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.
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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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References
H. Ehrig and B. Mahr, Fundamentals of Algebraic Specification 1, Equations and Initial Semantics, EATCS Monographs on Theoretical Computer Science 6, Springer Verlag, Berlin, 1985.
K. Meinke, Universal algebra in higher types, Theoretical Computer Science, 100, (1992) 385–417.
K. Meinke, Subdirect representation of higher type algebras, Report CSR 14-90, Dept. of Computer Science, University College Swansea, to appear in: K. Meinke and J.V. Tucker (eds), Many-Sorted Logic and its Applications, John Wiley, 1992.
K. Meinke, A recursive second order initial algebra specification of primitive recursion, Report CSR 8-91, Dept. of Computer Science, University College Swansea, 1991a.
K. Meinke, Equational specification of abstract types and combinators, Report CSR 11-91, Dept. of Computer Science, University College Swansea, to appear in: G. Jäger (ed), Proc. Computer Science Logic '91, Lecture Notes in Computer Science 626, Springer Verlag, Berlin, 1991b.
K. Meinke and L.J. Steggles, Specification and verification in higher order algebra: a case study of convolution, Report CSR 16-92, Dept. of Computer Science, University College Swansea, 1992.
K. Meinke and J.V. Tucker, Universal algebra, 189–411 in: S. Abramsky, D. Gabbay and T.S.E. Maibaum, (eds) Handbook of Logic in Computer Science, Oxford University Press, Oxford, 1992.
K. Meinke and E. Wagner, Algebraic specification of types and combinators, IBM research report, in preparation, 1992.
B. Möller, Higher-order algebraic specifications, Facultät für Mathematik und Informatik, Technische Universität München, Habilitationsschrift, 1987.
B. Möller, A. Tarlecki and M. Wirsing, Algebraic specifications of reachable higherorder algebras, in: D. Sannella and A. Tarlecki (eds), Recent Trends in Data Type Specification, Lecture Notes in Computer Science 332, (Springer Verlag, Berlin, 1988) 154–169.
A. Poigné, On specifications, theories and models with higher types, Information and Control 68, (1986) 1–46.
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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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