Memoization-Based Proof Search in LF

Memoization-Based Proof Search in LF - an Experimental Evaluation of a Prototype

Elf is a general meta-language for the specification and implementation of logical systems in the style of the logical framework LF. Proof search in this framework is based on the operational semantics of logic programming. In this paper, we discuss experiments with a prototype for memoization-based proof search for Elf programs. We compare the performance of memoization-based proof search, dep...

Small Proof Witnesses for LF

We instrument a higher-order logic programming search procedure to generate and check small proof witnesses for the Twelf system, an implementation of the logical framework LF. In particular, we extend and generalize ideas from Necula and Rahul [16] in two main ways: 1) We consider the full fragment of LF including dependent types and higher-order terms and 2) We study the use of caching of sub...

Memoization and DPLL: Formula Caching Proof Systems

A fruitful connection between algorithm design and proof complexity is the formalization of the DPLL approach to satisfiability testing in terms of tree-like resolution proofs. We consider extensions of the DPLL approach that add some version of memoization, remembering formulas the algorithm has previously shown unsatisfiable. Various versions of such formula caching algorithms have been sugge...

Narrowing Based Inductive Proof Search

Description : We present in this paper a narrowing-based proof search method for inductive theorems. It has the specificity to be grounded on deduction modulo and to yield a direct translation from a successful proof search derivation to a proof in the sequent calculus. The method is shown to be correct and refutationally complete in a proof theoretical way.

Flea: a Fast Proof Checker for Elliptical LF