A Machine-assisted Proof of the Subject Reduction Property for a Small Typed Functional Language

Abstract

at is, to investigate the production of verified implementations of programming languages. Writing programs in constructive type theory amounts to writing completely formal proofs of often complex theorems. This makes the practical applicability of type theory depends strongly on the availability of adequate programming environments (alias proof assistants). A number of these systems have been or are being developed. We expect our work to become a useful experience in this connection too. In the present work, we conduct a first experiment along the lines given above. We consider a small polymorphic functional language and write a formal proof in constructive type theory of the main property relating the type system of the language with the evaluation of its expressions, namely the Subject Reduction Property. We use the proof assistant ALF ([Alt 94]). The abstract syntax of the language considered is the following : e ::= x j x : e<