A Direct Proof of Strong Normalization for an Extended Herbelin?s Calculus
نویسنده
چکیده
Herbelin presented (at CSL’94) an explicit substitution calculus with a sequent calculus as a type system, in which reduction steps correspond to cut-elimination steps. The calculus, extended with some rules for substitution propagation, simulates β-reduction of ordinary λcalculus. In this paper we present a proof of strong normalization for the typable terms of the calculus. The proof is a direct one in the sense that it does not depend on the result of strong normalization for the simply typed λ-calculus, unlike an earlier proof by Dyckhoff and Urban.
منابع مشابه
Strong Normalization of Herbelin's Explicit Substitution Calculus with Substitution Propagation
Herbelin presented (at CSL'94) a simple sequent calculus for minimal implicational logic, extensible to full rst-order intuitionistic logic, with a complete system of cut-reduction rules which is both con uent and strongly normalising. Some of the cut rules may be regarded as rules to construct explicit substitutions. He observed that the addition of a cut permutation rule, for propagation of s...
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