Order Functional Pure Type Systems

Pure Type Systems for Functional Programming

We present a functional programming language based on Pure Type Systems (PTSs). We show how we can de ne such a language by extending the PTS framework with algebraic data types, case expressions and de nitions. Furthermore, we present an e cient type checking algorithm and an interpreter for this language. PTSs are well suited as a basis for a functional programming language because they are a...

A Pure First Order Representation for Undamped Second Order Descriptor Systems

The aim of this paper is to analyze the undamped second order descriptor systems to show the possibility of transform an undamped second order descriptor system to a pure first order descriptor system ,on different ways, while stating some of its benefits. Meanwhile we will introduce pure first order systems and undamped second order systems and indicate that under some assumptions every undamp...

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...

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...