Results 1 
2 of
2
A Notion of Classical Pure Type System
 Proc. of 13th Ann. Conf. on Math. Found. of Programming Semantics, MFPS'97
, 1997
"... We present a notion of classical pure type system, which extends the formalism of pure type system with a double negation operator. 1 Introduction It is an old idea that proofs in formal logics are certain functions and objects. The BrowerHeytingKolmogorov (BHK) interpretation [15,51,40], in the ..."
Abstract

Cited by 7 (5 self)
 Add to MetaCart
We present a notion of classical pure type system, which extends the formalism of pure type system with a double negation operator. 1 Introduction It is an old idea that proofs in formal logics are certain functions and objects. The BrowerHeytingKolmogorov (BHK) interpretation [15,51,40], in the form stated by Heyting [40], states that a proof of an implication P ! Q is a "construction " which transforms any proof of P into a proof of Q. This idea was formalized independently by Kleene's realizability interpretation [46,47] in which proofs of intuitionistic number theory are interpreted as numbers, by the CurryHoward (CH) isomorphism [21,43] in which proofs of intuitionistic implicational propositional logic are interpreted as simply typed terms, and by the LambekLawvere (LL) isomorphism [52,55] in which proofs of intuitionistic positive propositional logic are interpreted as morphisms in a cartesian closed category. In the latter cases, the interpretations have an inverse, in th...
Niels Jakob Rehof Morten Heine Srensen
 Theoretical Aspects of Computer Software
, 1994
"... . By restriction of Felleisen's control operator F we obtain an operator \Delta and a fully compatible, ChurchRosser control calculus \Delta enjoying a number of desirable properties. It is shown that \Delta contains a strongly normalizing typed subcalculus with a reduction corresponding clos ..."
Abstract
 Add to MetaCart
. By restriction of Felleisen's control operator F we obtain an operator \Delta and a fully compatible, ChurchRosser control calculus \Delta enjoying a number of desirable properties. It is shown that \Delta contains a strongly normalizing typed subcalculus with a reduction corresponding closely to systems of proof normalization for classical logic. The calculus is more than strong enough to express a callbyname catch=throw programming paradigm. 1 Background and motivation The first subsection describes previous work in the CurryHoward Isomorphism. The second subsection describes our contribution: a typed calculus with a number of desirable properties, not all shared by the systems mentioned in the first subsection. The CurryHoward Isomorphism and classical logic. The socalled CurryHoward Isomorphism states a correspondence between typed calculi and systems of formal logic. 2 At the heart of the isomorphism is the perception of proofs as functions, as formalized ...