F. Barbanera and S. Berardi. A symmetric lambda calculus for "classical" program extraction. Inf. Comput., 125(2):103--117, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....superimposed by the classical proof. 1 Introduction Much work has been done in the past 6 7 years to extract the computational content from classical proofs. On the proof theoretical side, let s quote for example [Girard 91] LC) Parigot 91] FD) DJS 95] LK tq and its restrictions) and [BarBer 95] the symmetric calculus) With the notable exception of the symmetric calculus of [BarBer 95] which enjoys only strong normalization, all the systems previously mentioned enjoy the usual good computational properties (strong normalization and confluence) and have a denotational semantics. To ....

....to extract the computational content from classical proofs. On the proof theoretical side, let s quote for example [Girard 91] LC) Parigot 91] FD) DJS 95] LK tq and its restrictions) and [BarBer 95] the symmetric calculus) With the notable exception of the symmetric calculus of [BarBer 95] which enjoys only strong normalization, all the systems previously mentioned enjoy the usual good computational properties (strong normalization and confluence) and have a denotational semantics. To obtain such good properties, it is necessary to cope with the non determinism of classical ....

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Barbanera F., Berardi S., A Symmetric Lambda Calculus for "classical" Program extraction, to appear in I&C, 1995

....For a set V of e proofs, we put (u; V ) 4 = S p2V (u; p) and (u; V ) 4 = S p2V (u; p) Let 0 be a context, 1 be a tag context and ffl be an environment. We define a proposition environment whose domain is dom(1) by putting (u) 4 = ffl[ E] where u E 2 1. We will write ffl[[1]] for this . Now, suppose that the judgment 0 P : A; 1 is derivable in PA c=t . Then for any environment ffl such that ffl j= 0 , we will define a set ffl[ P ] of e proofs and will show that ffl[ P ] is non empty and ffl[ P ] ffl[ A] ffl[ 1] 1. ffl[ u(P ) 4 = u; ffl[ P ] 2. ....

....ffl[ E] where u E 2 1. We will write ffl[ 1] for this . Now, suppose that the judgment 0 P : A; 1 is derivable in PA c=t . Then for any environment ffl such that ffl j= 0 , we will define a set ffl[ P ] of e proofs and will show that ffl[ P ] is non empty and ffl[ P ] ffl[ A] ffl[[1]] 1. ffl[ u(P ) 4 = u; ffl[ P ] 2. ffl[ u: P ] 4 = u; ffl[ P ] 3. ffl[ x] 4 = fffl:xg. 4. ffl[ id(a) 4 = fffl[ a] g. 5. ffl[ repl(P; Q) 4 = ffl[ Q] 6. ffl[ succ(P ) 4 = fk 1 j k 2 ffl[ P ] pg [ ffl[ P ] e . 7. ffl[ abort(P ) 4 = ffl[ P ] 8. ....

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Barbanera, F. and Berardi, S., A symmetric lambda calculus for "classical" program extraction, pp. 495-515, in Theoretical Aspects of Computer Software, Lecture Note in Computer Science 789, Hagiya, M. and Mitchell, J.C. (eds.), SpringerVerlag, 1994.

....we have studied a framework for classical calculi and proved that the theory of classical calculus carry over to systems of dependent types. Much work remains to be done. At a practical level, the appropriateness of CPTSs as a foundation for classical theorem proving and program extraction [3, 4, 5, 6, 7] should be investigated. At a theoretic level, one needs to examine criteria for distinguishing between principal and minor rules further and study CPS translations in more depth. ....

F. Barbanera and S. Berardi. A symmetric lambda calculus for "classical" program extraction. In M. Hagiya and J.C. Mitchell, editors, Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 495--515. Springer-Verlag, 1994.

....logic, control operators, and the Curry Howard isomorphism some initiated independently of his work. It is not possible here to explain the aims and achievements of the individual lines of work; it must suffice simply to mention the work of Murthy [14, 59, 60, 61, 62] Barbanera and Berardi [2, 3, 4, 5, 6], Rezus [74, 75] Parigot [66, 67, 68, 69] de Groote [25, 27, 28, 29, 30] Krivine [57] Girard [42] Danos, Joinet, and Schellinx [18] Rehof and S rensen [73] Duba, Harper, and MacQueen[32] Harper and Lillibridge [46, 47] Coquand [15] Berardi, Bezem, and Coquand [11] Ong [65] Underwood ....

F. Barbanera and S. Berardi. A symmetric lambda calculus for "classical" program extraction. In M. Hagiya and J.C. Mitchell, editors, Theoretical Aspects of Computer Software, volume 789 of Lecture Notes in Computer Science, pages 495--515. Springer-Verlag, 1994.

....programming with proofs paradigm, as Parigot did with his calculus [8] obtained out of his system FD. A question that naturally arises is whether you can manage to obtain some good proof theoretical properties without being compelled to lose the feature of symmetry of classical logic. In [1] a calculus for classical logic was developed in which the symmetry is retained to some degree and which, at the same time, provides a basis for a classical programming with proofs paradigm. This calculus, called Sym PA , is strongly normalizing and a Normal Form Theorem holds for it. It ....

....and symmetric reduction rules. Sym PA preserves the non determinism of classical logic: it is indeed a non confluent calculus. This is a relevant aspect, since it gives the opportunity of investigating the non determinism of classical logic in a good proof theoretical environment. In [1], however, there is no analysis of the non confluence of Sym PA . The present paper carries on the study of Sym PA by focusing the attention on its non confluence. In particular we shall address the following questions. 1. Which are the causes of non confluence 2. Is non confluence a real ....

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Barbanera, F. and Berardi, S. (1996) A symmetric lambda calculus for "classical" program extraction, Information and Computation, Symposium issue on TACS'94, 125(2):103-117.

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F. Barbanera and S. Berardi. A symmetric lambda calculus for "classical" program extraction. Inf. Comput., 125(2):103--117, 1996.

No context found.

F. Barbanera and S. Berardi. A symmetric lambda calculus for "classical" program extraction. Inf. Comput., 125(2):103--117, 1996.

No context found.

F. Barbanera and S. Berardi. A Symmetric Lambda Calculus for "Classical" Program Extraction. In Theoretical Aspects of Computer Software, volume 789 of LNCS, pages 495--515. Springer Verlag, 1994.

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