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Présentations d'opérades et systèmes de réécriture
Thèses et HDR   Open Access

Présentations d'opérades et systèmes de réécriture

Yves Guiraud
Doctoral, Université de Montpellier
28/06/2004

Résumé

word rewriting explicit substitutions lambda-calculus explicit resource management term rewriting Petri nets universal algebra rewriting Operad presentations Penrose diagrams substitutions explicites lambda-calcul gestion explicite des ressources réécriture de termes réseaux de Petri réécriture de mots algèbre universelle diagrammes de Penrose réécriture Présentations d'opérades
This thesis studies the computational properties of operad presentations, or Penrose diagrams rewrite systems, together with their links with classical types of rewrite systems. With new criteria for termination and confluence, the convergence of the presentation L(Z2) of Z/2Z-vector spaces, a commutative equational theory, is proved. Operad presentations are shown to be generalizations of both word rewrite systems and Petri nets; furthermore, they provide explicit resource management calculi for left-linear term rewrite systems. This work is concluded by the description of obstructions for proving the same result for the lambda-calculus. Two appendices present the links between operads and other structures from universal algebra, together with a calculus of explicit substitutions.

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