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Characterising Explicit Substitutions which Preserve Termination (Extended Abstract)
 In Typed Lambda Calculi and Applications
, 1999
"... Contrary to all expectations, the lambdasigmacalculus, the canonical simplytyped lambdacalculus with explicit substitutions, is not strongly normalising. This result has led to a proliferation of calculi with explicit substitutions. This paper shows that the reducibility method provides a genera ..."
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Contrary to all expectations, the lambdasigmacalculus, the canonical simplytyped lambdacalculus with explicit substitutions, is not strongly normalising. This result has led to a proliferation of calculi with explicit substitutions. This paper shows that the reducibility method provides a general criterion when a calculus of explicit substitution is strongly normalising for all untyped lambdaterms that are strongly normalising. This result is general enough to imply preservation of strong normalisation of the calculi considered in the literature. We also propose a version of the lambdasigmacalculus with explicit substitutions which is strongly normalising for strongly normalising lambdaterms.
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.