1. Kripke semantics for higher-order type theory applied to constraint logic programming languages.
- Author
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Lipton, James and Nieva, Susana
- Subjects
- *
KRIPKE semantics , *LOGIC programming , *PROGRAMMING languages , *PREDICATE calculus , *PROBLEM solving - Abstract
We define a Kripke semantics for Intuitionistic Higher-Order Logic with constraints formulated within Church's Theory of Types via the addition of a new constraint base type. We then define an executable fragment, hoHH ( C ) , of the logic: a higher-order logic programming language with typed λ -abstraction, implication and universal quantification in goals and constraints, and give a modified model theory for this fragment. Both formal systems are shown sound and complete for their respective semantics. We also solve the impredicativity problem in λ Prolog semantics, namely how to give a definition of truth without appealing to induction on subformula structure. In the last section we give a simple semantics-based conservative extension proof that the language hoHH ( C ) satisfies a uniformity property along the lines of [39] . [ABSTRACT FROM AUTHOR]
- Published
- 2018
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