Encoding of Predicate Subtyping with Proof Irrelevance in the λΠ-Calculus Modulo Theory

Gabriel Hondet (1) , Frédéric Blanqui (1)

1 DEDUCTEAM - Deduction modulo, interopérabilité et démonstration automatique

The λΠ-calculus modulo theory is a logical framework in which various logics and type systems can be encoded, thus helping the cross-verification and interoperability of proof systems based on those logics and type systems. In this paper, we show how to encode predicate subtyping and proof irrelevance, two important features of the PVS proof assistant. We prove that this encoding is correct and that encoded proofs can be mechanically checked by Dedukti, a type checker for the λΠ-calculus modulo theory using rewriting.

Keywords: Type theory; Higher order logic; Equational logic; Logical Framework; PVS; Dedukti; Proof Irrelevance; Rewriting

Domains: Logic [math.LO]; Logic in Computer Science [cs.LO]

Gabriel Hondet, Frédéric Blanqui. Encoding of Predicate Subtyping with Proof Irrelevance in the λΠ-Calculus Modulo Theory. TYPES 2020 - 26th International Conference on Types for Proofs and Programs, Mar 2020, Turino, Italy. ⟨10.4230/LIPIcs.TYPES.2020.6⟩. ⟨hal-03279766v1⟩