Abstract
Launchbury defines a natural semantics for lazy evaluation and proposes an alternative version which introduces indirections, eliminates blackholes and does not update closures. Equivalence of both semantics is not straightforward. In this paper we focus on the introduction of indirections during \(\beta \)-reduction and study how the heaps, i.e., the sets of bindings, obtained with this kind of evaluation do relate with the heaps produced by substitution. As a heap represents the context of evaluation for a term, we first define an equivalence that identifies terms with the same meaning under a given context. This notion of context equivalence is extended to heaps. Finally, we define a relation between heap/term pairs to establish the equivalence between Launchbury’s alternative natural semantics and its corresponding version without indirections.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Since the ordering of indirections is irrelevant, \(\mathtt {dom}(\varGamma )-\mathtt {dom}(\varGamma ')\) represents any sequence with the names defined in \(\varGamma \) but undefined in \(\varGamma '\).
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), Montreal, Canada, pp. 162–173, September 2000
Barendregt, H.P.: The Lambda Calculus: Its Syntax and Semantics. Studies in Logic and the Foundations of Mathematics, vol. 103. North-Holland, Amsterdam (1984)
Bertot, Y.: Coq in a hurry. CoRR, abs/cs/0603118 (2006)
Breitner, J.: The correctness of launchbury’s natural semantics for lazy evaluation. Archive of Formal Proofs, January 2013. Formal proof development, Amended version May 2014. http://afp.sf.net/entries/Launchbury.shtml
Charguéraud, A.: The locally nameless representation. J. Autom. Reason. 46(3), 363–408 (2012)
de Bruijn, N.G.: Lambda calculus notation with nameless dummies, a tool for automatic formula manipulation, with application to the Church-Rosser theorem. Indag. Math. 75(5), 381–392 (1972)
Hidalgo-Herrero, M., Ortega-Mallén, Y.: An operational semantics for the parallel language Eden. Parallel Process. Lett. (World Scientific Publishing Company) 12(2), 211–228 (2002)
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. J. Funct. Program. 19(6), 699–722 (2009)
Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL. LNCS, vol. 2283. Springer, Heidelberg (2002)
Sánchez-Gil, L., Hidalgo-Herrero, M., Ortega-Mallén, Y.: Call-by-need, call-by-name, and natural semantics. Technical report UU-CS-2010-020, Department of Information and Computing Sciences, Utrech University (2010)
Sánchez-Gil, L., Hidalgo-Herrero, M., Ortega-Mallén, Y.: An operational semantics for distributed lazy evaluation. In: Trends in Functional Programming, pp. 65–80, vol. 10. 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. Univ. Complutense de Madrid (2012). http://federwin.sip.ucm.es/sic/investigacion/publicaciones/pdfs/SIC-1-12.pdf
Sánchez-Gil, L., Hidalgo-Herrero, M., Ortega-Mallén, Y.: A locally nameless representation for a natural semantics for lazy evaluation. In: Roychoudhury, A., D’Souza, M. (eds.) ICTAC 2012. LNCS, vol. 7521, pp. 105–119. Springer, Heidelberg (2012)
Sánchez-Gil, L., Hidalgo-Herrero, M., Ortega-Mallén, Y.: The role of indirections in lazy natural semantics (extended version). Technical report 13/13, Dpt. Sistemas Informáticos y Computación. Univ. Complutense de Madrid (2013). http://federwin.sip.ucm.es/sic/investigacion/publicaciones/pdfs/TR-13-13.pdf
Sestoft, P.: Deriving a lazy abstract machine. J. Funct. Program. 7(3), 231–264 (1997)
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. Log. Methods Comput. Sci. 8(2:14), 1–35 (2012)
van Eekelen, M., de Mol, M.: Proving lazy folklore with mixed lazy/strict semantics. In: Barendsen, E., Capretta, V., Geuvers, H., Niqui, M. (eds.) Reflections on Type Theory, \(\lambda \)-calculus, and the Mind. Essays dedicated to Henk Barendregt on the Occasion of his 60th Birthday, pp. 87–101. Radboud University Nijmegen (2007)
Acknowledgments
This work is partially supported by the projects: TIN2012-39391-C04-04 and S2009/TIC-1465.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sánchez-Gil, L., Hidalgo-Herrero, M., Ortega-Mallén, Y. (2015). The Role of Indirections in Lazy Natural Semantics. In: Voronkov, A., Virbitskaite, I. (eds) Perspectives of System Informatics. PSI 2014. Lecture Notes in Computer Science(), vol 8974. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-46823-4_24
Download citation
DOI: https://doi.org/10.1007/978-3-662-46823-4_24
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-46822-7
Online ISBN: 978-3-662-46823-4
eBook Packages: Computer ScienceComputer Science (R0)