Abstract
We illustrate the use of intersection types as a tool for synthesizing λ-models which exhibit special purpose features. We focus on semantical proofs of easiness. This allows us to prove that the class of λ-theories induced by graph models is strictly included in the class of λ-theories induced by non-extensional filter models.
Partially supported by MURST Cofin’ 99 TOSCA Project, CNR-GNSAGA and FGV ’99.
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References
S. Abramsky. Domain theory in logical form. Ann. Pure Appl. Logic, 51(1-2):1–77, 1991.
S. Abramsky and C.-H. L. Ong. Full abstraction in the lazy lambda calculus. Inform. and Comput., 105(2):159–267, 1993.
F. Alessi. Strutture di tipi, teoria dei domini e modelli del lambda calcolo. PhD thesis, Torino University, 1991.
J. Baeten and B. Boerboom. ω can be anything it shouldn’t be. Indag.Math., 41:111–120, 1979.
H. Barendregt. The Lambda Calculus: its Syntax and Semantics. North-Holland, Amsterdam, revised edition, 1984.
H. Barendregt, M. Coppo, and M. Dezani-Ciancaglini. A filter lambda model and the completeness of type assignment. J. Symbolic Logic, 48(4):931–940, 1983.
H. Barendregt et. al. Typed λ-calculus and applications. North-Holland, 2001. (to appear).
A. Berarducci and B. Intrigila. Some new results on easy lambda-terms. Theoret. Comput. Sci., 121:71–88, 1993.
A. Berarducci and B. Intrigila. Church-Rosser λ-theories, infinite λ-calculus and consistency problems. In W. Hodges and M. Hyland et al., editors, Logic: From Foundations to applications, pages 33–58. Oxford Sci. Publ., New York, 1996.
M. Coppo and M. Dezani-Ciancaglini. An extension of the basic functionality theory for the λ-calculus. Notre Dame J. Formal Logic, 21(4):685–693, 1980.
M. Coppo, M. Dezani-Ciancaglini, F. Honsell, and G. Longo. Extended type structures and filter lambda models. In Logic colloquium’ 82, pages 241–262. North-Holland, Amsterdam, 1984.
M. Coppo, M. Dezani-Ciancaglini, and B. Venneri. Principal type schemes and λ-calculus semantics. In R. Hindley and J. Seldin, editors, To H. B. Curry: essays on combinatory logic, lambda calculus and formalism, pages 535–560. Academic Press, London, 1980.
M. Coppo, M. Dezani-Ciancaglini, and M. Zacchi. Type theories, normal forms, and D ∞-lambda-models. Inform. and Comput., 72(2):85–116, 1987.
M. Dezani-Ciancaglini, F. Honsell, and F. Alessi. A complete characterization of the complete intersection-type theories. In J. Rolim and A. Broder et al., editors, ICALP Workshops 2000, volume 8 of Proceedings in Informatics, pages 287–302. Carleton-Scientific, Canada, 2000.
M. Dezani-Ciancaglini, F. Honsell, and Y. Motohama. Compositional characterization of λ-terms using intersection types. In M. Nielsen and B. Rovan, editors, Mathematical Foundations of Computer Science 2000, volume 1893 of Lecture Notes in Comput. Sci., pages 304–313. Springer, 2000.
P. Di Gianantonio and F. Honsell. An abstract notion of application. In M. Bezem and J.F. Groote, editors, Typed lambda calculi and applications, volume 664 of Lecture Notes in Comput. Sci., pages 124–138. Springer, Berlin, 1993.
L. Egidi, F. Honsell, and S. Ronchi Della Rocca. Operational, denotational and logical descriptions: a case study. Fund. Inform., 16(2):149–169, 1992.
R. Hindley and G. Longo. Lambda-calculus models and extensionality. Z. Math. Logik Grundlag. Math., 26(4):289–310, 1980.
F. Honsell and M. Lenisa. Semantical analysis of perpetual strategies in λ-calculus. Theoret. Comput. Sci., 212(1-2):183–209, 1999.
F. Honsell and S. Ronchi Della Rocca. A filter model for μ. Technical report, Torino University, 1984.
F. Honsell and S. Ronchi Della Rocca. An approximation theorem for topological lambda models and the topological incompleteness of lambda calculus. J. Comput. System Sci., 45(1):49–75, 1992.
B. Intrigila. A problem on easy terms in λ-calculus. Fund. Inform., 15.1:99–106, 1991.
G. Jacopini. A condition for identifying two elements of whatever model of combinatory logic. In C. Böhm, editor, λ-calculus and computer science theory, volume 37 of Lecture Notes in Comput. Sci., pages 213–219. Springer, Berlin, 1975.
G. Jacopini and M. Venturini Zilli. Easy terms in the lambda calculus. Fund. Inform., 80:225–233, 1985.
R. Kerth. Isomorphisme et Équivalence Équationnelle entre Modèles du λ-Calcul. PhD thesis, Equipe de Logique Mathématique, Université Paris VII, 1995.
J. Kuper. On the Jacopini technique. Inform. and Comput., 138:101–123, 1997.
J. Mitchell. Foundation for Programmimg Languages. MIT Press, 1996.
G. D. Plotkin. Set-theoretical and other elementary models of the λ-calculus. Theoret. Comput. Sci., 121(1-2):351–409, 1993.
G. Pottinger. A type assignment for the strongly normalizable λterms. In R. Hindley and J. Seldin, editors, To H. B. Curry: essays on combinatory logic, lambda calculus and formalism, pages 561–577. Academic Press, London, 1980.
A. Pravato, S. Ronchi, and L. Roversi. The call-by-value lambda calculus: a semantic investigation. Math. Struct. in Comput. Sci., 9(5):617–650, 1999.
D. Scott. Continuous lattices. In F. Lawvere, editor, Toposes, algebraic geometry and logic, volume 274 of Lecture Notes in Math., pages 97–136. Springer, Berlin, 1972.
S. Vickers. Topology via logic. Cambridge University Press, Cambridge, 1989.
C. Zylberajch. Syntaxe et Semantique de la Facilité en Lambda-calcul. PhD thesis, Université Paris VII, 1991.
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Alessi, F., Dezani-Ciancaglini, M., Honsell, F. (2001). Filter Models and Easy Terms. In: Theoretical Computer Science. ICTCS 2001. Lecture Notes in Computer Science, vol 2202. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45446-2_2
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DOI: https://doi.org/10.1007/3-540-45446-2_2
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