suo.ieee.org/ontology/msg03955.html
38.  http://suo.ieee.org/ontology/msg03956.html
39.  http://suo.ieee.org/ontology/msg03958.html
40.  http://suo.ieee.org/ontology/msg03960.html
41.  http://suo.ieee.org/ontology/msg03963.html
42.  http://suo.ieee.org/ontology/msg03977.html
43.  http://suo.ieee.org/ontology/msg03979.html
44.  http://suo.ieee.org/ontology/msg04013.html

2.3.  Products and Coproducts

45.  http://suo.ieee.org/ontology/msg04014.html
46.  http://suo.ieee.org/ontology/msg04015.html
47.  http://suo.ieee.org/ontology/msg04018.html
48.  http://suo.ieee.org/ontology/msg04037.html

All of the above material is excerpted from:

| Ernest G. Manes & Michael A. Arbib,
|'Algebraic Approaches to Program Semantics',
| Springer-Verlag, New York, NY, 1986.

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