Pervasive Parallelism in Highly-Trustable Interactive Theorem Proving Systems

Interactive theorem proving is a technology of fundamental importance for mathematics and computer-science. It is based on expressive logical foundations and implemented in a highly trustable way. Applications include huge mathematical proofs and semi-automated verifications of complex software systems. Interactive development of larger and larger proofs increases the demand for computing power, which means explicit parallelism on current multicore hardware [6]. The architecture of contemporary interactive provers such as Coq [13, §4], Isabelle [13, §6] or the HOL family [13, §1] goes back to the influential LCF system [4] from 1979, which has pioneered key principles like correctness by construction for primitive inferences and definitions, free programmability in userspace via ML, and toplevel command interaction. Both Coq and Isabelle have elaborated the prover architecture over the years, driven by the demands of sophisticated proof procedures, derived specification principles, large libraries of formalized mathematics etc. Despite this success, the operational model of interactive proof checking was limited by sequential ML evaluation and the sequential read-eval-print loop, as inherited from LCF.