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International Conference on Mathematics of Program Construction

MPC 1998: Mathematics of Program Construction pp 315–337Cite as

Convergence of program transformers in the metric space of trees

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1422))

Abstract

In recent years increasing consensus has emerged that program transformers, e.g., partial evaluation and unfold/fold transformations, should terminate; a compiler should stop even if it performs fancy optimizations! A number of techniques to ensure termination of program transformers have been invented, but their correctness proofs are sometimes long and involved.

We present a framework for proving termination of program transformers, cast in the metric space of trees. We first introduce the notion of an abstract program transformer; a number of well-known program transformers can be viewed as instances of this notion. We then formalize what it menus that an abstract program transformer terminates and give a general sufficient condition for an abstract program transformer to terminate. We also consider some specific techniques for satisfying the condition. As applications we show that termination of some well-known program transformers either follows directly from the specific techniques or is easy to establish using the general condition.

Our framework facilitates simple termination proofs for program transformers. Also, since our framework is independent of the language being transformed, a single correctness proof can be given in our framework for program transformers using essentially the same technique in the context of different languages. Moreover, it is easy to extend termination proofs for program transformers to accommodate changes to these transformers. Finally, the framework may prove useful for designing new termination techniques for program transformers.

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Authors and Affiliations

  1. Department of Computer Science, University of Copenhagen (DIKU), Universitetsparken 1, DK-2100, Copenhagen ø, Denmark

    Morten Heine B. Sørensen

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  1. Morten Heine B. Sørensen
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Johan Jeuring

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Sørensen, M.H.B. (1998). Convergence of program transformers in the metric space of trees. In: Jeuring, J. (eds) Mathematics of Program Construction. MPC 1998. Lecture Notes in Computer Science, vol 1422. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054297

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  • DOI: https://doi.org/10.1007/BFb0054297

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  • Print ISBN: 978-3-540-64591-7

  • Online ISBN: 978-3-540-69345-1

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