Sciweavers

Share
CADE
2006
Springer

Extracting Programs from Constructive HOL Proofs Via IZF Set-Theoretic Semantics

10 years 2 months ago
Extracting Programs from Constructive HOL Proofs Via IZF Set-Theoretic Semantics
Church's Higher Order Logic is a basis for proof assistants -- HOL and PVS. Church's logic has a simple set-theoretic semantics, making it trustworthy and extensible. We factor HOL into a constructive core plus axioms of excluded middle and choice. We similarly factor standard set theory, ZFC, into a constructive core, IZF, and axioms of excluded middle and choice. Then we provide the standard set-theoretic semantics in such a way that the constructive core of HOL is mapped into IZF. We use the disjunction, numerical existence and term existence properties of IZF to provide a program extraction capability from proofs in the constructive core. We can implement the disjunction and numerical existence properties in two different ways: one modifying Rathjen's realizability for CZF and the other using a new direct weak normalization result for intensional IZF by Moczydlowski. The latter can also be used for the term existence property.
Robert L. Constable, Wojciech Moczydlowski
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2006
Where CADE
Authors Robert L. Constable, Wojciech Moczydlowski
Comments (0)
books