Translating Higher-Order Problems to First-Order Clauses
نویسندگان
چکیده
Proofs involving large specifications are typically carried out through interactive provers that use higher-order logic. A promising approach to improve the automation of interactive provers is by integrating them with automatic provers, which are usually based on first-order logic. Consequently, it is necessary to translate higher-order logic formulae to first-order form. This translation should ideally be both sound and practical. We have implemented three higher-order to first-order translations, with particular emphasis on the translation of types. Omitting some type information improves the success rate, but can be unsound, so the interactive prover must verify the proofs. In this paper, we will describe our translations and experimental data that compares the three translations in respect of their success rates for various automatic provers.
منابع مشابه
Higher-order Program Verification as Satisfiability Modulo Theories with Algebraic Data-types
We report on work in progress on automatic procedures for proving properties of programs written in higher-order functional languages. Our approach encodes higher-order programs directly as first-order SMT problems over Horn clauses. It is straight-forward to reduce Hoare-style verification of first-order programs into satisfiability of Horn clauses. The presence of closures offers several chal...
متن کاملCan a Higher-Order and a First-Order Theorem Prover Cooperate?
State-of-the-art first-order automated theorem proving systems have reached considerable strength over recent years. However, in many areas of mathematics they are still a long way from reliably proving theorems that would be considered relatively simple by humans. For example, when reasoning about sets, relations, or functions, first-order systems still exhibit serious weaknesses. While it has...
متن کاملStratified Partial-Order Logic Programming
The stable semantics has become a prime candidate for knowledge representation and reasoning. The rules associated with propositional logic programs and the stable semantics are not expressive enough to let one write concise optimization programs. We propose an extension to the language of logic programs that allows one to express optimization problems in a suitable well. In earlier work we def...
متن کاملAn Improved Propositional Approach to First-Order Theorem Proving
Ordered semantic hyper-linking (OSHL) is a theorem prover for first-order logic that generates models and uses them to instantiate first-order clauses to ground clauses, and applies a propositional prover to these ground clauses. OSHL-U extends OSHL with rules for unit clauses and with heuristics. The unit rules in OHSL-U are designed to minimize the use of blind instantiation to generate groun...
متن کاملVerification of Security Protocols with a Bounded Number of Sessions Based on Resolution for Rigid Variables
First-order logic resolution is a standard way to automate the verification of security protocols. However, it sometimes fails to produce security proofs for secure protocols because of the detection of false attacks. For the verification of a bounded number of sessions, false attacks can be avoided by introducing rigid variables. Unfortunately, this yields complicated resolution procedures. We...
متن کامل