Abstract
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 λ-calculus. 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.
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Kikuchi, K. (2004). A Direct Proof of Strong Normalization for an Extended Herbelin’s Calculus. In: Kameyama, Y., Stuckey, P.J. (eds) Functional and Logic Programming. FLOPS 2004. Lecture Notes in Computer Science, vol 2998. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24754-8_18
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DOI: https://doi.org/10.1007/978-3-540-24754-8_18
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