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TEA: Automatically proving termination of programs in a non-strict higher-order functional language

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Book cover Static Analysis (SAS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1302))

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Abstract

We present TEA, a tool that is able to detect termination of functions written in a non-strict high-level functional programming language like Haskell. Since almost every compiler for lazy functional languages transforms programs into a functional core language, we use such a core language as the source language for the analysis. TEA is able to detect two kinds of termination: nf-termination and lazy termination. Intuitively, nf-termination of f means that given arguments a i in normal form, the normal order evaluation of the expression f a 1 ... a n terminates with a normal form. If an expression evaluates to an infinite normal form, we will call it lazy terminating.

In order to prove nf-termination of an expression, TEA tries to generate a preclosed tableau using abstract reduction and path analysis. The preclosed tableau issues a set of ordering constraints, which have to be satisfied by some Noetherian ordering. A subsystem is called to generate this Noetherian ordering, and to verify that the set of ordering constraint is satisfied. In the case of success, this proves termination of the expression at the root of the tableau. Lazy termination is recognized using a specialized check on a preclosed tableau.

TEA performs the analysis automatically in reasonable time with a success rate of about 90 % for the functions of a real program script written in Haskell.

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Authors and Affiliations

  1. Fachbereich Informatik, Johann Wolfgang Goethe-Universität, Postfach 11 19 32, D-60054, Frankfurt, Germany

    Sven Eric Panitz & Manfred Schmidt-Schauß

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  1. Sven Eric Panitz
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  2. Manfred Schmidt-Schauß
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Pascal Van Hentenryck

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© 1997 Springer-Verlag Berlin Heidelberg

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Panitz, S.E., Schmidt-Schauß, M. (1997). TEA: Automatically proving termination of programs in a non-strict higher-order functional language. In: Van Hentenryck, P. (eds) Static Analysis. SAS 1997. Lecture Notes in Computer Science, vol 1302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032752

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  • DOI: https://doi.org/10.1007/BFb0032752

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63468-3

  • Online ISBN: 978-3-540-69576-9

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