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2014 | OriginalPaper | Chapter

Higher-Order Languages: Bisimulation and Coinductive Equivalences (Extended Abstract)

Author : Davide Sangiorgi

Published in: Coalgebraic Methods in Computer Science

Publisher: Springer Berlin Heidelberg

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Abstract

Higher-order languages have been widely studied in functional programming, following the \(\lambda \)-calculus. In a higher-order calculus, variables may be instantiated with terms of the language. When multiple occurrences of the variable exist, this mechanism results in the possibility of copying the terms of the language.

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Literature
[Abr90]
go back to reference Abramsky, S.: The lazy lambda calculus. In: Turner, D.A. (ed.) Research Topics in Functional Programming, pp. 65–117. Addison-Wesley, Reading (1990) Abramsky, S.: The lazy lambda calculus. In: Turner, D.A. (ed.) Research Topics in Functional Programming, pp. 65–117. Addison-Wesley, Reading (1990)
[ALS14]
go back to reference Alberti, M., Lago, U.D., Sangiorgi, D.: On coinductive equivalences for higher-order probabilistic functional programs. In: Proceedings of POPL’14. ACM (2014) Alberti, M., Lago, U.D., Sangiorgi, D.: On coinductive equivalences for higher-order probabilistic functional programs. In: Proceedings of POPL’14. ACM (2014)
[BSV14]
go back to reference Bernardo, M., Sangiorgi, D., Vignudelli, V.: On the discriminating power of passivation and higher-order interaction, Submitted (2014) Bernardo, M., Sangiorgi, D., Vignudelli, V.: On the discriminating power of passivation and higher-order interaction, Submitted (2014)
[CRM03]
go back to reference Comaniciu, D., Ramesh, V., Meer, P.: Kernel-based object tracking. IEEE Trans. Pattern Anal. Mach. Intell. 25(5), 564–577 (2003)CrossRef Comaniciu, D., Ramesh, V., Meer, P.: Kernel-based object tracking. IEEE Trans. Pattern Anal. Mach. Intell. 25(5), 564–577 (2003)CrossRef
[FHJ98]
[GAB+13]
go back to reference Gordon, A.D., Aizatulin, M., Borgström, J., Claret, G., Graepel, T., Nori, A.V., Rajamani, S.K., Russo, C.V.: A model-learner pattern for bayesian reasoning. In: POPL, pp. 403–416 (2013) Gordon, A.D., Aizatulin, M., Borgström, J., Claret, G., Graepel, T., Nori, A.V., Rajamani, S.K., Russo, C.V.: A model-learner pattern for bayesian reasoning. In: POPL, pp. 403–416 (2013)
[GH05a]
go back to reference Godskesen, ChJ, Hildebrandt, T.: Extending Howe’s method to early bisimulations for typed mobile embedded resources with local names. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 140–151. Springer, Heidelberg (2005) Godskesen, ChJ, Hildebrandt, T.: Extending Howe’s method to early bisimulations for typed mobile embedded resources with local names. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 140–151. Springer, Heidelberg (2005)
[Goo13]
go back to reference Goodman, N.D.: The principles and practice of probabilistic programming. In: POPL, pp. 399–402 (2013) Goodman, N.D.: The principles and practice of probabilistic programming. In: POPL, pp. 399–402 (2013)
[Gor93]
go back to reference Gordon, A.D.: Functional programming and input/output. Ph.D. thesis, University of Cambridge (1993) Gordon, A.D.: Functional programming and input/output. Ph.D. thesis, University of Cambridge (1993)
[GR96]
go back to reference Gordon, A.D., Rees, G.D.: Bisimilarity for a first-order calculus of objects with subtyping. In: Proceedings of the 23rd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 386–395 (1996) Gordon, A.D., Rees, G.D.: Bisimilarity for a first-order calculus of objects with subtyping. In: Proceedings of the 23rd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 386–395 (1996)
[How96]
[JP89]
go back to reference Jones, C., Plotkin, G.D.: A probabilistic powerdomain of evaluations. In: LICS, pp. 186–195 (1989) Jones, C., Plotkin, G.D.: A probabilistic powerdomain of evaluations. In: LICS, pp. 186–195 (1989)
[JR99]
go back to reference Jeffrey, A., Rathke, J.: Towards a theory of bisimulation for local names. In: 14th Annual IEEE Symposium on Logic in Computer Science, pp. 56–66 (1999) Jeffrey, A., Rathke, J.: Towards a theory of bisimulation for local names. In: 14th Annual IEEE Symposium on Logic in Computer Science, pp. 56–66 (1999)
[KH13]
go back to reference Koutavas, V., Hennessy, M.: Symbolic bisimulation for a higher-order distributed language with passivation. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 167–181. Springer, Heidelberg (2013) CrossRef Koutavas, V., Hennessy, M.: Symbolic bisimulation for a higher-order distributed language with passivation. In: D’Argenio, P.R., Melgratti, H. (eds.) CONCUR 2013 – Concurrency Theory. LNCS, vol. 8052, pp. 167–181. Springer, Heidelberg (2013) CrossRef
[KLS11]
go back to reference Koutavas, V., Levy, P.B., Sumii, E.: From applicative to environmental bisimulation. Electr. Notes Theor. Comput. Sci. 276, 215–235 (2011)MathSciNetCrossRef Koutavas, V., Levy, P.B., Sumii, E.: From applicative to environmental bisimulation. Electr. Notes Theor. Comput. Sci. 276, 215–235 (2011)MathSciNetCrossRef
[KW06]
go back to reference Koutavas, V., Wand, M.: Small bisimulations for reasoning about higher-order imperative programs. In: Proceedings of the 33rd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 141–152 (2006) Koutavas, V., Wand, M.: Small bisimulations for reasoning about higher-order imperative programs. In: Proceedings of the 33rd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 141–152 (2006)
[Las98]
go back to reference Lassen, S.B.: Relational reasoning about functions and nondeterminism. Ph.D. thesis, Department of Computer Science, University of Aarhus (1998) Lassen, S.B.: Relational reasoning about functions and nondeterminism. Ph.D. thesis, Department of Computer Science, University of Aarhus (1998)
[LPSS11]
go back to reference Lanese, I., Pérez, J.A., Sangiorgi, D., Schmitt, A.: On the expressiveness and decidability of higher-order process calculi. Inf. Comput. 209(2), 198–226 (2011)MATHCrossRef Lanese, I., Pérez, J.A., Sangiorgi, D., Schmitt, A.: On the expressiveness and decidability of higher-order process calculi. Inf. Comput. 209(2), 198–226 (2011)MATHCrossRef
[LSS09a]
go back to reference Lenglet, S., Schmitt, A., Stefani, J.-B.: Howe’s method for calculi with passivation. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 448–462. Springer, Heidelberg (2009) CrossRef Lenglet, S., Schmitt, A., Stefani, J.-B.: Howe’s method for calculi with passivation. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 448–462. Springer, Heidelberg (2009) CrossRef
[LSS09b]
go back to reference Lenglet, S., Schmitt, A., Stefani, J.-B.: Normal bisimulations in calculi with passivation. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 257–271. Springer, Heidelberg (2009) CrossRef Lenglet, S., Schmitt, A., Stefani, J.-B.: Normal bisimulations in calculi with passivation. In: de Alfaro, L. (ed.) FOSSACS 2009. LNCS, vol. 5504, pp. 257–271. Springer, Heidelberg (2009) CrossRef
[LSS11]
go back to reference Lenglet, S., Schmitt, A., Stefani, J.-B.: Characterizing contextual equivalence in calculi with passivation. Inf. Comput. 209(11), 1390–1433 (2011)MATHMathSciNetCrossRef Lenglet, S., Schmitt, A., Stefani, J.-B.: Characterizing contextual equivalence in calculi with passivation. Inf. Comput. 209(11), 1390–1433 (2011)MATHMathSciNetCrossRef
[Mil89]
go back to reference Milner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River (1989)MATH Milner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River (1989)MATH
[Mor68]
go back to reference Morris, J.H. Jr.: Lambda-calculus models of programming languages. Ph.D. thesis, Massachusetts Institute of Technology (1968) Morris, J.H. Jr.: Lambda-calculus models of programming languages. Ph.D. thesis, Massachusetts Institute of Technology (1968)
[MS99]
go back to reference Manning, C.D., Schütze, H.: Foundations of Statistical Natural Language Processing, vol. 999. MIT Press, Cambridge (1999)MATH Manning, C.D., Schütze, H.: Foundations of Statistical Natural Language Processing, vol. 999. MIT Press, Cambridge (1999)MATH
[Par81a]
go back to reference Park, D.: A new equivalence notion for communicating systems. In: Maurer, G. (ed.) Bulletin EATCS, vol. 14, pp. 78–80 (1981). Abstract of the talk presented at the Second Workshop on the Semantics of Programming Languages, Bad Honnef, 16–20 March 1981. Abstracts collected in the Bulletin by B. Mayoh Park, D.: A new equivalence notion for communicating systems. In: Maurer, G. (ed.) Bulletin EATCS, vol. 14, pp. 78–80 (1981). Abstract of the talk presented at the Second Workshop on the Semantics of Programming Languages, Bad Honnef, 16–20 March 1981. Abstracts collected in the Bulletin by B. Mayoh
[Par81b]
go back to reference Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) Theoretical Computer Science. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981) CrossRef Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) Theoretical Computer Science. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981) CrossRef
[Pea88]
go back to reference Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988) Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo (1988)
[Pfe01]
go back to reference Pfeffer, A.: IBAL: a probabilistic rational programming language. In: IJCAI, pp. 733–740. Morgan Kaufmann (2001) Pfeffer, A.: IBAL: a probabilistic rational programming language. In: IJCAI, pp. 733–740. Morgan Kaufmann (2001)
[Pit97]
go back to reference Pitts, A.: Operationally-based theories of program equivalence. In: Pitts, A.M., Dybjer, P. (eds.) Semantics and Logics of Computation, pp. 241–298. Publications of the Newton Institute/Cambridge University Press, Cambridge (1997)CrossRef Pitts, A.: Operationally-based theories of program equivalence. In: Pitts, A.M., Dybjer, P. (eds.) Semantics and Logics of Computation, pp. 241–298. Publications of the Newton Institute/Cambridge University Press, Cambridge (1997)CrossRef
[PPT08]
go back to reference Park, S., Pfenning, F., Thrun, S.: A probabilistic language based on sampling functions. ACM Trans. Program. Lang. Syst. 31(1), 1–46 (2008)CrossRef Park, S., Pfenning, F., Thrun, S.: A probabilistic language based on sampling functions. ACM Trans. Program. Lang. Syst. 31(1), 1–46 (2008)CrossRef
[PS12]
go back to reference Piérard, A., Sumii, E.: A higher-order distributed calculus with name creation. In: LICS, pp. 531–540. IEEE (2012) Piérard, A., Sumii, E.: A higher-order distributed calculus with name creation. In: LICS, pp. 531–540. IEEE (2012)
[RP02]
go back to reference Ramsey, N., Pfeffer, A.: Stochastic lambda calculus and monads of probability distributions. In: POPL, pp. 154–165 (2002) Ramsey, N., Pfeffer, A.: Stochastic lambda calculus and monads of probability distributions. In: POPL, pp. 154–165 (2002)
[San98]
go back to reference Sands, D.: Improvement theory and its applications. In: Gordon, A.D., Pitts, A.M. (eds.) Higher Order Operational Techniques in Semantics, pp. 275–306. Publications of the Newton Institute/Cambridge University Press, Cambridge (1998) Sands, D.: Improvement theory and its applications. In: Gordon, A.D., Pitts, A.M. (eds.) Higher Order Operational Techniques in Semantics, pp. 275–306. Publications of the Newton Institute/Cambridge University Press, Cambridge (1998)
[San09]
go back to reference Sangiorgi, D.: On the origins of bisimulation and coinduction. ACM Trans. Program. Lang. Syst. 31(4), 15:1–15:41 (2009) Sangiorgi, D.: On the origins of bisimulation and coinduction. ACM Trans. Program. Lang. Syst. 31(4), 15:1–15:41 (2009)
[San12]
go back to reference Sangiorgi, D.: Introduction to Bisimulation and Coinduction. Cambridge University Press, Cambridge (2012)MATH Sangiorgi, D.: Introduction to Bisimulation and Coinduction. Cambridge University Press, Cambridge (2012)MATH
[SKS07]
go back to reference Sangiorgi, D., Kobayashi, N., Sumii, E.: Logical bisimulations and functional languages. In: Arbab, F., Sirjani, M. (eds.) FSEN 2007. LNCS, vol. 4767, pp. 364–379. Springer, Heidelberg (2007) CrossRef Sangiorgi, D., Kobayashi, N., Sumii, E.: Logical bisimulations and functional languages. In: Arbab, F., Sirjani, M. (eds.) FSEN 2007. LNCS, vol. 4767, pp. 364–379. Springer, Heidelberg (2007) CrossRef
[SKS11]
go back to reference Sangiorgi, D., Kobayashi, N., Sumii, E.: Environmental bisimulations for higher-order languages. ACM Trans. Program. Lang. Syst. 33(1), 5 (2011) Sangiorgi, D., Kobayashi, N., Sumii, E.: Environmental bisimulations for higher-order languages. ACM Trans. Program. Lang. Syst. 33(1), 5 (2011)
[SP05]
go back to reference Sumii, E., Pierce, B.C.: A bisimulation for type abstraction and recursion. In: Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 63–74 (2005) Sumii, E., Pierce, B.C.: A bisimulation for type abstraction and recursion. In: Proceedings of the 32nd ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 63–74 (2005)
[SS03]
go back to reference Schmitt, A., Stefani, J.-B.: The m-calculus: a higher-order distributed process calculus. In: Proceedings POPL’03, pp. 50–61. ACM (2003) Schmitt, A., Stefani, J.-B.: The m-calculus: a higher-order distributed process calculus. In: Proceedings POPL’03, pp. 50–61. ACM (2003)
[SW01]
go back to reference Sangiorgi, D., Walker, D.: The Pi-Calculus - A Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)MATH Sangiorgi, D., Walker, D.: The Pi-Calculus - A Theory of Mobile Processes. Cambridge University Press, Cambridge (2001)MATH
[Thr02]
go back to reference Thrun, S.: Robotic Mapping: A survey, pp. 1–35. Exploring Artificial Intelligence in the New Millennium, Schefferville (2002) Thrun, S.: Robotic Mapping: A survey, pp. 1–35. Exploring Artificial Intelligence in the New Millennium, Schefferville (2002)
Metadata
Title
Higher-Order Languages: Bisimulation and Coinductive Equivalences (Extended Abstract)
Author
Davide Sangiorgi
Copyright Year
2014
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-662-44124-4_1

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