Abstract
We propose a locally nameless representation for Launchbury’s natural semantics for lazy evaluation. Names are reserved for free variables, while bound variable names are replaced by indices. This avoids the use of α-conversion and Barendregt’s variable convention, and facilitates proof formalization. Our definition includes the management of multi-binders to represent simultaneous recursive local declarations. We use cofinite quantification to express the semantic rules that require the introduction of fresh names, but we show that existential rules are admissible too. Moreover, we prove that the choice of names during the evaluation of a term is irrelevant as long as they are fresh enough.
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References
Aydemir, B.E., Charguéraud, A., Pierce, B.C., Pollack, R., Weirich, S.: Engineering formal metatheory. In: ACM Symposium on Principles of Programming Languages, POPL 2008, pp. 3–15. ACM Press (2008)
Baker-Finch, C., King, D., Trinder, P.W.: An operational semantics for parallel lazy evaluation. In: ACM-SIGPLAN International Conference on Functional Programming (ICFP 2000), pp. 162–173. ACM Press (2000)
Barendregt, H.P.: The Lambda Calculus: Its Syntax and Semantics. Studies in Logic and the Foundations of Mathematics, vol. 103. North-Holland (1984)
Bertot, Y.: Coq in a hurry. CoRR, abs/cs/0603118 (2006)
Charguéraud, A.: The locally nameless representation. Journal of Automated Reasoning, 1–46 (2011)
de Bruijn, N.G.: Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indagationes Mathematicae 75(5), 381–392 (1972)
Launchbury, J.: A natural semantics for lazy evaluation. In: ACM Symposium on Principles of Programming Languages, POPL 1993, pp. 144–154. ACM Press (1993)
Nakata, K., Hasegawa, M.: Small-step and big-step semantics for call-by-need. CoRR, abs/0907.4640 (2009)
Nipkow, T., Paulson, L.C., Wenzel, M.T.: Isabelle/HOL — A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)
Pitts, A.M.: Nominal logic, a first order theory of names and binding. Information and Computation 186(2), 165–193 (2003)
Sánchez-Gil, L., Hidalgo-Herrero, M., Ortega-Mallén, Y.: An Operational Semantics for Distributed Lazy Evaluation. In: Trends in Functional Programming, vol. 10, pp. 65–80. Intellect (2010)
Sánchez-Gil, L., Hidalgo-Herrero, M., Ortega-Mallén, Y.: A locally nameless representation for a natural semantics for lazy evaluation. Technical Report 01/12, Dpt. Sistemas Informáticos y Computación. Universidad Complutense de Madrid (2012), http://maude.sip.ucm.es/eden-semantics/
Sestoft, P.: Deriving a lazy abstract machine. Journal of Functional Programming 7(3), 231–264 (1997)
Urban, C.: Nominal techniques in Isabelle/HOL. Journal of Automatic Reasoning 40(4), 327–356 (2008)
Urban, C., Berghofer, S., Norrish, M.: Barendregt’s Variable Convention in Rule Inductions. In: Pfenning, F. (ed.) CADE 2007. LNCS (LNAI), vol. 4603, pp. 35–50. Springer, Heidelberg (2007)
Urban, C., Kaliszyk, C.: General Bindings and Alpha-Equivalence in Nominal Isabelle. In: Barthe, G. (ed.) ESOP 2011. LNCS, vol. 6602, pp. 480–500. Springer, Heidelberg (2011)
van Eekelen, M., de Mol, M.: Reflections on Type Theory, λ-calculus, and the Mind. Essays dedicated to Henk Barendregt on the Occasion of his 60th Birthday, chapter Proving Lazy Folklore with Mixed Lazy/Strict Semantics, pp. 87–101. Radboud University Nijmegen (2007)
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Sánchez-Gil, L., Hidalgo-Herrero, M., Ortega-Mallén, Y. (2012). A Locally Nameless Representation for a Natural Semantics for Lazy Evaluation. In: Roychoudhury, A., D’Souza, M. (eds) Theoretical Aspects of Computing – ICTAC 2012. ICTAC 2012. Lecture Notes in Computer Science, vol 7521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32943-2_8
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DOI: https://doi.org/10.1007/978-3-642-32943-2_8
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