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Summary: A Proof-Theoretic Foundation of
Abortive Continuations
Zena M. Ariola
University of Oregon
Hugo Herbelin
INRIA-Futurs
Amr Sabry y
Indiana University
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 clas-
sical natural deduction. We then move on to the computational side and emphasize
that Parigot's corresponds to minimal classical logic. A continuation constant
must be added to to get full classical logic. We then map the extended to a
new theory of control, -C -top, which extends Felleisen's reduction theory. -C -top
allows one to distinguish between aborting and throwing to a continuation. It is also
in correspondence with the proofs of a re nement of Prawitz's natural deduction.
Keywords: callcc, continuation
1. Introduction
Traditionally, classical logic is de ned by extending intuitionistic logic
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