Higher-order logic programming languages with constraints: a semantics

Authors:
James Lipton;Susana Nieva
Affiliations:
Wesleyan University and Univ. Politécnica de Madrid, Spain;Dep. Sistemas Informáticos y Computación, Univ. Complutense de Madrid, Spain
Venue:
TLCA'07 Proceedings of the 8th international conference on Typed lambda calculi and applications
Year:
2007

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Abstract

A Kripke Semantics is defined for a higher-order logic programming language with constraints, based on Church's Theory of Types and a generic constraint formalism. Our syntactic formal system, hoHH(C) (higher-order hereditary Harrop formulas with constraints), which extends λProlog's logic, is shown sound and complete. A Kripke semantics for equational reasoning in the simply typed lambda-calculus (Kripke Lambda Models) was introduced by Mitchell and Moggi in 1990. Our model theory extends this semantics to include full impredicative higher-order intuitionistic logic, as well as the executable hoHH fragment with typed lambda-abstraction, implication and universal quantification in goals and constraints. This provides a Kripke semantics for the full higher-order hereditarily Harrop logic of λProlog as a special case (with the constraint system chosen to be β,η-conversion).