**Abstract:**

We present a functional programming language based on Pure Type Systems (PTSs). We show how we can define such a language by extending the PTS framework with algebraic data types, case expressions and definitions. To be able to experiment with our language we present an implementation of a type checker and an interpreter for our language.

PTSs are well suited as a basis for a functional programming language
because they are at the top of a hierarchy of increasingly stronger type
systems. The concepts of `existential types', `rank-*n* polymorphism'
and `dependent types' arise naturally in functional programming languages
based on the systems in this hierarchy. There is no need for ad-hoc extensions
to incorporate these features.

The type system of our language is more powerful than the Hindley-Milner system. We illustrate this fact by giving a number of meaningful programs that cannot be typed in Haskell but are typable in our language. A `real world' example of such a program is the mapping of a specialisation of a Generic Haskell function to a Haskell function.

Unlike the description of the Henk language by Simon Peyton Jones and Erik Meijer we give a complete formal definition of the type system and the operational semantics of our language. Another difference between Henk and our language is that our language is defined for a large class of Pure Type Systems instead of only for the systems of the lambda-cube.

**Masters Thesis & Slides:**

- Pure Type Systems for Functional Programming (Masters Thesis, University of Utrecht, INF/SCR-00-13) [ps]
- Slides [ps]

Implementation: |

We have implemented an interpreter for the language described in the thesis. In honor of the designers of the Henk language we have named our language Henk 2000. The source of the interpreter can be downloaded from this page. Unfortunately, at this moment there is no manual available.

The interpreter uses Daan Leijen's parser combinators [homepage] and John Hughes' pretty printing library [homepage].

- source, including examples [zip]

*A screenshot of the interpreter in action!*

**Relevant Literature:**

- Henk, a typed intermediate language, Erik Meijer & Simon Peyton Jones [ps]
- Type-checking Injective Pure Type Systems, Gilles Barthe [ps]
- Lambda Calculi with Types, Henk Barendregt [ps]
- The Curry-Howard Isomorphism, Morten Heine B. Sørensen & Pawel Urzyczyn [ps]