Section: New Results

Proof-search with quantifiers and theories

Participant : Stéphane Graham-Lengrand.

We published our approach to proof-search on quantified problems in presence of one theory [22] , where we identify the specifications required of the theory for the proof-search process to be sound and complete. Theories with unification procedures or quantifier elimination procedures satisfy our specifications, where constraint streams and constraint projections play a key role key. Interestingly enough, Bjorner and Janota  [52] independently achieved a similar result with model projections. Our theory-generic approach allows a clear formulation of what it could mean to combine several quantifier-handling theories, hopefully generalising what the Nelson-Oppen combination technique does in a quantifier-free context. We recently obtained two new results towards this:

• First, the cumbersome, stream-querying, and backtracking mechanisms that were required to implement [22] have been re-expressed in a more satisfying message-passing computational framework.

• Second, we re-expressed the standard quantifier-free combination techniques, mentioned above, as a concurrent message-passing interaction between different theory-specific procedures, and simplified their proofs of correctness. This led to the major redesign of Psyche, mentioned above.