J.-L. Krivine. Classical logic, storage operators and second order -calculus. Ann. of Pure and Appl. Logic, 68:53--78, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....not shared) of another coroutine. Related work The extension of the well known formulas as types paradigm to classical logic has been widely investigated by T. G. Griffin [10] C. R. Murthy [14] F. Barbanera and S. Berardi [1] N. J. Rehof and M. H. Srensen [23] P. De Groote [6] J. L. Krivine [13], and M. Parigot [18, 19] H. Nakano, Y. Kameyama and M. Sato [16, 15, 17, 11, 12, 26] have proposed various logical frameworks that are intended to provide a type system for a lexical variant of the catch throw mechanism used in functional languages such as Lisp. Moreover, H. Nakano has ....

J.-L. Krivine. Classical logic, storage operators and second order -calculus. Ann. of Pure and Appl. Logic, 68:53--78, 1994.

.... by its double negation) The Godel translation was simplified to use only one negation (this is possible if we use no predicate constant in the logic) and finally the result was proved for a large variety of translations by Nour in [11] Krivine also extends the theorem to classical logic in [7] (in classical logic, storage operators enjoy the property of translating classical proofs to intuitionistic ones) and Nour in [12] extends it to Parigot system TTR [16] However, Nour gives a counter example to the storage operator theorem for a type with a negative quantifier. We show that a ....

J.-L. Krivine. Classical logic, storage operators and second order -calculus. APAL, 1994.

....(such as the C operator of Felleisen et al. 10] and relating them to classical proofs, there has been a great deal of interest in classical proofs. The following is a tentative (and incomplete) classification: ffl Algorithm extraction, control operators: Griffin [14] Murthy [22] Krivine [21], de Groote [9] Nakano [23] Hirokawa [16] Schwichtenberg and Berger [4] Coquand [6] etc. ffl Formal systems and calculi: Girard [11, 12] Parigot [24] Berardi and Barbanera [2] Danos, Joinet and Schellinx [8] etc. ffl Proofs and semantics of cut elimination: Girard [11] Hofmann [17] ....

J.-L. Krivine. Classical logic, storage operators and second order -calculus. Annals of Pure and Applied Logic, 68:53--78, 1994.

....before accepting it as an appropriate foundation. This is what we achieve in this paper by developing an environment machine for the typed calculus. The problem we have to solve may be explained as follows. The existing control operators obey computation rules that are akin to those used in (Krivine 1994). This rule, using the notation of the calculus, may be written as follows: ff: M ) A 0 : An M [ff : f: f A 0 : An ] Such a computation rule does not correspond to an actual notion of reduction (in the sense of (Barendregt 1984) firstly, it is not compatible with the term ....

J.-L. Krivine. Classical logic, storage operators and second order -calculus. Annals of Pure and Applied Logic, 68:53--78, 1994.

....provided one augments functions by appropriate control constructs. In particular he proposed the tautology : A ) A as the type for Felleisen s C operator. A spate of research into the semantics and computational contents of classical proofs ensued (some of which quite independently of Griffin s) [6, 13, 25, 28, 2, 21, 4, 7, 42], etc. Church s calculus is by now widely accepted as the logical basis of functional programming. A goal of our research is to find the calculus of functional computation with first class access to the flow of control, or functional computation with control, for short. In Sec tion 2 of ....

J.-L. Krivine. Classical logic, storage operators and second order -calculus. Annals of Pure and Applied Logic, 68:53-- 78, 1994.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC