A Mechanically Verified, Efficient, Sound and Complete Theorem Prover For First Order Logic
نویسنده
چکیده
Building on work by Wainer and Wallen, formalised by James Margetson, we present soundness and completeness proofs for a system of first order logic. The completeness proofs naturally suggest an algorithm to derive proofs. This algorithm can be implemented in a tail recursive manner. We provide the formalisation in Isabelle/HOL. The algorithm can be executed via the rewriting tactics of Isabelle. Alternatively, we transport the definitions to OCaml, to give a directly executable program.
منابع مشابه
A Mechanically Verified, Sound and Complete Theorem Prover for First Order Logic
We present a system of first order logic, together with soundness and completeness proofs wrt. standard first order semantics. Proofs are mechanised in Isabelle/HOL. Our definitions are computable, allowing us to derive an algorithm to test for first order validity. This algorithm may be executed in Isabelle/HOL using the rewrite engine. Alternatively the algorithm has been ported to OCaML.
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ورودعنوان ژورنال:
- Archive of Formal Proofs
دوره 2004 شماره
صفحات -
تاریخ انتشار 2004