Abstract
We introduce a method for establishing that a reduction strategy is normalising and minimal, or dually, that it is perpetual and maximal, in the setting of abstract rewriting. While being complete, the method allows to reduce these global properties to the verification of local diagrams. We show its usefulness both by giving uniform proofs of some known results and by establishing new ones.
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References
Terese.: Term Rewriting Systems. Cambridge University Press, Cambridge (2003)
Newman, M.: On Theories with a Combinatorial Definition of ”Equivalence”. Annals of Mathematics 43(2), 223–243 (1942)
Toyama, Y.: Strong sequentiality of left-linear overlapping term rewriting systems. In: Proceedings of the 7th LICS, pp. 274–284. IEEE Computer Society Press, Los Alamitos (1992)
Oostrom, V.v.: Confluence by decreasing diagrams. Theoretical Computer Science 126(2), 259–280 (1994)
Sørensen, M.: Efficient longest and infinite reduction paths in untyped λ-calculi. In: Kirchner, H. (ed.) CAAP 1996. LNCS, vol. 1059, pp. 287–301. Springer, Heidelberg (1996)
Barendregt, H., Kennaway, R., Klop, J., Sleep, M.: Needed reduction and spine strategies for the lambda calculus. Information and Computation 75(3), 191–231 (1987)
Bloo, R.: Preservation of Termination for Explicit Substitution. PhD thesis, Technische Universiteit Eindhoven (1997)
Khasidashvili, Z., Ogawa, M., van Oostrom, V.: Uniform Normalisation beyond Orthogonality. In: Middeldorp, A. (ed.) RTA 2001. LNCS, vol. 2051, pp. 122–136. Springer, Heidelberg (2001)
Bonelli, E.: Substitutions explicites et réécriture de termes. PhD thesis, Paris XI (2001)
Oostrom, V.v.: Bowls and Beans, Available from author’s homepage (2004)
Simpson, A.: Reduction in a linear lambda-calculus with applications to operational semantics. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 219–234. Springer, Heidelberg (2005)
Jantzen, M.: Confluent String Rewriting. EATCS Monographs on Theoretical Computer Science, vol. 14. Springer, Heidelberg (1988)
Lafont, Y.: Interaction nets. In: Proceedings of the 17th POPL, pp. 95–108. ACM Press, New York (1990)
Stark, E.: Concurrent transition systems. Theoretical Computer Science 64, 221–269 (1989)
Toyama, Y.: Reduction strategies for left-linear term rewriting systems. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds.) Processes, Terms and Cycles: Steps on the Road to Infinity. LNCS, vol. 3838, pp. 198–223. Springer, Heidelberg (2005)
Gramlich, B.: On some abstract termination criteria, WST 1999, Talk (1999)
Pol, J.v.d., Zantema, H.: Generalized innermost rewriting. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 2–16. Springer, Heidelberg (2005)
de’Liguoro, U., Piperno, A.: Nondeterministic extensions of untyped λ-calculus. Information and Computation 122(2), 149–177 (1995)
Krishna Rao, M.: Some characteristics of strong innermost normalization. Theoretical Computer Science 239, 141–164 (2000)
Fernández, M.L., Godoy, G., Rubio, A.: Orderings for innermost termination. In: Giesl, J. (ed.) RTA 2005. LNCS, vol. 3467, pp. 17–31. Springer, Heidelberg (2005)
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van Oostrom, V. (2007). Random Descent. In: Baader, F. (eds) Term Rewriting and Applications. RTA 2007. Lecture Notes in Computer Science, vol 4533. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73449-9_24
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DOI: https://doi.org/10.1007/978-3-540-73449-9_24
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