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Amortized Resource Analysis with Polymorphic Recursion and Partial Big-Step Operational Semantics

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Programming Languages and Systems (APLAS 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6461))

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Abstract

This paper studies the problem of statically determining upper bounds on the resource consumption of first-order functional programs. A previous work approached the problem with an automatic type-based amortized analysis for polynomial resource bounds. The analysis is parametric in the resource and can be instantiated to heap space, stack space, or clock cycles. Experiments with a prototype implementation have shown that programs are analyzed efficiently and that the computed bounds exactly match the measured worst-case resource behavior for many functions. This paper describes the inference algorithm that is used in the implementation of the system. It can deal with resource-polymorphic recursion which is required in the type derivation of many functions. The computation of the bounds is fully automatic if a maximal degree of the polynomials is given. The soundness of the inference is proved with respect to a novel operational semantics for partial evaluations to show that the inferred bounds hold for terminating as well as non-terminating computations. A corollary is that run-time bounds also establish the termination of programs.

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Author information

Authors and Affiliations

  1. Ludwig-Maximilians-Universität München, Germany

    Jan Hoffmann & Martin Hofmann

Authors
  1. Jan Hoffmann
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  2. Martin Hofmann
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Editor information

Editors and Affiliations

  1. Dept. of Computer Science and Engineering, Waseda University, 3-4-1, Okubo, Shinjuku-ku, 169-8555, Tokyo, Japan

    Kazunori Ueda

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Hoffmann, J., Hofmann, M. (2010). Amortized Resource Analysis with Polymorphic Recursion and Partial Big-Step Operational Semantics. In: Ueda, K. (eds) Programming Languages and Systems. APLAS 2010. Lecture Notes in Computer Science, vol 6461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17164-2_13

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  • DOI: https://doi.org/10.1007/978-3-642-17164-2_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17163-5

  • Online ISBN: 978-3-642-17164-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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