Minimal Classical Logic and Control Operators

Strong Normalization of the Dual Classical Sequent Calculus

“…This initiated a vigorous line of research: on the one hand classical calculi can be seen as pure programming languages with explicit representations of control, while at the same time terms can be tools for extracting the constructive content of classical proofs [21,3]. In particular the λµ calculus of Parigot [23] has been the basis of a number of investigations [24,11,22,5,1] into the relationship between classical logic and theories of control in programming languages.…”

Relational Parametricity and Control

“…It is well known that the double-negation elimination is as expressible as the Peirce law together with Ex Falso Quodlibet, see e.g. [2]. This is also the case at the level of (uniformity of) proofs.…”

On semantics of a term calculus for classical logic

“…The base cases are the rules ( 1 ) and ( 4 ) from Definition 3.1. For any other term of the calculus, we apply the induction hypothesis to the immediate subterms of (rules ( 2 ), ( 3 ), ( 5 )- ( 7 )). …”

“…Next cornerstone in the study of theories of control in programming languages was Parigot's calculus [27].︀ calculus of Curien and Herbelin [6] is a system with a more fine-grained analysis of calculations within languages with control operators. Since it was introduced in [6],̃︀ calculus has had a strong influence on further understanding between calculi with control operators and classical logic (see [2,3,39,40]). …”