Abstract
We provide sufficient conditions for categorical models living in arbitrary cpo-enriched cartesian closed categories to have the maximal consistent sensible λ-theory as their equational theory. Finally, we prove that a model of pure λ-calculus we have recently introduced in a cartesian closed category of sets and (multi-)relations fulfils these conditions.
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Amadio, R., Curien, P.-L.: Domains and lambda-calculi. Cambridge Tracts in Theor. Comp. Sci., vol. 46. Cambridge University Press, New York (1998)
Barendregt, H.P.: The lambda calculus: Its syntax and semantics. North-Holland Publishing Co., Amsterdam (1984)
Berry, G.: Stable models of typed lambda-calculi. In: Ausiello, G., Böhm, C. (eds.) ICALP 1978. LNCS, vol. 62. Springer, Heidelberg (1978)
Bucciarelli, A., Ehrhard, T.: On phase semantics and denotational semantics: the exponentials. Ann. Pure Appl. Logic 109(3), 205–241 (2001)
Bucciarelli, A., Ehrhard, T.: Sequentiality and strong stability. In: LICS 1991, pp. 138–145 (1991)
Bucciarelli, A., Ehrhard, T., Manzonetto, G.: Not enough points is enough. In: Duparc, J., Henzinger, T.A. (eds.) CSL 2007. LNCS, vol. 4646, pp. 298–312. Springer, Heidelberg (2007)
Di Gianantonio, P., Franco, G., Honsell, F.: Game semantics for untyped λβ η-calculus. In: Girard, J.-Y. (ed.) TLCA 1999. LNCS, vol. 1581, pp. 114–128. Springer, Heidelberg (1999)
Girard, J.-Y.: Normal functors, power series and the λ-calculus. Annals of pure and applied logic 37, 129–177 (1988)
Gouy, X.: Etude des théories équationnelles et des propriétés algébriques des modèles stables du λ-calcul. PhD Thesis, University of Paris 7 (1995)
Hyland, J.M.E.: A syntactic characterization of the equality in some models for the lambda calculus. J. London Math. Soc. (2) 12(3), 361–370 (1975)
Hyland, M., Nagayama, M., Power, J., Rosolini, G.: A category theoretic formulation for Engeler-style models of the untyped λ-calculus. ENTCS 161, 43–57 (2006)
Ker, A.D., Nickau, H., Ong, C.-H.L.: A universal innocent game model for the Böhm tree lambda theory. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 405–419. Springer, Heidelberg (1999)
Salibra, A.: A continuum of theories of lambda calculus without semantics. In: Proc. LICS 2001, pp. 334–343 (2001)
Scott, D.S.: Continuous lattices. Toposes, algebraic geometry and logic, Berlin (1972)
Wadsworth, C.P.: The relation between computational and denotational properties for Scott’s D ∞ -models of the lambda-calculus. SIAM J. Comp. 5(3), 488–521 (1976)
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Manzonetto, G. (2009). A General Class of Models of \(\mathcal{H}^*\) . In: Královič, R., Niwiński, D. (eds) Mathematical Foundations of Computer Science 2009. MFCS 2009. Lecture Notes in Computer Science, vol 5734. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03816-7_49
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DOI: https://doi.org/10.1007/978-3-642-03816-7_49
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