Reduction Operators and Completion of Rewriting Systems

Cyrille Chenavier 1, 2
2 PI.R2 - Design, study and implementation of languages for proofs and programs
PPS - Preuves, Programmes et Systèmes, UPD7 - Université Paris Diderot - Paris 7, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We propose a functional description of rewriting systems where reduction rules are represented by linear maps called reduction operators. We show that reduction operators admit a lattice structure. Using this structure we define the notions of confluence and of Church-Rosser property. We show that these notions are equivalent. We give an algebraic formulation of completion and show that such a completion exists using the lattice structure. We interpret the confluence for reduction operators in terms of Gröbner bases. Finally, we introduce generalised reduction operators relative to non totally ordered sets.
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  • HAL Id : hal-01325907, version 2
  • ARXIV : 1605.00174

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Cyrille Chenavier. Reduction Operators and Completion of Rewriting Systems. Journal of Symbolic Computation, Elsevier, In press. ⟨hal-01325907v2⟩

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