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Stochastic λ-calculi: An extended abstract

Published: 01 September 2014 Publication History

Abstract

It is shown how the operators in the ''graph model'' for @l-calculus (which can function as a programming language for Recursive Function Theory) can be expanded to allow for ''random combinators''. The result then is a model for a new language for random algorithms.

References

[1]
http://www.cs.tulane.edu/~mwm/Michael_Misloves_Home_Page/Research.html
[2]
Cardone, F. and Hindley, J.R., Lambda-calculus and combinators in the 20th century. In: Gabbay, Dov M., Woods, John (Eds.), Handbook of the History of Logic, vol. 5. North-Holland/Elsevier Science. pp. 723-818.
[3]
de'Liguoro, U. and Piperno, A., Nondeterministic extensions of untyped λ-calculus. Inf. Comput. v122. 149-177.
[4]
Friedberg, Richard M. and Rogers Jr., Hartley, Reducibility and completeness for sets of integers. Math. Log. Q. v5. 117-125.
[5]
Gierz, G., Hofmann, K.H., Keimel, K., Lawson, J.D., Mislove, M. and Scott, D.S., Continuous Lattices and Domains. 2003. Encyclopedia of Mathematics and Its Applications, 2003.Cambridge University Press.
[6]
Lago, Ugo Dal and Zorzi, Margherita, Probabilistic operational semantics for the lambda calculus. RAIRO Theor. Inform. Appl. v46. 413-450.
[7]
Myhill, John and Shepherdson, John C., Effective operations on partial recursive functions. Z. Math. Log. Grundl. Math. v1. 310-317.
[8]
Plotkin, Gordon D., Set-theoretical and other elementary models of the λ-calculus. Theor. Comput. Sci. v121. 351-409.
[9]
Rogers Jr., Hartley, Theory of Recursive Functions and Effective Computability. 1967. McGraw-Hill.
[10]
Scott, Dana S., Data types as lattices. SIAM J. Comput. v5. 522-587.

Cited By

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  • (2024)A Cartesian Closed Category for Random VariablesProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662126(1-14)Online publication date: 8-Jul-2024
  • (2021)Universal semantics for the stochastic λ-calculusProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470747(1-12)Online publication date: 29-Jun-2021
  • (2019)Lambda calculus and probabilistic computationProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470186(1-13)Online publication date: 24-Jun-2019
  • Show More Cited By

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Information & Contributors

Information

Published In

cover image Journal of Applied Logic
Journal of Applied Logic  Volume 12, Issue 3
September, 2014
148 pages

Publisher

Elsevier Science Publishers B. V.

Netherlands

Publication History

Published: 01 September 2014

Author Tags

  1. λ -calculus
  2. Enumeration operators
  3. Probabilistic computation
  4. Recursion theory

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Cited By

View all
  • (2024)A Cartesian Closed Category for Random VariablesProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662126(1-14)Online publication date: 8-Jul-2024
  • (2021)Universal semantics for the stochastic λ-calculusProceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS52264.2021.9470747(1-12)Online publication date: 29-Jun-2021
  • (2019)Lambda calculus and probabilistic computationProceedings of the 34th Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3470152.3470186(1-13)Online publication date: 24-Jun-2019
  • (2018)Boolean-Valued Semantics for the Stochastic λ-CalculusProceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3209108.3209175(669-678)Online publication date: 9-Jul-2018
  • (2018)Full Abstraction for Probabilistic PCFJournal of the ACM10.1145/316454065:4(1-44)Online publication date: 26-Apr-2018
  • (2017)A convenient category for higher-order probability theoryProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330072(1-12)Online publication date: 20-Jun-2017
  • (2017)Stack semantics of type theoryProceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science10.5555/3329995.3330065(1-11)Online publication date: 20-Jun-2017
  • (2015)Conditioning in Probabilistic ProgrammingElectronic Notes in Theoretical Computer Science (ENTCS)10.1016/j.entcs.2015.12.013319:C(199-216)Online publication date: 21-Dec-2015

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