Abstract

Introduction We present a categorical proof of the normalization theorem for simply typed -calculus, i.e. we derive a computable function nf which assigns to every typed -term a normal form, s.t. M ' N nf(M ) = nf(N ) nf(M ) ' M where ' is fij equality. Both the function nf and its correctness properties can be deduced from the categorical construction. To substantiate this, we present an ML program in the appendix which can be extracted from our argument. We emphasize that this presentation of normalization is reduction free, i.e. we do not mention term rewriting or use properties of term rewriting systems such as the Church-Rosser property. An immediate consequence of normalization is the decidability of ' but there are other useful corollaries; for instance we can show that

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