T. Genet. Termination proofs using gpo ordering constraints. In M. Bidoit and M. Dauchet, editors, Proceedings 22nd International Colloquium on Trees in Algebra and Programming, volume 1214 of Lecture Notes in Computer Science, pages 249--260. Springer-Verlag, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... the rewriting process [18, 19] This group and their collaborators have developed a very impressive collection of examples and case studies in areas such as logic programming languages, constraint solving, higher order substitution, equational theorem proving and other such computational systems [79, 160, 81, 16, 26, 145, 61, 62]. Besides the ELAN interpreter, there is ongoing work on compilation techniques, including compilation of ACrewriting [130] A nice feature of rewriting logic, namely its natural way of dealing with concurrency and interaction, is exploited by Viry to treat input output for ELAN within the logic ....

.... automated deduction inference systems, including logical languages, unification and narrowing [79, 160] Knuth Bendix completion with constraints [81] higher order unification [16] combination of unification algorithms [145] constraint solving [26] and termination and tree automata techniques [61, 62]. In a somewhat similar vein, the work of Levy and Agust i [96, 95, 97] and of Schorlemmer [148] explores the relationships between rewriting logic and their general bi rewriting approach to automated deduction. Using a high performance reflective rewriting logic language like Maude it is ....

T. Genet. Termination proofs using gpo ordering constraints. In M. Bidoit and M. Dauchet, editors, Proceedings 22nd International Colloquium on Trees in Algebra and Programming, volume 1214 of Lecture Notes in Computer Science, pages 249--260. Springer-Verlag, 1997.

....ELAN was used in order to implement a predicate prover based on the rules proposed by J. R. Abrial, and implemented in the B tools [Abr96] We developed also a propositional sequent calculus, completion procedures for rewrite systems [20] sufficient conditions for the termination problem [17]. A library for automata construction and manipulation has been designed. Approximation automata are used to check conditions for reachability, sufficient completeness, absence of conflicts in systems described by non conditional rewrite rules [16] Solving: The notion of rewriting controlled by ....

T. Genet and I. Gnaedig. Termination Proofs using gpo Ordering Constraints. In M. Bidoit and M. Dauchet, editors, Proceedings 22nd International Colloquium on Trees in Algebra and Programming, Lille (France), volume 1214 of Lecture Notes in Computer Science, pages 249--260. Springer-Verlag, 1997.

....which we call, non inductive simply terminating functions form an important class of functions used in recursive data structures and hence, automatically establishing their termination is an important property. This is witnessed by the recent literature where techniques coming from rewriting [6, 1, 2, 8] have been proposed to automate the termination of such functions. We are interested in automating the termination (inductive or non inductive) of recursive functions in a theorem proving framework. We choose the framework of the system called ProPre developed in [17, 15, 16] which is also the one ....

T. Genet and I. Gnaedig. Termination proofs using gpo ordering constraints. TAPSOFT, LNCS 1214, 249-260, 1997.

....completes rewrite systems using the general path ordering found before. These applications do not need to be modified. Other applications, even not written in ELAN, may be combined in a similar way. For example, we could replace the ELAN implementation of the procedure gpo by its ECLIPSE version [10], or by another implementation of a different ordering. An alternative approach extends these applications by a REF interface. Now, it is possible only for applications written in ELAN, C or JAVA, because the parsers of the REF format are currently available only for these environments. In our ....

T. Genet and I. Gnaedig. Termination Proofs using gpo Ordering Constraints. In M. Dauchet, editor, Proceedings 22nd International Colloquium on Trees in Algebra and Programming, Lille (France), volume 1214 of Lecture Notes in Computer Science, pages 249--260. Springer-Verlag, 1997.

....(iii) Theta(s) lex Theta(t) ioe Theta(s) lex Theta(t) or Theta(s) lex Theta(t) With this extension of the termination functions to T (F; X) the de nition of the general path ordering is extended to T (F; X) From now on, we will use the de nition of gpo on T (F; X) Theorem 4. [5] The general path ordering gpo is a quasi ordering on T (F; X) having the subterm property. Proposition 5. 5] Ground stability) Let s; t 2 T (F; X) and Phi = Theta; lex ) If s Phi gpo t (resp. s Phi gpo t) then for any substitution oe s.t. soe; toe 2 T (F ) we have soe Phi ....

....of the termination functions to T (F; X) the de nition of the general path ordering is extended to T (F; X) From now on, we will use the de nition of gpo on T (F; X) Theorem 4. 5] The general path ordering gpo is a quasi ordering on T (F; X) having the subterm property. Proposition 5. [5] (Ground stability) Let s; t 2 T (F; X) and Phi = Theta; lex ) If s Phi gpo t (resp. s Phi gpo t) then for any substitution oe s.t. soe; toe 2 T (F ) we have soe Phi gpo toe (resp soe Phi gpo toe) Thanks to Proposition 5, for proving the rst condition of Theorem 2 ....

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T. Genet and I. Gnaedig. Termination proofs using gpo ordering constraints (extended version). Technical report, INRIA, 1997. RR-3087, available at http://www.loria.fr/equipe/protheo.html.

....: g. Verifying if a division by 0 can occur is equivalent to check whether the pattern div(x; 0) is R reachable from E, i.e. whether 9C[ 9oe, s.t. C[div(x; 0)oe] 2 R (E) 2. 3 Termination under Sequential Reduction Strategy Many works are devoted to automatising termination proofs of TRSs [1,14]. On the other hand, it is interesting to study weaker forms of termination, since for many purposes weak normalisation is enough. In theorem provers and programming languages, rules are always applied under a specific strategy, and it is enough to ensure termination under this strategy. In ....

T. Genet and I. Gnaedig. Termination proofs using gpo ordering constraints. In M. Dauchet, editor, Proc. 22nd CAAP Conf., Lille (France), volume 1214 of LNCS, pages 249--260. Springer-Verlag, 1997.

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