Project description
The future of automatic theorem provers
Proof assistants, or interactive theorem provers, are generally considered tedious to use. Nevertheless, there have recently been significant improvements in the form of the integration of first-order automatic theorem provers and optimised higher-order calculi. Funded by the European Research Council, the Nekoka project aims to further this progress, thereby improving the formal verification of software and mathematics. Initially, the project will concentrate on expanding higher-order satisfiability modulo theories (SMT) and λ-superposition, two higher-order calculi, and integrating them into automated provers, enabling push-button-proof automation for lemmas expressed in higher-order logics. The enhanced higher-order SMT and λ-superposition calculi will propel higher-order automation and automated reasoning, providing benefits to computer scientists, mathematicians and society at large.
Objective
Proof assistants (also called interactive theorem provers) have a long history of being very tedious to use. The situation has improved markedly in the past decade with the integration of first-order automatic theorem provers as backends. And recently, there have been exciting developments for more expressive logics, with the emergence of automatic provers based on optimized higher-order calculi. The Nekoka project's aim is to make higher-order SMT and -superposition a perfect fit for logical problems emerging from the verification of software and mathematics. We will start by extending higher-order SMT and -superposition and implementing them in automatic provers to provide push-button proof automation for lemmas expressed in higher-order logics. To reach end users, we will integrate the automatic provers in interactive tools: both general-purpose proof assistants and software verification platforms. As case studies, we will use our own provers and integrations to formalize quantum information theory and verify a big data framework in collaboration with domain experts. Beyond providing representative case studies, this will help build a user community around our tools and technologies. In terms of scientific impact, the improved higher-order SMT and -superposition calculi will substantially advance the art of higher-order automation and help reorient research in automated reasoning towards the needs of end users, whether computer scientists or mathematicians. Our tools will outlive the project, serving end users and continuing to be useful for future research. At the societal level, the project will herald a future in which automatic provers and proof assistants are routinely deployed in tandem to verify critical computing infrastructure and to formalize research in computer science and mathematics, thereby leading to more trustworthy software and science.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques.
- natural sciencescomputer and information sciencessoftware
- humanitieshistory and archaeologyhistory
- social sciencessociologyindustrial relationsautomation
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Keywords
Programme(s)
- HORIZON.1.1 - European Research Council (ERC) Main Programme
Funding Scheme
HORIZON-ERC - HORIZON ERC GrantsHost institution
80539 MUNCHEN
Germany