%0 Book Section
%T Higher-order logic programming languages with constraints: A semantics
publisher Springer Verlag BerlĂn
%D 2007
%U 978-3-540-73227-3
%@ https://hdl.handle.net/20.500.14352/53172
%X 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 lambda Prolog'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 lambda Prolog as a special case (with the constraint system chosen to be,13,beta,eta-conversion).
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