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International Colloquium on Theoretical Aspects of Computing

ICTAC 2017: Theoretical Aspects of Computing – ICTAC 2017 pp 70–76Cite as

A Probabilistic Semantics for the Pure \(\lambda \)-Calculus

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10580))

Abstract

From a programming language viewpoint, the \(\lambda \)-calculus formalises several features of the modern description of computation and its implementation. We present a denotational semantics for the untyped calculus that captures a basic feature of probabilistic programming languages, namely probability distributions as both the objects and the result of a computation.

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Notes

  1. 1.

    We can show that this indeed defines a inner product.

  2. 2.

    It can be shown that a linear mapping is continuous if and only if it is bounded. For a proof see Theorem 1.5.7 of [2].

References

  1. Barendregt, H.P.: The Lambda Calculus. Studies in Logic and the Foundations of Mathematics, vol. 103. North-Holland, Amsterdam (1991). revised edn

    MATH  Google Scholar 

  2. Debnath, L., Mikusinski, P.: Introduction to Hilbert Spaces with Applications. 3rd revised edn. Elsevier Science Publishing, San Diego (2005). reprint from Academic Press edition 2005

    Google Scholar 

  3. Kadison, R., Ringrose, J.: Fundamentals of the Theory of Operator Algebras: Volume I – Elementary Theory. Graduate Studies in Mathematics, vol. 15. American Mathematical Society, Providence (1997). reprint from Academic Press edition 1983

    MATH  Google Scholar 

  4. Roman, S.: Advanced Linear Algebra, 2nd edn. Springer, Heidelberg (2005)

    MATH  Google Scholar 

  5. Slonneger, K., Kurtz, B.: Formal Syntax and Semantics of Programming Languages: A Laboratory Based Approach, 1st edn. Addison-Wesley Longman Publishing Co., Inc., Boston (1995)

    MATH  Google Scholar 

  6. Draheim, D.: Semantics of the Probabilistic Typed Lambda Calculus - Markov Chain Semantics, Termination Behavior, and Denotational Semantics. Springer, Heidelberg (2017). doi:10.1007/978-3-642-55198-7

    Book  MATH  Google Scholar 

  7. Ehrhard, T., Pagani, M., Tasson, C.: The computational meaning of probabilistic coherence spaces. In: 2011 IEEE 26th Annual Symposium on Logic in Computer Science, pp. 87–96 (2011)

    Google Scholar 

  8. Kozen, D.: Semantics of probabilistic programs. J. Comput. Syst. Sci. 22(3), 328–350 (1981)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica, Università di Verona, Verona, Italy

    Alessandra Di Pierro

Authors
  1. Alessandra Di Pierro
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Correspondence to Alessandra Di Pierro .

Editor information

Editors and Affiliations

  1. Vietnam National University, Hanoi, Vietnam

    Dang Van Hung

  2. University of New Mexico, Albuquerque, New Mexico, USA

    Deepak Kapur

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Di Pierro, A. (2017). A Probabilistic Semantics for the Pure \(\lambda \)-Calculus. In: Hung, D., Kapur, D. (eds) Theoretical Aspects of Computing – ICTAC 2017. ICTAC 2017. Lecture Notes in Computer Science(), vol 10580. Springer, Cham. https://doi.org/10.1007/978-3-319-67729-3_5

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  • DOI: https://doi.org/10.1007/978-3-319-67729-3_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67728-6

  • Online ISBN: 978-3-319-67729-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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