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Equational formulas in order-sorted algebras

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Automata, Languages and Programming (ICALP 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 443))

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Abstract

We propose a set of transformation rules for first order formulas whose atoms are either equations between terms or “sort constraints” t ε s where s is a regular tree language (or a sort in the algebraic specification community). This set of rules is proved to be correct, terminating and complete. This shows in particular that the first order theory of any rational tree language is decidable, extending the results of [Mal71,CL89,Mah88]. We also show how to apply our results to automatic inductive proofs in equational theories.

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Authors and Affiliations

  1. CNRS and LRI, Université de Paris Sud, Bat. 490, 91405, Orsay cedex, France

    Hubert Comon

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  1. Hubert Comon
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Michael S. Paterson

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© 1990 Springer-Verlag Berlin Heidelberg

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Comon, H. (1990). Equational formulas in order-sorted algebras. In: Paterson, M.S. (eds) Automata, Languages and Programming. ICALP 1990. Lecture Notes in Computer Science, vol 443. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032066

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  • DOI: https://doi.org/10.1007/BFb0032066

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52826-5

  • Online ISBN: 978-3-540-47159-2

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