Abstract
We present a universal algebraic framework for rewriting terms and types over an arbitrary equational specification of types and typed combinators. Equational type specifications and their initial algebra semantics were introduced in Meinke [1991b]. For an arbitrary equational type specification (ɛ, E) we prove that the corresponding rewriting relation \(R\underrightarrow {(\varepsilon ,E)}*\) coincides with the provability relation (ɛ, E) ⊢ for the equational calculus of terms and types. Using completeness results for this calculus we deduce that rewriting for ground terms and ground types coincides with calculation in the initial model I(ɛ, E) of the equational type specification.
We thank J.R. Hindley, J.V. Tucker and E.G. Wagner for helpful comments on this work. We also acknowledge the financial support of the Science and Engineering Research Council, the British Council and IBM T.J. Watson Research Center.
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© 1993 Springer-Verlag Berlin Heidelberg
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Meinke, K. (1993). Algebraic semantics of rewriting terms and types. In: Rusinowitch, M., Rémy, JL. (eds) Conditional Term Rewriting Systems. CTRS 1992. Lecture Notes in Computer Science, vol 656. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56393-8_1
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DOI: https://doi.org/10.1007/3-540-56393-8_1
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