Reusing Proofs

Patching Proofs for Reuse

1 We investigate the application of machine learning paradigms in automated reasoning in order to improve a theorem prover by reusing previously computed proofs. Our reuse procedure generalizes a previously computed proof of a conjecture yielding a schematic proof which can be instantiated subsequently if a new, similar conjecture is given. We show that for exploiting the full exibility of seco...

Reusing Formal Proofs Through Isomorphisms Invited Talk

ABSTRACT Formalization of computational objects, software and hardware, is the unique manner to guarantee well-behavior of computer programs and hardware, at least from the mathematical and logical point of view. Several verification and testing approaches have been proved of great applicability in this area being their usability made evident through real applications in the development of crit...

Second-Order Matching modulo Evaluation: A Technique for Reusing Proofs

We investigate the improvement of theorem provers by reusing previously computed proofs. A proof of a conjecture is generalized by replacing function symbols with function variables. This yields a schematic proof of a schematic conjecture which is instantiated subsequently for obtaining proofs of new, similar conjectures. Our reuse method requires solving so-called free function variables, i.e....

Proof Transformations for Reusing Proofs after Changing

Verified Efficient Implementation of Gabow's Strongly Connected Component Algorithm

We present an Isabelle/HOL formalization of Gabow’s algorithm for finding the strongly connected components of a directed graph. Using data refinement techniques, we extract efficient code that performs comparable to a reference implementation in Java. Our style of formalization allows for reusing large parts of the proofs when defining variants of the algorithm. We demonstrate this by verifyin...