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Thorsten Altenkirch, Martin Hofmann, and Thomas Streicher (1996)

Reduction-Free Normalisation for a Polymorphic System

In: ISTCS, pp. 146.

We give a semantical proof that every term of a combinator version of system F has a normal form. As the argument is entirely formalisable in an impredicative constructive type theory a reduction-free normalisation algorithm can be extracted from this. The proof is presented as the construction of a model of the calculus inside a category of presheaves. Its definition is given entirely in terms of the internal language.

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