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( \({\cal C}\) ) (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).
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Lipton, J., Nieva, S. (2007). Higher-Order Logic Programming Languages with Constraints: A Semantics. In: Della Rocca, S.R. (eds) Typed Lambda Calculi and Applications. TLCA 2007. Lecture Notes in Computer Science, vol 4583. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73228-0_20
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