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Using commutativity properties for controlling coercions

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Integrating Symbolic Mathematical Computation and Artificial Intelligence (AISMC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 958))

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Abstract

This paper investigates some soundness conditions which have to be fulfilled in systems with coercions and generic operators. A result of Reynolds on unrestricted generic operators is extended to generic operators which obey certain constraints. We get natural conditions for such operators, which are expressed within the theoretic framework of category theory.

However, in the context of computer algebra, there arise examples of coercions and generic operators which do not fulfil these conditions. We describe a framework — relaxing the above conditions — that allows distinguishing between cases of ambiguities which can be resolved in a quite natural sense and those which cannot. An algorithm is presented that detects such unresolvable ambiguities in expressions.

Supported by the Swiss National Science Foundation.

Supported by the Deutsche Forschungsgemeinschaft, grant Lo 231/5-1.

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Author information

Authors and Affiliations

  1. Institute for Theoretical Computer Science, ETH Zürich, CH-8092, Zürich, Switzerland

    Stephan A. Missura

  2. Wilhelm-Schickard-Institut für Informatik, UniversitÄt Tübingen, 72076, Tübingen, Germany

    Andreas Weber

Authors
  1. Stephan A. Missura
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  2. Andreas Weber
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Editor information

Jacques Calmet John A. Campbell

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© 1995 Springer-Verlag Berlin Heidelberg

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Missura, S.A., Weber, A. (1995). Using commutativity properties for controlling coercions. In: Calmet, J., Campbell, J.A. (eds) Integrating Symbolic Mathematical Computation and Artificial Intelligence. AISMC 1994. Lecture Notes in Computer Science, vol 958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60156-2_10

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  • DOI: https://doi.org/10.1007/3-540-60156-2_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60156-2

  • Online ISBN: 978-3-540-49533-8

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