Expansion postponement for normalising pure type systems

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...

Monadic Type Systems: Pure Type Systems for Impure Settings

Pure type systems and computational monads are two parameterized frameworks that have proved to be quite useful in both theoretical and practical applications. We join the foundational concepts of both of these to obtain monadic type systems. Essentially, monadic type systems inherit the parameterized higher-order type structure of pure type systems and the monadic term and type structure used ...

A Module Calculus for Pure Type Systems

An induction principle for pure type systems

We present an induction principle for Pure Type Systems and use that principle to deene CPS translations and to solve partially the|open| problem of Expansion Postponement. Our principle strengthens and generalises similar principles by Dowek, Huet and Werner 12] and Barthe, Hatclii and SSrensen 5], which have been respectively used to deene-long normal forms and CPS translations for the system...