Effective Normalization Techniques for HOL
نویسندگان
چکیده
Normalization procedures are an important component of most automated theorem provers. In this work we present an adaption of advanced first-order normalization techniques for higher-order theorem proving which have been bundled in a stand-alone tool. It can be used in conjunction with any higher-order theorem prover, even though the implemented techniques are primarily targeted on resolution-based provers. We evaluated the normalization procedure on selected problems of the TPTP using multiple HO ATPs. The results show a significant performance increase, in both speed and proving capabilities, for some of the tested problem instances.
منابع مشابه
Extracting a Normalization Algorithm in Isabelle/HOL
We present a formalization of a constructive proof of weak normalization for the simply-typed λ-calculus in the theorem prover Isabelle/HOL, and show how a program can be extracted from it. Unlike many other proofs of weak normalization based on Tait’s strong computability predicates, which require a logic supporting strong eliminations and can give rise to dependent types in the extracted prog...
متن کاملProgram Extraction from Normalization Proofs
This paper describes formalizations of Tait’s normalization proof for the simply typed λ-calculus in the proof assistants Minlog, Coq and Isabelle/HOL. From the formal proofs programs are machine-extracted that implement variants of the well-known normalization-by-evaluation algorithm. The case study is used to test and compare the program extraction machineries of the three proof assistants in...
متن کاملVerification of BDD Normalization
We present the verification of the normalization of a binary decision diagram (BDD). The normalization follows the original algorithm presented by Bryant in 1986 and transforms an ordered BDD in a reduced, ordered and shared BDD. The verification is based on Hoare logics and is carried out in the theorem prover Isabelle/HOL. The work is both a case study for verification of procedures on a comp...
متن کاملExtracting Programs from Constructive HOL Proofs Via IZF Set-Theoretic Semantics
Church’s Higher Order Logic is a basis for proof assistants — HOL and PVS. Church’s logic has a simple set-theoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of excluded middle and choice. We similarly factor standard set theory, ZFC, into a constructive core, IZF, and axioms of excluded middle and choice. Then we provide the standard s...
متن کاملStrong Normalization of Moggis's Computational Metalanguage
Handling variable binding is one of the main difficulties in formal proofs. In this context, Moggi’s computational metalanguage serves as an interesting case study. It features monadic types and a commuting conversion rule that rearranges the binding structure. Lindley and Stark have given an elegant proof of strong normalization for this calculus. The key construction in their proof is a notio...
متن کامل