Rapport de recherche n° 2000-05

Auteur : Christian Lair & Dominique Duval

First part: Compositive Graphs

Nbre de pages : 55

Documents : Article (PDF)

Abstract: SKETCHES AND SPECIFICATIONS is a common denomination for several papers which deal with applications of Ehresmann's sketch theory to computer science. These papers can be considered as the first steps towards a unified theory for software engineering. However, their aim is not to advocate a unification of computer languages; they are designed to build a frame for the study of notions which arise from several areas in computer science.

These papers are arranged in two complementary families:


The reference manual provides general definitions and results, with comprehensive proofs. On the other hand, the user's guide places emphasis on motivations and gives a detailed description of several examples. These two families, though complementary, can be read independently. No prerequisite is assumed; however, it can prove helpful to be familiar either with specification techniques in computer science or with category theory in mathematics.

These papers are under development, they are, or will be, available at: http://www.unilim.fr/laco/rapports.

In addition, further papers about APPLICATIONS are in progress, with several co-authors. They deal with various topics, including the notion of state in computer science, overloading, coercions and subsorts.

These articles owe a great deal to the working group sketches and computer algebra; we would like to thank its participants, specially Catherine Oriat and Jean-Claude Reynaud, as well as the CNRS.

These papers have been processed with LATEX and XY-pic.  

First Part: Compositive Graphs

This paper is the first part of this reference manual. The aim of this first part is to introduce the compositive graphs, which will be used in order to define the projective sketches. This paper includes a detailed study of various tensor products and enrichments of compositive graphs and the description of the category freely generated by a given compositive graph. No prerequisite is assumed to read it.


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