Deciding equivalence with sums and the empty type

Gabriel Scherer (1, 2)

1 Northeastern University [Boston]
2 PARSIFAL - Proof search and reasoning with logic specifications

The logical technique of focusing can be applied to the λ-calculus; in a simple type system with atomic types and negative type form-ers (functions, products, the unit type), its normal forms coincide with βη-normal forms. Introducing a saturation phase gives a notion of quasi-normal forms in presence of positive types (sum types and the empty type). This rich structure let us prove the decidabil-ity of βη-equivalence in presence of the empty type, the fact that it coincides with contextual equivalence, and a finite model property.

Domaines: Langage de programmation [cs.PL]; Logique en informatique [cs.LO]

Gabriel Scherer. Deciding equivalence with sums and the empty type. POPL 2017, Jan 2017, Paris, France. ⟨hal-01646064⟩