V. Gaspes and J. M. Smith. Machine checked normalization proofs for typed combinator calculi. In Proceedings of the 1992 Workshop on Types for Proofs and Programs, June 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....case of typed combinatory logic) This proof is also expressed as a model construction, but is standard in the sense that it defines a reducibility predicate a la Tait. Another proof of normalization for typed combinators (also using Tait reducibility) was implemented in ALF by Gaspes and Smith [13], but the relationship between this proof and our extracted algorithm seems somewhat less direct. We shall here show that we can optimize this proof too and again extract nf When formalizing an informal proof one always has to make explicit certain choices which were left implicit. Here we have ....

V. Gaspes and J. M. Smith. Machine checked normalization proofs for typed combinator calculi. In Proceedings of the 1992 Workshop on Types for Proofs and Programs, June 1992.

....at all. This means that the correctness of a de nition is the user s responsibility. Among the examples developed in ALF, we can mention a proof that Ackermann s function is not primitive recursive [38] functional completeness of combinatorial logic [16] Tait s normalization proof for G#del s T [17], the fundamental theorem of arithmetic [40] a constructive version of Ramsey s theorem [15] and a semantical analysis of simply typed lambda calculus with explicit substitution [7] ....

Veronica Gaspes and Jan M. Smith. Machine Checked Normalization Proofs for Typed Combinator Calculi. In Proceeding from the logical framework workshop at B#stad, June 1992.

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