Year: 1993
Type: book-chapter
Abstract: Suppose a formal proof of Vz3ySpec(x,y) is given, where Spec(x,y) is an atomic formula expressing some specification for natural numbers x, y.For any particular number n we then obtain a formal proof of 3ySpec(n, y).Now the proof-theoretic normalization procedure yields another proof of 3ySpec(n,j/) which is in normal form.In particular, it does not use induction axioms any more, and it also does not contain non-evaluated terms.Hence we can read off, linearly in the size of the normal proof, an instance m for y such that Spec(n, m) holds.In this way a formal proof can be seen as a program, and the central part in implementing this programming language consists in an implementation of the proof-theoretic normalization procedure.
Author: Helmut Schwichtenberg
Institution: Ludwig-Maximilians-Universität München
Language: English
Subfield: Software
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1897683944