F. Barbanera, S. Berardi, "A constructive valuation interpretation for classical logic and its use in witness extraction", Proceedings of Colloquium on Trees in Algebra and Programming (CAAP), LNCS 581, Springer Verlag, 1992. Home/Search Document Not in Database Summary Related Articles Check |
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A Notion of Classical Pure Type System - Barthe, Hatcliff, Sørensen (1997) (6 citations) (Correct)
....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 constructive valuation interpretation for classical logic and its use in witness extraction. In Colloquium on Trees in Algebra and Programming, volume 581 of Lecture Notes in Computer Science. Springer-Verlag, 1992.
CPS Translations and Applications: The Cube and Beyond - Barthe, Hatcliff, Sørensen (1996) (5 citations) (Correct)
.... C hi = Ch PiV : C: Ki = PiV : ChCi: ChKi Ch PiV 2 : K: K 0 i = PiV 2 : ChKi: ChK 0 i Contexts C h Deltai = Delta Ch Gamma; V : Ci = Ch Gammai; V : ChCi Ch Gamma; V 2 : Ki = Ch Gammai; V 2 : ChKi Top level translation Ch[O]i = ChOi Ch[C]i = ChCi Ch[K]i = ChKi Ch[2]i = 2 Ch[ Gamma]i = Ch Gammai Figure 4: Call by name CPS translation into the domain free cube 4 12 legal terms in the image of CPS translation closed under fi reduction. This section presents CPS pseudoterms, and then gives rules for deriving legal CPS terms. Although the CPS translation ....
....A : B OE 2 fans; cntg The following property states that the domain free CPS language does indeed contain the image of the CPS translation. Property 3 Gamma O : C ) Ch[ Gamma]i com ChOi : Ch[C]i Gamma C : K ) Ch[ Gamma]i con ChCi : Ch[K]i Gamma K : 2 ) Ch[ Gamma]i knd ChKi : Ch[2]i The following property states that legal terms in the CPS language are closed under reduction. Property 4 Gamma A : B and A fi A 0 ) Gamma A 0 : B 2 fcom; val; arg; con; kndg h Gammai hk : Ci OE A : B and A fi A 0 ) h Gammai hk : Ci OE A 0 : B OE 2 fans; cntg ....
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F. Barbanera and S. Berardi. A constructive valuation interpretation for classical logic and its use in witness extraction. In Colloquium on Trees in Algebra and Programming, volume 581 of Lecture Notes in Computer Science. Springer-Verlag, 1992.
A Constructive Valuation Semantics for Classical Logic - Barbanera, Berardi Self-citation (Barbanera Berardi) (Correct)
....be shown in Subsection 4.3 to make explicit our interpretation of classical logical connectives and proofs. The extraction procedure of [1] will then be interpreted in the context of our valuation system in Subsection 4.4. An incomplete and preliminary version of the present paper was presented in [2]. 2 Natural Deduction for Classical logic and Prawitz s reduction rules In this section we recall the system of Natural Deduction for Classical Logic [8] and the set of reduction rules devised by Prawitz. Natural Deduction Classical Logic [ A] A A :A A 1 A 2 A 1 A 2 A 1 A 2 A ....
F. Barbanera, S. Berardi, "A constructive valuation interpretation for classical logic and its use in witness extraction", Proceedings of Colloquium on Trees in Algebra and Programming (CAAP), LNCS 581, Springer Verlag, 1992.
Extracting Constructive Content from Classical Logic via.. - Barbanera, Berardi (13 citations) Self-citation (Barbanera Berardi) (Correct)
.... instead investigated as an environment in which it is possible to interpret the constructive content of classical connectives and proofs (see, among others, Coquand [3] In this last direction an interpretation of classical logic in terms of a valuation semantic has been given by the authors in [1]. However, one of the most appealing directions for the computer scientist, not only the theoretical one, is that which has begun being developed with works by Griffin To Roberta Gottardi [8] and Murthy [10] indeed it was these works that made raise the interest for the topic we are ....
Barbanera F., Berardi S. A constructive valuation interpretation for classical logic and its use in witness extraction. Proceedings of Colloquium on Trees in Algebra and Programming (CAAP), LNCS 581, Springer Verlag, 1992.
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