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Implementing tactics and tacticals in a higher-order logic programming language

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Abstract

We argue that a logic programming language with a higher-order intuitionistic logic as its foundation can be used both to naturally specify and implement tactic-style theorem provers. The language extends traditional logic programming languages by replacing first-order terms with simply-typed λ-terms, replacing first-order unification with higher-order unification, and allowing implication and universal quantification in queries and the bodies of clauses. Inference rules for a variety of inference systems can be naturally specified in this language. The higher-order features of the language contribute to a concise specification of provisos concerning variable occurrences in formulas and the discharge of assumptions present in many inference systems. Tactics and tacticals, which provide a framework for high-level control over search for proofs, can be directly and naturally implemented in the extended language. This framework serves as a starting point for implementing theorem provers and proof systems that can integrate many diversified operations on formulas and proofs for a variety of logics. We present an extensive set of examples that have been implemented in the higher-order logic programming language λProlog.

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  1. AT&T Bell Laboratories, 600 Mountain Ave., 07974, Murray Hill, NJ, USA

    Amy Felty

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  1. Amy Felty
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Felty, A. Implementing tactics and tacticals in a higher-order logic programming language. J Autom Reasoning 11, 43–81 (1993). https://doi.org/10.1007/BF00881900

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