A Shallow Embedding of Resolution and Superposition Proofs into the $\lambda\Pi$-Calculus Modulo

Abstract

The λΠ-calculus modulo is a proof language that has been proposed as a proof standardfor (re-)checking and interoperability. Resolution and superposition are proof-search methods that are used in state-of-the-art first-order automated theorem provers. We provide a shallow embedding of resolution and superposition proofs in the λΠ-calculus modulo, thus offering a way to check these proofs in a trusted setting, and to combine them with other proofs. We implement this embedding as a backend of the prover iProver Modulo.

ML Pattern-Matching, Recursion, and Rewriting: From FoCaLiZe to Dedukti

“…Through the Curry-Howard correspondence, Dedukti can be used as a proof-checker for a wide variety of logics [8,2,1]. It is commonly used to check proofs coming from the Deduction modulo provers Iprover Modulo [4] and Zenon Modulo [6].…”

Mixing HOL and Coq in Dedukti (Extended Abstract)

“…Several tools have been developed to translate the proofs of various systems to Dedukti [6,3,11,8]. The translations are based on the encodings of Cousineau and Dowek in the λ Π-calculus modulo rewriting [10].…”

Greedy pebbling for proof space compression

“…This is the common way to process all kinds of proofs in proof checking systems such as CERes [25], GAPT [24,26,36,44,55], the Checkers tool [19] for foundational proof certificates [20] and Dedukti [2,17]. Moreover, when the conclusion clauses of resolution inferences (or chains of inferences) are omitted in propositional resolution proofs in the TraceCheck format, only top-down checking is possible, because the conclusion clauses need to be recomputed based on their premises.…”