Gödel’s functional interpretation [Göd58] can be used to extract programs from non-constructive proofs. Though correct by construction, the obtained terms can be computationally inefficient. One reason for slow execution is the re-evaluation of equal subterms due to the use of substitution during the extraction process. In the present paper we define a variant of the interpretation, which avoid...

Constructive Zermelo-Fraenkel Set Theory, CZF, has emerged as a standard reference theory that relates to constructive predicative mathematics as ZFC relates to classical Cantorian mathematics. A hallmark of this theory is that it possesses a type-theoretic model. Aczel showed that it has a formulae-as-types interpretation in Martin-Löf’s intuitionist theory of types [14, 15]. This paper, thoug...

Proofs in constructive logic correspond to functional programs in a direct and natural way. Computational content can also be found in proofs which use non-constructive principles, but more advanced techniques are required to interpret such proofs. Various methods have been developed to harvest programs from derivations in classical logic and experiments have yielded surprising and counterintui...

The purpose of this article is to study the role of Gödel’s functional interpretation in the extraction of programs fromproofs inwell quasi-order theory. Themain focus is on the interpretation of Nash-Williams’ famous minimal bad sequence construction, and the exploration of a number of much broader problems which are related to this, particularly the question of the constructive meaning of Zor...