Validated Proof-Producing Decision Procedures

A widely used technique to integrate decision procedures (DPs) with other systems is to have the DPs emit proofs of the formulas they report valid. One problem that arises is debugging the proof-producing code; it is very easy in standard programming languages to write code which produces an incorrect proof. This paper demonstrates how proof-producing DPs may be implemented in a programming language, called Rogue-Sigma-Pi (RSP), whose type system ensures that proofs are manipulated correctly. RSP combines the Rogue rewriting language and the Edinburgh Logical Framework (LF). Type-correct RSP programs are partially correct: essentially, any putative LF proof object produced by a type-correct RSP program is guaranteed to type check in LF. The paper describes a simple proof-producing combination of propositional satisfiability checking and congruence closure implemented in RSP.