Psyche: A Proof-Search Engine Based on Sequent Calculus with an LCF-Style Architecture

Abstract

Psyche is a modular proof-search engine designed for either interactive or automated theorem proving, and aiming at two things: a high level of confidence about the output of the theorem proving process and the ability to apply and combine a wide range of techniques. It addresses the first aim by adopting and extending the LCF architecture to guarantee, using private types, not only the correctness but also the completeness of proof search. It addresses the second by offering a much more appropriate API than just the primitives corresponding to the inference rules of the logic in natural deduction: it uses instead a focused sequent calculus for polarised classical logic. Finally, Psyche features the ability to call decision procedures such as those used in Sat-Modulo-Theories solvers. We therefore illustrate Psyche by using it for SMT-solving.

Axiomatic Constraint Systems for Proof Search Modulo Theories

“…Psyche is a platform for proof search, where a kernel offers an API for programming various search strategies as plugins, while guaranteeing the correctness of the search output [13]. 1 , and a theory component is required to provide the implementation of the concepts developed in the previous sections, as shown in the module type above.…”

“…The latter indicates which literals of the input have been used to close the branch, which is useful information for lemma learning (see e.g. [13]). …”

A bisimulation between DPLL(T) and a proof-search strategy for the focused sequent calculus

“…The above description of DPLL(T ) as a proof-search mechanism of LK p (T ) has been implemented as a plugin for PSYCHE [20,33], a proof-search engine for LK p (T ).…”

“…The implementation of plugins is however not trusted for soundness: the worst that a plugin can do is crash the program, not affect its output. A expanded description of PSYCHE can be found in [20].…”

“…In order to validate the theoretical simulation of DPLL(T ), and to evaluate its efficiency as a proof-search method in LK p (T ), we have implemented the simulation as a plugin for PSYCHE [20,33], a proof-search tool based on LK p (T ). This tool has a modular architecture in a style similar to LCF [29]: a simple kernel offers proof-search primitives for LK p (T ), and plugins are programmed with these primitives to drive the kernel through the construction of a proof-tree.…”