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A resource aware semantics for a focused intuitionistic calculus

  • DELIA KESNER (a1) and DANIEL VENTURA (a2)
Abstract

We investigate a new computational interpretation for an intuitionistic focused sequent calculus which is compatible with a resource aware semantics. For that, we associate to Herbelin's syntax a type system based on non-idempotent intersection types, together with a set of reduction rules – inspired from the substitution at a distance paradigm – that preserves (and decreases the size of) typing derivations. The non-idempotent approach allows us to use very simple combinatorial arguments, only based on this measure decreasingness, to characterize linear-head and strongly normalizing terms by means of typability. For the sake of completeness, we also study typability (and the corresponding strong normalization characterization) in the calculus obtained from the former one by projecting the explicit cuts.

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J. Andreoli (1992). Logic programming with focusing proofs in linear logic. Journal of Logic and Computation 2 (3) 297347.

F. Baader and T. Nipkow (1998). Term Rewriting and All That, Cambridge University Press.

H. Barendregt , M. Coppo and M. Dezani-Ciancaglini (1983). A filter lambda model and the completeness of type assignment. Bulletin of Symbolic Logic 48 (4) 931940.

A. Bernadet and S. Lengrand (2013). Non-idempotent intersection types and strong normalisation. Logical Methods in Computer Science 9 (4). doi: 10.2168/LMCS-9(4:3)2013

G. Boudol , P.-L. Curien and C. Lavatelli (1999). A semantics for lambda calculi with resources. Mathematical Structures in Computer Science 9 (4) 437482.

M. Coppo and M. Dezani-Ciancaglini (1978). A new type-assignment for lambda terms. Archiv für Mathematische Logik und Grundlagenforschung 19 (1) 139156.

M. Coppo and M. Dezani-Ciancaglini (1980). An extension of the basic functionality theory for the λ-calculus. Notre Dame, Journal of Formal Logic 21 (4) 685693.

M. Coppo , M. Dezani-Ciancaglini and B. Venneri (1981). Functional characters of solvable terms. Mathematical Logic Quarterly 27 (2–6) 4558.

R. Dyckhoff and C. Urban (2003). Strong normalization of herbelin's explicit substitution calculus with substitution propagation. Journal of Logic and Computation 13 (5) 689706.

J. Espírito Santo (2009). The lambda-calculus and the unity of structural proof theory. Theory of Computing Systems 45 (4) 963994.

P. Gardner (1994). Discovering needed reductions using type theory. In: M. Hagiya and J. C. Mitchell (eds.) Proceedings of the Theoretical Aspects of Computer Software, International Conference TACS '94, Lecture Notes in Computer Science, vol. 789, Springer, 555574.

J.-Y. Girard (1987). Linear logic. Theoretical Computer Science 50 1102.

D. Kesner and D. Ventura (2015). A resource aware computational interpretation for herbelin's syntax. In: M. Leucker , C. Rueda and F. D. Valencia (eds.) 12th International Colloquium Theoretical Aspects of Computing – ICTAC 2015, Lecture Notes in Computer Science, vol. 9399, Springer-Verlag, 388403.

A. Kfoury and J. B. Wells (2004). Principality and type inference for intersection types using expansion variables. Theoretical Computer Science 311 (1–3) 170.

S. Lengrand , P. Lescanne , D. Dougherty , M. Dezani-Ciancaglini and S. van Bakel (2004). Intersection types for explicit substitutions. Information and Computation 189 (1) 1742.

D. Miller , G. Nadathur , F. Pfenning and A. Scedrov (1991). Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic 51 (1–2) 125157.

R. Milner (2007). Local bigraphs and confluence: Two conjectures: (extended abstract). Electronic Notes in Theoretical Computer Science 175 (3) 6573.

G. Pottinger (1977). Normalization as a homomorphic image of cut-elimination. Annals of Mathematical Logic 12 323357.

P. Urzyczyn (1999). The emptiness problem for intersection types. Journal of Symbolic Logic 64 (3) 11951215.

S. Valentini (2001). An elementary proof of strong normalization for intersection types. Archive of Mathematical Logic 40 (7) 475488.

S. van Bakel (1992). Complete restrictions of the intersection type discipline. Theoretical Computer Science 102 (1) 135163.

J. Zucker (1974). The correspondence between cut-elimination and normalization I. Annals of Mathematical Logic 7 (1) 1112.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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