# Program extraction from normalization proofs

## Abstract

From a constructive proof of strong normalization plus uniqueness of the long beta-normal form for the simply typed lambda-calculus a normalization program is extracted using Kreisel's modified realizability interpretation for intuitionistic logic. The proof — which uses Tait's computability predicates — is not completely formalized: Induction is done on the meta level, and therefore not a single program but a family of program, one for each term is obtained. Nevertheless this may be used to write a short and efficient normalization program in a type free programming functional programming language (e.g. LISP) which has the interesting feature that it first evaluates a term *r* of type *π* to a functional ¦*r*¦ of type *p* and then collapses ¦*r*¦ to the normal form of *r*.

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