Currying of order-sorted term rewriting systems
- 122 Downloads
Term rewriting system is a helpful tool for implementing functional programming languages. We focus upon a transformation of term rewriting systems called currying. Currying transforms a term rewriting system with symbols of arbitrary arity into another one, which contains only nulary symbols with a single binary symbol called application. Currying in single-sorted case is explored in  but currying in typed case remains as a problem. This paper first proposes currying of order-sorted term rewriting systems. Then, we prove that compatibility and confluence of order-sorted term rewriting systems are preserved by currying.
KeywordsNormal Form Function Symbol Combinatory Logic Applicative Term Functional Programming Language
Unable to display preview. Download preview PDF.
- 1.J.R.Kennaway, J.W.Klop, M.R.Sleep, and F.J. de Vries. Comparing curried and uncurried rewriting. Technical Report, ftp://ftp.sys.uea.ac.uk/pub/kennaway/, 1994.Google Scholar
- 2.S.Kahrs. Confluence of Curried Term-Rewriting Systems. Technical Report, Laboratory for Foundations of Computer Science, University of Edinburgh, January 1994.Google Scholar
- 3.Jan Willem Klop. Term rewriting systems. In S.Abramsky, D.M. Gabbai,and T.S.E. Maibaum, editors, Handbook of Logic in Computer Science, Volume 2, pages 1–116. Oxford University Press, 1992.Google Scholar
- 4.G.Smolka, W.Nutt, J.A.Goguen, and J.Meseguer. Order-Sorted Equational Computation. In H.Aït-Kaci and M.Niyat, editors, Resolution of Equations in Algebraic Structures, volume 2, pages 297–367. Academic Press, 1989.Google Scholar
- 5.M.Schmidt-Schauß. Computational Aspects of an Order-Sorted Logic with Term Declarations. J.Siekmann, editor, LNAI 395. Springer-Verlag, 1989.Google Scholar
- 6.Uwe Waldmann. Unification in Order-Sorted Signatures. Technical Report 298, Universität Dortmund(Germany), 1989.Google Scholar
- 7.Uwe Waldmann. Compatibility of Order-Sorted Rewrite Rules. In S.Kaplan and M.Okada, editors, 2nd International CTRS Workshop, Conditional and Typed Rewriting Systems. Proceedings. Montreal, Canada, LNCS 516, pages 407–416. Springer-Verlag, 1990.Google Scholar