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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion(More)
We show how to prove (and disprove) theorems in the initial algebra of an equational variety by a simple extension of the Knuth-Bendix completion algorithm. This allows us to prove by purely equational reasoning theorems whose proof usually requires induction. We show applications of this method to proofs of programs computing over data structures, and to(More)
We propose a program transformation method based on rewriting-rules composed of second-order schemas. A complete second-order matching algorithm is presented that allows effective use of these rules. We show how to formally prove the correctness of the rules using a denotational semantics for the programming language. We establish the correctness of the(More)
A refutational system of logic for a language of order w ia presented. This langage is a slight modification of Church's \-calculus with types. The system is complete, in the sense that a refutation of a set of sentences exists if and only if this set does not possess a general Henkin model. The main rule of inference is a generalization of Robinson's(More)
We present the complete development, in Gallina, of the residual theory of β-reduction in pure λ-calculus. The main result is the Prism Theorem, and its corollary Lévy's Cube Lemma, a strong form of the parallel-moves lemma, itself a key step towards the confluence theorem and its usual corollaries (Church-Rosser, uniqueness of normal forms). Gallina is the(More)
This paper gives new results, and presents old ones m a umfied formahsm, concerning Church-Rosser theorems for rewrmng systems Abstract confluence propentes, depending solely on axioms for a binary relatton called reduction, are first presented Results of Newman and others are presented m a unified formahsm The systemattc use of a powerful mductmn pnnciple(More)