2014•arXiv (Cornell University)Open access

Developments in Formal Proofs

Thomas Hales

Abstract

This report describes three particular technological advances in formal proofs. The HOL Light proof assistant will be used to illustrate the design of a highly reliable system. Today, proof assistants can verify large bodies of advanced mathematics; and as an example, we turn to the formal proof in Coq of the Feit-Thompson Odd Order theorem in group theory. Finally, we discuss advances in the automation of formal proofs, as implemented in proof assistants such as Mizar, Coq, Isabelle, and HOL Light.

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Key concepts: Mathematical proof, HOL, Proof assistant, Automated theorem proving, Automated proof checking, Formal proof, Computer science, Programming language