Differential systems of pure Gaussian type

Pure Type Systems with

Pure Type Systems Formalized

This paper is about our hobby. For us, machine-checked mathematics is a passion, and constructive type theory (in the broadest sense) is the way to this objective. Efficient and correct type-checking programs are necessary, so a formal theory of type systems leading to verified type synthesis algorithms is a natural goal. For over a year the second author has been developing a machine-checked p...

Extensions of Pure Type Systems

We extend pure type systems with quotient types and subset types and establish an equivalence between four strong normalisation problems: subset types, quotient types, deenitions and the so-called K-rules. As a corollary, we get strong normalisation of ECC with deeni-tions, subset and quotient types.

Domain-Free Pure Type Systems

Pure type systems make use of domain-full-abstractions x : D : M. We present a variant of pure type systems, which we call domain-free pure type systems, with domain-free-abstractions x : M. Domain-free pure type systems have a number of advantages over both pure type systems and so-called type assignment systems (they also have some disadvantages) and have been used in theoretical developments...

Type-checking injective pure type systems

Injective Pure Type Systems form a large class of Pure Type Systems for which one can compute by purely syntactic means two sorts elmt(?jM) and sort(?jM), where ? is a pseudo-context and M is a pseudo-term, and such that for every sort s, ? ` M : A ^ ? ` A : s) elmt(?jM) = s ? ` M : s) sort(?jM) = s By eliminating the problematic clause in the (abstraction) rule in favour of constraints over el...