Martelli, A., Moiso, C., Rossi, G. F., An algorithm for unification in equational theories, In Symposium on Logic Programming (1986), ieee Comp. Soc. Press, pp. 180--186  Home/Search   Document Not in Database   Summary   Related Articles   Check

....They pose interesting but very di#cult semantic questions. 6 Operation of the prototype The interpreter is essentially Prolog with a modified unification algorithm to allow defined functions within terms. The unification algorithm is similar to that given by Martelli, Moiso and Rossi [31]. It e#ectively uses a selection strategy for narrowing described as outer narrowing by You [45, 46] You describes a matching algorithm; we have extended this to a unification algorithm but have not attempted a proof of correctness. The occurs check during unification could perhaps be omitted ....

Martelli, A., Moiso, C., Rossi, G. F., An algorithm for unification in equational theories, In Symposium on Logic Programming (1986), ieee Comp. Soc. Press, pp. 180--186

....variables, say x and y, are to be unified. In this case the equation x =y is delayed and considered as a constraint. It is processed again if either x or y is being instantiated. Herbrand s or Martelli Montanari s transformations have been extended by Kirchner [Kirchner, 1984] Martelli et al. [Martelli et al. 1986], Gallier Snyder [Gallier and Snyder, 1989] and Holldobler [Holldobler, 1987; Holldobler, 1988b] to universal unification procedures for (classes of) conditional equational theories. By theorem 7 lazy resolution and each of these sets of transformations is strongly complete. Yamamoto s ....

Martelli, A., Moiso, C., and Rossi, C. F. (1986). An algorithm for unification in equational theories. In Proceedings of the Symposium on Logic Programming, pages 180--186.

....of two expressions can be computed. This can be done by flattening and SLD resolution (e.g. Barbuti et al. 1986] by paramodulation or special forms of it (e.g. Robinson and Wos, 1969; Fribourg, 1985; Reddy, 1985; Furbach et al. 1989] or by complete sets of transformations [Kirchner, 1984; Martelli et al. 1986; Gallier and Snyder, 1987; Holldobler, 1987b] Let us briefly recall these techniques. Flattening a clause means to replace nested functional expressions by new variables and to add equations between the new variables and the replaced functional expressions to the clause. For example, an atom P ....

....canonical term rewriting system. Then, Gamma v(fx c(a)g) 2 with computed answer substitution fy c(a)g. It should be noted that imitation is the only inference rule which is applicable to y =c(f(y) 7 Discussion We have generalized results obtained by Gallier Snyder [1987; 1988a] and Martelli et al. 1986] to hold for arbitrary equational programs (resp. conditional term rewriting systems) Moreover, we have refined their results: To ensure the completeness of their sets of transformations for canonical term rewriting system, Gallier Snyder as well as Martelli et al. have modified the lazy ....

[Article contains additional citation context not shown here]

A. Martelli, C. Moiso, and C. F. Rossi. An algorithm for unification in equational theories. In Proceedings of the Symposium on Logic Programming, Computer Society, Press of the IEEE, Washington, pages 180--186, 1986.

....is applied, yielding M d 1 . A second instance that was implemented is for EQ as underlying equality theory. The completion of a ground TRS can be computed [9] 25] and moreover, efficient algorithms exist ( 25] Hence, EQ is an equality theory with completion. Our prototype uses narrowing [19] to compute normal E unifiers, and an optimised form of the Knuth Bendix algorithm [15] as completion procedure. The model generator operates on range restricted programs. The fairness condition is implemented using level saturation. Experiments with both systems are promising. They show that the ....

A. Martelli, C. Moiso, and C.F. Rossi. An Algorithm for Unification in Equational Theories. In Proc. of the Symposium on Logic Programming, pages 180--186, 1986.

....influence the complexity of MGU and no relevant advantages can be foreseen by limiting the depth of terms involved in the computation. As a final contribution, we consider these results with respect to the algorithms for parallel unification discussed in the literature [DKM84, Yas84, HJ87, Rob85, MMR86, VS86, KR89, Bar90, Cla91] Most of them do not include reasonable mechanisms to deal with depth, so they have a complexity that is linear with the input depth. We show a version of the currently best known algorithm [DKM84, Yas84, KR89] and discuss the relevance of propagation closure in dealing ....

....homogeneous and acyclic. Section 6 introduces a unification algorithm (see Figure 1) which is based on the computation of the unification closure. The algorithms, defined in the literature, for the computation of mgu by sequential machines [Rob76, Hue76, Bax76, PW78, MM82, CB83, Muk83, Jaf84, MMR86, RP90, BO99] compute in a similar way but exploit different algebraic frameworks and use slightly different presentations of substitutions and hence, of the unifier. Definition 2 (Unification problem) The unification problem MGU is the following decision problem: MGU = fft 1 ; t 2 g j mguft 1 ; ....

[Article contains additional citation context not shown here]

A. Martelli, C. Moiso, and G.F. Rossi. An algorithm for unification in equational theories. In Symposium on Logic Programming, pages 259--282, 1986.

....forces are represented as superscripts in deductive tableaux. 4.3 Deduction Rules We first introduce the basic forms of deduction rules in the deductive tableau synthesis system without the transaction entries. The unification algorithm used in the system is based on equational unification [23]. Two expressions p and q unify under a most general unifier with respect to an equation s = r, if s = r implies that p = q . There are six groups of deduction rules in the system. The propositional and predicate logic tautologies [22] are built into the rewrite rules . The split rules are ....

....the synthesis of iterative programs from relational query specifications [7] There has been essentially no work in the deductive synthesis of database transactions. There have been numerous proposals on improving the effectiveness of theorem proving systems. In particular, equational unification [23] and theory resolution [37] have been widely used by researchers. The strategic aspect of resolution with equality matching has also been investigated [19] These strategies all share the common objective to build axioms into deduction rules. The benefit is to invoke these axioms only when needed, ....

Martelli, A., and Rossi, G., "An Algorithm for Unification in Equational Theories"; Proceedings of the Third Symposium on Logic Programming , 1986, 180-186.

....the annotation of strict arguments, OBJ3 features annotations for the evaluation order of arguments which are somewhat more explicit than ours. It appears that a similar transformation can implement OBJ s annotations. A rule occuring in the context of an E unification algorithm, presented in [MMR86] is called lazy rewriting in [Klo92] It might be interesting to investigate whether our technique of implementing lazy rewriting on eager machinery is useful in that context. In CAML (Categorial ML, CH90] there are lazy constructors, which can be used to achieve effects similar to our ....

A. Martelli, C. Moiso, and C.F. Rossi. An algorithm for unification in equational theories. In Proceedings of the Symposium on Logic Programming, pages 180--186. IEEE Computer Society, 1986.

....it is impossible to construct a (most general) unifier. However, if we can turn the set of equalities under which we want to unify into a complete (normalising and confluent) set of rewriting rules, we can use one of the two algorithms (using narrowing or lazy term rewriting) from Martelli et al. [21, 25] to obtain a most general unifier for terms that are unifiable. If we replace the equality symbol by in our equalities, we obtain a complete set of rewriting rules. We use the recursive path orderings technique as developed by Dershowitz [7, 21] to prove that the rules are normalising, and we ....

.... i j S i (T i Gamma1 Gamma 0 ) w e i : i 8 Tn Gamma 0 (S n Delta Delta Delta S i 1 (P i ) i ) ff 7 f i gae T 0 = fg; T i = S i T i Gamma1 Gamma w polytypic x : ae = case f of ff i e i g : fl Figure 7: The alternative for polytypic in W unification and Martelli et al. s [25] algorithm for semantic unification, and oe is a most general unifier for C and C 0 . Conversely, if no unifier exists, then the unification algorithm fails. 3.4 Type checking the polytypic construct Instances of polytypic functions generated by means of a function defined with the polytypic ....

A. Martelli, C. Moiso, and C.F. Rossi. An algorithm for unification in equational theories. In Proc. Symposium on Logic Programming, pages 180--186, 1986.

....This means that we don t lose completeness when we restrict applications of the narrowing rule to a single equation in each goal. Since narrowing is not easily implemented, several authors studied calculi consisting of a small number of more elementary inference rules that simulate narrowing (e.g. [16, 8, 9, 14, 22, 6]) In this paper we are concerned with a subset (actually the specialization to confluent TRSs) of the calculus trans proposed by Holldobler [9] We call this calculus lazy narrowing calculus (lnc for short) Because the purpose of lnc is to simulate narrowing by more elementary inference rules, ....

....completeness of lnc like calculi is proved under the additional termination assumption. Without this assumption the completeness proof is significantly more involved. It is known that lnc like calculi generate many derivations which produce the same solutions (up to subsumption) Martelli et al. [16, 14] and Holldobler [9] among others, pointed out that many of these redundant derivations can be avoided by giving the variable elimination rule, one of the inference rules of lnc like calculi, precedence over the other inference rules. The problem whether this strategy is complete or not is called ....

[Article contains additional citation context not shown here]

A. Martelli, G.F. Rossi, and C. Moiso, An Algorithm for Unification in Equational Theories, in: Proceedings 1986 Symposium on Logic Programming, (1986) 180--186.

No context found.

Martelli, A., Moiso, C., and Rossi, G. F. (1986), An algorithm for unification in equational theories, Proc. Third Conference on Logic Programming.

No context found.

A. Martelli, C. Moiso, and G. F. Rossi. An algorithm for unification in equational theories. In Proceedings of the IEEE Symposium on Logic Programming, pages 180--186, Salt Lake City, UT, September 1986.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC