N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1):69-- 116, 1987. Home/Search Document Not in Database Summary Related Articles Check |
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Termination Proofs for a Lazy Functional Language by Abstract.. - Panitz (1996) (Correct)
....and variable values. It has to be shown that when a previous state is reached again, then the values of arguments and variables will have decreased in some Noetherian ordering. Such orderings for termination proofs have extensively been studied in the area of term rewriting systems, see e.g. [Der87]. Automatic termination provers for functional languages often stay in the tradition of term rewriting and try to generate sufficient ordering relations [Wal94, Gie95a, Gie95b] Such methods can only give termination proofs for applications to arguments that have a finite normal form, i.e. they ....
....means that the path between a recursive pair minimizes an expression. Here we can plug in modules which try to find one of the numerous different orderings for termination proofs proposed in the literature, e.g. polynomial orderings as proposed in [Ste92, Lan79] one of the orderings presented in [Der87] or some sort of generalized orderings based on multi sets as presented in [Mar87] A simple ordering which in many cases is sufficient enough is the ordering which is based on the number of constructors the normal form of an expression has. be a recursive pair such that its ordering ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1):69--116, 1987.
Two Solutions to Incorporate Zero, Successor and Equality in.. - Badban, Pol (Correct)
....R OBDD. It su#ces to prove termination: We apply TRS rules to a given BDD, until we reach a normal form after a finite number of steps, which is guaranteed by termination. The so derived BDD is the R OBDD. We prove termination by means of a powerful tool, the recursive path ordering (# rpo ) [13, 29]. This is a standard way to extend a (total) well founded order on a set of labels to a (total) well founded order on trees over these labels. To this end, we view guards as labels, ordered by Definition 8, and BDDs are viewed as binary trees, so ITE(g, T 1 , T 2 ) corresponds to the tree g(T 1 , ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1--2):69--115, 1987.
Termination Checking with Types: Strong Normalization for.. - Abel (Correct)
....Traditionally, termination has been investigated in the context of term rewriting systems. Research has focused on developing more and more powerful algorithms which accepted more and more programs as terminating. To this end, increasingly strong term orderings have been described (cf. Dershowitz [16], Steinbach [32] Giesl and Arts [7] The methods of term rewriting are transferable to functional and logic programming as follows: The given (untyped) program is translated into a term rewriting system which then is checked for termination. The advantage of this procedure is that the full ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69-- 115, 1987.
MU-TERM version 1.0 User's manual - Lucas (Correct)
....A number of methods have been developed for proving termination of CSR [FR99, GM99, GM01, Luc96, Zan97] they are transformations Theta from TRSs R and replacement maps that produce TRSs R Theta . Then, if we are able to prove termination of R Theta (using the standard methods, see [Der87] for a classic survey) termination of CSR under is ensured for R. Example 2 Consider R and as in Example 1. According to [Luc96] termination of CSR for TRS R under can be proved by proving termination of the following TRS R L : first(0,x) from(x) x) first(s(x) y) y) This ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69-115, 1987.
Improving Dependency Pairs - Giesl, Thiemann, Schneider-Kamp.. (2003) (Correct)
....implemented our results in the automated termination prover AProVE and evaluated them on large collections of examples. 1 Introduction Termination is an essential property of term rewrite systems. Most traditional methods to prove termination of TRSs (automatically) use simplification orders [8, 26], where a term is greater than its proper subterms (subterm property) Examples for simplification orders include lexicographic or recursive path orders [7, 17] the Knuth Bendix order [18] and (most) polynomial orders [20] However, there are numerous important TRSs which are not simply ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69--116, 1987.
Two Solutions to Incorporate Zero, Successor and Equality in.. - Badban, Pol (2002) (Correct)
....R OBDD. It su#ces to prove termination: We apply TRS rules to a given BDD, until we reach a normal form after a finite number of steps, which is guaranteed by termination. The so derived BDD is the R OBDD. We prove termination by means of a powerful tool, the recursive path ordering (# rpo ) [13, 29]. This is a standard way to extend a (total) well founded order on a set of labels to a (total) well founded order on trees over these labels. To this end, we view guards as labels, ordered by Definition 8, and BDDs are viewed as binary trees, so ITE(g,T 1 ,T 2 ) corresponds to the tree g(T 1 ,T 2 ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1--2):69--115, 1987.
Computational Properties of Term Rewriting with Strategy Annotations - Lucas Self-citation (Rewriting) (Correct)
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N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69-115, 1987.
Termination of Associative-Commutative Rewriting.. - Keiichirou.. (2002) Self-citation (Rewriting) (Correct)
....issues, it is very important to authorize extended matching on these kinds of rules. In the rest of the paper, we always consider flat AC rewriting, so for easier reading, we abbreviate into . 2. 3 Term orderings For general notions about term orderings and termination, we refer to [15]. We briefly recall here what we need. With dependency pair criteria, both quasiorderings and strict orderings are used to compare terms. We follow here the notion of ordering pair [10, 20] although we still call it term ordering for simplicity. Definition 2.7 A term ordering is a pair ( of ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1):69--115, Feb. 1987.
Simple Termination of Context-Sensitive Rewriting - Gramlich, Lucas (2002) (3 citations) Self-citation (Rewriting) (Correct)
....languages and computational systems. For instance, in term rewriting systems (TRS s) a proof of termination can be achieved if we are able to find a (monotone and stable) well founded ordering on terms (i.e. a reduction ordering) such that l r for every rule l r of the rewrite system [10, 40]. In practice, if we want to implement a tool for proving termination of a TRS R , we need to make this problem decidable. It is well known that termination of TRSs is an undecidable problem, even for TRSs containing only one rule [7] Hence, we can only provide effective approaches (which yield ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1):69--116, 1987.
Context-Sensitive Rewriting Strategies - Lucas (2000) (2 citations) Self-citation (Rewriting) (Correct)
.... : y) is obtained by removing the non replacing arguments of terms that integrate the rules of R (and by appropriately decreasing the arities of symbols) Termination of R L ensures termination of CSR under for R (see [Luc96] Here, L is terminating: use a recursive path ordering (rpo [Der87, Zan02] with precedence terms : recip; sqr; sqr dbl; s; and first [ Friedman and Wise also use replacement restrictions to provide alternative (more efficient) definitions to logical connectives and, or. In fact, they implement their short cut definitions of these boolean ....
....with left normality, inductive sequentiality, strong sequentiality, etc. on the shape of rules of the TRSs [Ant92, AM96, DM97, HL91, Ken89, O Do77, O Do85, SR93, Toy92] Formal techniques for proving termination are much more general since they usually apply to arbitrary TRSs [AG00, BFR00, Der87] On the other hand, in contrast to termination analysis, checking whether a TRS satisfies the syntactic requirements for applying a given normalizing strategy is usually easy (e.g. with (almost) orthogonality, left normality, inductive sequentiality, etc. In order to formalize the claim that ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69-115, 1987.
Termination of Rewriting with Strategy Annotations - Lucas (2001) (4 citations) Self-citation (Rewriting) (Correct)
....under strategy annotations. Termination of CSR has been studied in [GM99,Luc96,Zan97] In these works, termination of CSR for a given TRS is demonstrated by proving termination of a transformed TRS. In this way, with CSR we can use the standard methods for proving termination of rewriting (see [Der87] for a survey) We prove that the (two) transformations of [GM99] are correct for proving the innermost termination of CSR. The transformation of [Luc96] is correct in the cases that we characterize below. Zantema s transformation [Zan97] does not provide correct proofs of innermost termination of ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69-115, 1987.
Simple Termination of Context-Sensitive Rewriting - Gramlich, Lucas (2002) (3 citations) Self-citation (Rewriting) (Correct)
....languages and computational systems. For instance, in term rewriting systems (TRS s) a proof of termination can be achieved if we are able to find a (monotone and stable) well founded ordering on terms (i.e. a reduction ordering) such that l r for every rule l r of the rewrite system [10, 40]. In practice, if we want to implement a tool for proving termination of a TRS R , we need to make this problem decidable. It is well known that termination of TRSs is an undecidable problem, even for TRSs containing only one rule [7] Hence, we can only provide effective approaches (which yield ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1):69--116, 1987.
Liveness in Rewriting - Giesl, Zantema (2002) (2 citations) Self-citation (Rewriting) (Correct)
....which is a contradiction to the induction hypothesis. ut We now prove that the top rules are crucial for L(R; p) s termination behavior. Lemma 13 Let L (R; p) L(R; p) n f(1) 2)g. Then L (R; p) is terminating. Proof. Termination of L (R; p) can be proved by the recursive path order [4] using the precedence active check match proper start f ok found mark for all f 2 [ fX j x 2 V(p)g. ut Before relating L(R; p) and G , we study the connection of L(R; p) and R . Lemma 14 Let t; u 2 T ( Then we have active(t) mark(u) i t R u and top(active(t) ....
N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69-116, 1987.
A Collection of Examples for Termination of Term Rewriting.. - Arts, Giesl (2001) (7 citations) Self-citation (Rewriting) (Correct)
....applications of term rewrite systems (TRSs) termination is an im portant property. A TRS is said to be terminating if it does not allow infinite reductions. Since termination is in general undecidable [HL78] several methods for proving this property have been developed; for surveys see e.g. Der87,Ste95b] Practically all known methods that are amenable to automation use simplifica tion orderings [Der79,Der87,Ste95b,MZ97] However, there exist numerous term rewrite systems for which termination cannot be proved by this kind of orderings. For that reason, Arts and Giesl ....
....if it does not allow infinite reductions. Since termination is in general undecidable [HL78] several methods for proving this property have been developed; for surveys see e.g. Der87,Ste95b] Practically all known methods that are amenable to automation use simplifica tion orderings [Der79,Der87,Ste95b,MZ97] However, there exist numerous term rewrite systems for which termination cannot be proved by this kind of orderings. For that reason, Arts and Giesl [AG97a,AG97b,AG98,AG00,GA01,GAO01] developed the so called dependency pair approach. Given a TRS, the dependency pair technique ....
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N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1-2):69- 116, 1987.
A Constraint-based Partial Evaluator for Functional - Logic Programs And (Correct)
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N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3(1):69-- 116, 1987.
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N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69--116, 1987.
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N. Dershowitz. Termination of Rewriting. Journal of Symbolic Computation, 3(1&2):69--115, 1987.
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N. Dershowitz. Termination of Rewriting. Journal of Symbolic Computation, 3(1&2):69--115, 1987.
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Dershowitz, N., Termination of rewriting, Journal of Symbolic Computation 3 (1987), pp. 69--116.
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N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69--116, 1987.
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N. Dershowitz. Termination of rewriting. Journal of Symbolic Computation, 3:69-116, 1987.
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N. Dershowitz. Termination of Rewriting. Journal of Symbolic Computation, 3(1,2):69-116, 1987.
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