Parallel Proof Checking in Isabelle/Isar

We address the “multicore problem” for mathematical assistants with full proof checking, with special focus on Isabelle/Isar and its main SML platform Poly/ML. On the one hand, working with explicit definitions, statements, and proofs requires significant runtime resources, so the question of parallel checking is really relevant. On the other hand, the inherent structure of formal theories provides various possibilities for parallelism (both implicit and explicit), which is in fact an almost ideal situation. Exploiting this potential in practice requires to reconsider various aspects of the ML platform, the inference engine, and some higher prover specific layers. We report on an implementation of all that for Isabelle/Isar, and point out some general considerations for parallelism in functional programming, and other provers like Coq and HOL.