Cezary Kaliszyk

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Nominal Isabelle is a definitional extension of the Isabelle/HOL theorem prover. It provides a proving infrastructure for reasoning about programming language calculi involving named bound variables (as opposed to de-Bruijn indices). In this paper we present an extension of Nominal Isabelle for dealing with general bindings, that means term-constructors(More)
Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the fact selector, heuristically ranks the thousands of facts (lemmas, definitions, or axioms) available and selects a subset, based on syntactic similarity to the current proof goal. We introduce MaSh, an alternative that learns from successful proofs.(More)
Sledgehammer integrates automatic theorem provers in the proof assistant Isabelle/HOL. A key component, the relevance filter, heuristically ranks the thousands of facts available and selects a subset, based on syntactic similarity to the current goal. We introduce MaSh, an alternative that learns from successful proofs. New challenges arose from our(More)
Higher-Order Logic (HOL) is based on a small logic kernel, whose only mechanism for extension is the introduction of safe definitions and of non-empty types. Both extensions are often performed in quotient constructions. To ease the work involved with such quotient constructions, we re-implemented in the Isabelle/HOL theorem prover the quotient package by(More)
This article describes the system ProofWeb that is currently being developed in Nijmegen and Amsterdam for teaching logic to undergraduate computer science students. This system is based on the higher order proof assistant Coq, and is made available to the students through an interactive web interface. Part of this system will be a large database of logic(More)
The considerable mathematical knowledge encoded by the Flyspeck project is combined with external automated theorem provers (ATPs) and machine-learning premise selection methods trained on the Flyspeck proofs, producing an AI system capable of proving a wide range of mathematical conjectures automatically. The performance of this architecture is evaluated(More)
As a present to Mizar on its 40th anniversary, we develop an AI/ATP system that in 30 seconds of real time on a 14-CPU machine automatically proves 40 % of the theorems in the latest official version of the Mizar Mathematical Library (MML). This is a considerable improvement over previous performance of large-theory AI/ATP methods measured on the whole MML.(More)
Two complementary AI methods are used to improve the strength of the AI/ATP service for proving conjectures over the HOL Light and Flyspeck corpora. First, several schemes for frequency-based feature weighting are explored in combination with distanceweighted k-nearest-neighbor classifier. This results in 16% improvement (39.0% to 45.5% Flyspeck problems(More)