HOL-lambdasigma: An Intentional First-Order Expression of Higher-Order Logic

Authors:
Gilles Dowek;Thérèse Hardin;Claude Kirchner
Affiliations:
-;-;-
Venue:
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Year:
1999

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Abstract

We propose a first-order presentation of higher-order logic based on explicit substitutions. It is intentionally equivalent to the usual presentation of higher-order logic based on λ-calculus, i.e. a proposition can be proved without the extensionality axioms in one theory if and only if it can in the other. The Extended Narrowing and Resolution firstorder proof-search method can be applied to this theory. This allows to simulate higher-order resolution step by step and furthermore leaves room for further optimizations and extensions.