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Unification via Explicit Substitutions: The Case of HigherOrder Patterns
 PROCEEDINGS OF JICSLP'96
, 1998
"... In [6] we have proposed a general higherorder unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higherorder patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient ..."
Abstract

Cited by 56 (14 self)
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In [6] we have proposed a general higherorder unification method using a theory of explicit substitutions and we have proved its completeness. In this paper, we investigate the case of higherorder patterns as introduced by Miller. We show that our general algorithm specializes in a very convenient way to patterns. We also sketch an efficient implementation of the abstract algorithm and its generalization to constraint simplification, which has yielded good experimental results at the core of a higherorder constraint logic programming language.
λν, a Calculus of Explicit Substitutions which Preserves Strong Normalisation
, 1995
"... Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and Lévy to internalise substitutions into λcalculus and to propose a mechanism for computing on substitutions. λν is another view of the same concept which aims to explain the process of substitution and to de ..."
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Explicit substitutions were proposed by Abadi, Cardelli, Curien, Hardin and Lévy to internalise substitutions into λcalculus and to propose a mechanism for computing on substitutions. λν is another view of the same concept which aims to explain the process of substitution and to decompose it in small steps. λν is simple and preserves strong normalisation. Apparently that important property cannot stay with another important one, namely confluence on open terms. The spirit of λν is closely related to another calculus of explicit substitutions proposed by de Bruijn and called Cλξφ. In this paper, we introduce λν, we present Cλξφ in the same framework as λν and we compare both calculi. Moreover, we prove properties of λν; namely λν correctly implements β reduction, λν is confluent on closed terms, i.e., on terms of classical λcalculus and on all terms that are derived from those terms, and finally λν preserves strong normalization of βreduction.
On Strong Normalisation of Explicit Substitution Calculi
, 1999
"... In this paper, we present an attempt to build a calculus of explicit substitution expected to be conuent on open terms, to preserve strong normalisation and to simulate one step reduction. We show why our attempt failed and we explain how we found a counterexample to the strong normalisation or ..."
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In this paper, we present an attempt to build a calculus of explicit substitution expected to be conuent on open terms, to preserve strong normalisation and to simulate one step reduction. We show why our attempt failed and we explain how we found a counterexample to the strong normalisation or termination of the substitution calculus. As a consequence, we provide also a counterexample to the strong normalisation of another calculus, namely (the substitution calculus of ) of Ris, for which the problem was open.