Maranget L. Optimal derivations in weak -calculi and in orthogonal Term Rewriting Systems. In: Proc. of the 18 th ACM Symposium on Principles of Programming Languages, POPL'91, pp. 255-269, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....relation on redexes in a term, and some axioms giving its important properties. Standard reductions then become some kind of outside in reductions. However, the [GLM92] axioms are 2 Relative Normalization in Stable Deterministic Residual Structures rather restrictive, since even orthogonal DAGs [Mar91, Mar92, KKSV93] do not satisfy them as pointed out by R. Kennaway. Our DRSs are more refined than CTSs [Sta89] since in the latter the residual relation is nonduplicating. We do not impose a nesting relation on redexes, but are still able to prove the RN theorem for all regular stable sets S. We actually prove ....

....results, except for the one in [GlKh94] which is covered by our second RN theorem. It is remarkable that, unlike the proofs in [CuFe58, HuL e91, BKKS87] our first proof does not use the notion of standard reduction. Similar proofs for orthogonal CRSs in [KeSl89] and for orthogonal DAGs in [Mar91, Mar92] use an even stronger termination argument, expressed by the [termination] axiom; they used suitable labelling systems to define notions of family. Our second proof can be seen as a UEA Norwich, UK Technical Report SYS C96 05 John Glauert and Zurab Khasidashvili 19 generalization of that proof ....

Maranget L. Optimal derivations in weak -calculi and in orthogonal Term Rewriting Systems. In: Proc. of the 18 th ACM Symposium on Principles of Programming Languages, POPL'91, pp. 255-269, 1991.

....L ev80] There was no other way Barendregt et al. [BBKV76] showed that there does not exist a onestep optimal recursive fi reduction strategy on terms. Such an implementation has indeed been achieved by Lamping [Lam90] and Kathail [Kat90] reviving interest in optimal graph reduction. Maranget [Mar91] generalized L evy s optimality theory to Orthogonal Term Rewriting Systems (OTRSs) Gonthier et al. [GAL92] simplified Lamping s technique, and Asperti and Laneve generalized both L evy s optimality theory, and Gonthier s implementation of it, to Interaction Systems, which cover most of the ....

.... and Sleep [KeSl89] defined their concept of labelling for orthogonal Combinatory Reduction Systems (CRSs) improving Klop s original labelling system for CRSs [Klo80] which cover orthogonal TRSs and Interaction Systems, and their labelling is different from both Maranget s labelling for OTRSs [Mar91] and Asperti Laneve s labelling for Interaction Systems [AsLa93] This variety of family concepts, and development of alternative graph rewriting algorithms for optimal implementation of orthogonal rewriting systems, such as Term Graph Rewriting [KKSV93] Jungle Rewriting [HoPl91] DAG (Directed ....

[Article contains additional citation context not shown here]

Maranget L. Optimal derivations in weak -calculi and in orthogonal Term Rewriting Systems. In: Proc. POPL'91, p. 255-269.

.... in a needed family (i.e. a family containing a needed redex) is optimal in the sense that it reaches a normal form (when it exists) in a minimal number of family reduction steps [L ev78, L ev80] This theory has been generalized to OTRSs, Interaction Systems, and higher order rewrite systems [Mar91, AsLa93, Oos96], and to the case of relative normalization, to all Deterministic Family Structures [GlKh96] The latter are abstract rewrite systems with axiomatized residual and family relations, and model family concepts in all orthogonal rewrite systems, OERSs among them. Redex families consist of redexes ....

Maranget L. Optimal derivations in weak -calculi and in orthogonal Term Rewriting Systems. In: Proc. POPL'91, p. 255-269.

....There was no other way Barendregt et al. [BBKV76] showed that there does not exist a one step optimal recursive fi reduction strategy on terms. Such an implementation has indeed been achieved by Lamping [Lam90] and Kathail [Kat90] reviving interest in optimal graph reduction. Maranget [Mar91] generalized L evy s optimality theory to Orthogonal Term Rewriting Systems (OTRSs) Gonthier et al. [GAL92] simplified Lamping s technique, and Asperti and Laneve generalized both L evy s optimality theory and Gonthier s implementation of it to Interaction Systems, which cover most of the ....

.... and Sleep [KeSl89] defined their concept of labelling for orthogonal Combinatory Reduction Systems (CRSs) improving Klop s original labelling system for CRSs [Klo80] which cover orthogonal TRSs and Interaction Systems, and their labelling is different from both Maranget s labelling for OTRSs [Mar91] and Asperti Laneve s labelling for Interaction Systems [AsLa93] This variety of family concepts, and development of alternative graph rewriting algorithms for optimal implementation of orthogonal rewriting systems, such as Term Graph Rewriting [KKSV93] Jungle rewriting [HP91] DAG (Directed ....

[Article contains additional citation context not shown here]

Maranget L. Optimal derivations in weak -calculi and in orthogonal Term Rewriting Systems. In: Proc. POPL'91, p. 255-269.

....The way standardization is understood in that paper requires a nesting relation on redexes in a term, and some axioms giving its important properties. Standard reductions then become some kind of outside in reductions. However, the [GLM92] axioms are rather restrictive, since even orthogonal DAGs [Mar91, Mar92, KKSV93] do not satisfy them as pointed out by R. Kennaway. Our DRSs are more refined than CTSs, since in the latter the residual relation is non duplicating. We do not impose a nesting relation on redexes, but are still able to prove the RN theorem for all regular stable sets S. We actually prove the ....

....results, except for the one in [GlKh94] which is covered by our second RN theorem. It is remarkable that, unlike the proofs in [CuFe58, HuL e91, BKKS87] our proof does not use the notion of standard reduction. Similar proofs for orthogonal CRSs in [KeSl89] and for orthogonal DAGs in [Mar91, Mar92] use an even stronger termination argument, expressed by the [termination] axiom; they used suitable labelling systems to define notions of family. Our second proof can be seen as a generalization of that proof method, which was used already by L evy in [L ev78, L ev80] It would be interesting to ....

Maranget L. Optimal derivations in weak -calculi and in orthogonal Term Rewriting Systems. In: Proc. POPL'91, p. 255-269.

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Maranget L. Optimal derivations in weak -calculi and in orthogonal Term Rewriting Systems. In: Proc. of POPL'91, p. 255-269.

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