Minimal Classical Logic and Control Operators

Abstract

We give an analysis of various classical axioms and characterize a notion of minimal classical logic that enforces Peirce's law without enforcing Ex Falso Quodlibet. We show that a "natural" implementation of this logic is Parigot's classical natural deduction. We then move on to the computational side and emphasize that Parigot's λµ corresponds to minimal classical logic. A continuation constant must be added to λµ to get full classical logic. We then map the extended λµ to a new theory of control, λ-C--top, which extends Felleisen's reduction theory. λ-C--top allows one to distinguish between aborting and throwing to a continuation. It is also in correspondence with the proofs of a refinement of Prawitz's natural deduction.