Continuation-passing Style Models Complete for Intuitionistic Logic
Abstract
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and the computational content of their composition is, in particular, a -normalisation-by-evaluation program for simply typed lambda calculus with sum types. Although the inspiration comes from Danvy's type-directed partial evaluator for the same lambda calculus, the there essential use of delimited control operators (i.e. computational effects) is avoided. The role of polymorphism is crucial -- dropping it allows one to obtain a notion of model complete for classical predicate logic. The connection between ours and Kripke models is made through a strengthening of the Double-negation Shift schema.
Cite
@article{arxiv.1102.1061,
title = {Continuation-passing Style Models Complete for Intuitionistic Logic},
author = {Danko Ilik},
journal= {arXiv preprint arXiv:1102.1061},
year = {2014}
}