Type-checking injective pure type systems

Abstract

Injective pure type systems form a large class of pure type systems for which one can compute by purely syntactic means two sorts elmt(Γ[mid ]M) and sort(Γ[mid ]M), where Γ is a pseudo-context and M is a pseudo-term, and such that for every sort s,formula hereBy eliminating the problematic clause in the (abstraction) rule in favor of constraints over elmt(.[mid ].) and sort(.[mid ].), we provide a sound and complete type-checking algorithm for injective pure type systems. In addition, we prove expansion postponement for a variant of injective pure type systems where the problematic clause in the (abstraction) rule is replaced in favor of constraints over elmt(.[mid ].) and sort(.[mid ].).