P. Arenas, A. Gil, F. L'opez-Fraguas. Combining Lazy Narrowing with Disequality Constraints. PLILP'94, Springer LNCS 844, 385-399, 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....alternative is really lazy, that is, it does not require further evaluation of e. Furthermore, the second alternative only requires the evaluation of the argument to hnf. Due to the lack of space, we are not able to describe the complete rules for . The rules described in [17] and formalized in [1] can be adapted to include universally quantified disequalities in the vein of [24] is also responsible of the decision about if a constraint c is satisfiable or not. In general, it is enough to have each e i ; e 0 j in head normal form (hnf) i.e. a variable or an expression with a ....

....context of lazy evaluation. The key point is the inclusion of new ffi expressions into the constraint, where they are handled lazily. We compare our work with some related papers in to areas. First, we deal with works about the combination of laziness and constraints. As far as we know, only [19, 17, 1] attack the problem. The first one introduces a general framework to integrate functional programming, logic programming and constraints. 17] presents a method to compute equality and disequality constraints over the (infinitary) Herbrand universe in a lazy way. The description is very related to ....

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P. Arenas, A. Gil, F. L'opez-Fraguas. Combining Lazy Narrowing with Disequality Constraints. PLILP'94, Springer LNCS 844, 385-399, 1994.

....the three first nodes develop their own approach, although the resulting boundaries are loose. UCM developed a generic framework for multiparadigm declarative programming with constraints, which was applied to the design of a functional logic programming language with disequality constraints [60, 5]. This work includes a model theoretic and operational semantics of functional logic languages [43, 59] as well as the study of extensions of first order logic allowing to reason about higher order functions and partially defined values [43] TUM made important progress in the theory of ....

P. Arenas-S'anchez, A. Gil-Luezas, and F.J. L'opez-Fraguas. Combining lazy narrowing with disequality constraints. In Programming Language Implementation and Logic Programming (PLILP'94), volume 844 of Lecture Notes in Computer Science, pages 385--399. Springer, 1994. Extended version available as TR DIA 94/2.

....#f represents the Prolog predicate associated to f . Every program rule f(t1 ; tn) r ( C is translated to #f(E1 ; En ; r) Gammaunif y(E1 ; t1 ) unify(En ; tn) solve conditions(C) This translation of a program rule differs from other translations in the literature [3]. In effect, instead of the computation of the head normal 8 Furthermore, in the goal solver we suppose a preprocess which collects in TV ar, type variables occurring in the goal, and a postprocess which collects in AX, type variables ff X of data variables X remaining free in the answer (remark ....

....Prolog variable if f(e 1 ; e n ) has not been evaluated, and otherwise it represents the evaluation state of f(e 1 ; e n ) that is, if f(e 1 ; e n ) has been evaluated to e 0 (not necessarily in head normal form) then S represents e 0 . This differs from previous works [3], which focus on head normal forms and not on intermediate steps. 6 Type Analysis Essentially, the idea of type analysis is to require a stronger static well typedness condition to program rules and queries. The static well typedness condition we have required so far allows to type program rules ....

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P.Arenas-S'anchez, A.Gil-Luezas, F.J.L'opez-Fraguas. Combining Lazy Narrowing with Disequality Constraints, Procs. PLILP'94, LNCS 844, pp. 385-399, 1994.

....53] and logic programming [55, 35, 12] showing how to add type conditions to program rules and goals and how to check and simplify them. Our framework has been developed in the context of the works [24, 23, 9, 22, 15] which have in uenced to the design of the functional logic languages BABLOG [8] and T OY[15, 41] The latter language additionally works with disequality constraints, constraints over real numbers and higher order functions. It is planned to extend the current implementation with algebraic types [9] and subtypes. Following this line of research, programs in our framework ....

P. Arenas-Sanchez, A. Gil-Luezas, and F. J. Lopez-Fraguas. Combining lazy narrowing with disequality constraints. In Proceedings of the PLILP'94, pages 385-401. Springer Verlag LNCS 844, 1994.

....result. It may be defined as follows: infixr 10 ( E1 E2 = E1 ( E1 E2 = E2 The infixr declaration fix the priority of the function as infix operator (10) and its associativity (right) 2 A full implementation of the function = requires to incorporate disequality constraints, like in [AGL94], and T OY indeed features them, but we will not use this aspect of the language. Our language adopts the so called call time choice semantics for non deterministic functions, following [Hus93, GH 96] Call time choice has the following intuitive meaning: given a function call (f e 1 . e n ....

P. Arenas-S'anchez, A.Gil-Luezas, F.J. L'opez-Fraguas. Combining Lazy Narrowing with Disequality Constraints. Procs. of PLILP'94, Springer LNCS 844, 385--399, 1994.

....fff1 ; ff mg = tvar( 0 )n [ n i=1 tvar( i ) We suppose in the rest of the paper that the signature has been completed in this way. 3. 2 Typed Programs Typed programs in our language consist of a set of conditional constructor based rewriting rules in the line of BABEL [MoRo92] and BABLOG [AGL94]. Definition 6 (Program Rule) A program rule is of the form: f(t 1 ; t n ) r ( CD2C T where f(t 1 ; t n ) is called head, r is called body and CD2C T is called rule condition (CD is called data condition and C T type condition) satisfying the following requirements: ffl f 2 FUN of ....

P. Arenas-S' anchez, A.Gil-Luezas, F.L' opez-Fraguas. Combining Lazy Narrowing with Disequality Constraints, Procs. PLILP'94, Springer LNCS 844, pp. 385-399, 1994.

....the sense of, e.g. 22] in the same way that CLP (X ) extended traditional logic programming. There are other proposals [3, 23] for CFLP (see [21] for a comparison) but, as far as we know, they have not fructi ed in the development of concrete, practical languages, maybe with the exception of [1] where a lazy FLP language is extended to cope with disequality constraints over syntactic terms (see [21] for a thorough exposition of that language and the CFLP (X ) scheme) We have recently known of a work [5] still in quite an early stage of development, where the functional logic language ....

....the ETC translation the technique introduced by Cheong for implementing sharing 4 by means of Prolog variables. There are still many sources for optimizing the translation. For instance, the occur check scheme performs redundant work in many occasions. A more eOEcient version similar to that in [1, 21] could be implemented. 4 Due to space limitations we omit the needed modi cations which can be found in [2] Multi Paradigm Logic Programming For dds and similar strategies, there are some additional known optimizations [10] that may be successfully applied as redundant constructor elimination ....

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Arenas-S#nchez P., Gil-Luezas A., L#pez-Fraguas F.J.: Combining Lazy Narrowing with Disequality Constraints. Procs. of Int. Symp. on Programming Language Implementation and Logic Programming (PLILP'94), Springer LNCS 844, 385399, 1994.

....Project TIC95 0433 C03 01 CPD . The implementation of the language is presented by giving a Prolog specification of the operational semantics. This specification is based on ideas of [CF93] for the translation of lazy narrowing into Prolog, and extends previous implementations of lazy narrowing [LLR93, AGL94] to typed lazy narrowing. 2 The Programming Language Both parametric and order sorted polymorphisms are expressed in our language by using polymorphic signatures Sigma which consist of: a type specification containing a ranked set of polymorphic type constructors, partially ordered by . For ....

.... For instance, second(X) head(tail(X) X : nelist(ff) tail(X) nelist(ff) would be translated as: #second(E; head(tail(X) Gammaunif y(E; X) solve conditions(X : nelist(ff) tail(X) nelist(ff) This translation of a program rule differs from other translations in the literature [AGL94]. In effect, instead of the computation of the head normal form of f( e) the #f predicate computes a first approximation of f( e) the body r of a rule) via the application of the rule. This is due to the fact that type constraints solving does not need head normal norms. Then hnf predicate is ....

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P. Arenas-S' anchez, A. Gil-Luezas, F. J. L' opez-Fraguas. Combining Lazy Narrowing with Disequality Constraints, Procs. PLILP'94, LNCS 844, pp. 385-399, 1994.

....show in figure 3 a generic module Sorting which requires a data type with total order to define the generic sort operator and the generic predicate ordered on sequences. This module uses the generic type of sequences which is available in the predefined library of lpg and values can be written as [1,2,3] instead of cons(1,cons(2,cons(3,nil) The notation seq[elem] stands for the sort of the sequences where the sort of elements is elem. In the module Sorting, the equation number 4 contains a conditional expression, like in functional languages. Such an equation is equivalent to the two ....

....to denote such instantiated objects. Specially, a notation with explicit parameters is allowed; generic sorts are associated with sorts of the model, as in seq[nat] and operators or predicates are associated with effective operators and predicates of the parameter passing model, as in sort[ [3,2,4]) which is an occurrence of the operator declared in Sorting with the model of decreasing order on the natural numbers. In Figure 4, we present examples of definitions of generic predicates which can be used as higher order predicates. property Function sorts t1,t2 operators f: t1 t2 ....

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P. Arenas-Sanchez, A. Gil-Luezas, and J. Lopez-Fraguas. Combining Lazy narrowing with Disequality Constraints. In Proc. of PLILP'94, pages 385--399. LNCS 844, 1994.

.... bindings (bindings which do not hold) GK93, LG97a, SGJ94, Tur86] We think that we can strengthen this effect in the setting of (equational) constraint logic programming [AFL95, JL87] by using some kind of narrowing procedure with disunification, such as the ones defined in Arenas et al. AGL94] Bert and Echahed [BE95] Fern andez [Fer92] and Ram irez and Falaschi [RF93] in order to propagate (negative) bindings which can be gathered during the transformation as (disequality) constraints. Our results are also relevant for the definition of a compositional semantics for functional ....

P. Arenas, A. Gil, and F. L'opez. Combining lazy narrowing with disequality constraints. In Proceedings of the 6th International Symposium on Programming Language Implementation and Logic Programming, volume 844 of Lecture Notes in Computer Science, pages 385--399, Berlin, 1994. Springer-Verlag.

....deduce the type. The type system we present is based on that presented in [HiTo92] Hence it allows subtype relations between type constructors with the same arity, defining a quasi lattice and satisfying the monotonicity property. Our language ISHTAR follows the line of BABEL [MoRo92] and BABLOG [AGL94]. The programs consist of a specification of types, type declarations for data constructors and functions and a set of constructor based well typed conditional rewriting rules. The rule conditions include data and type conditions and work as constraints for the rule applicability. The user can ....

P. Arenas-S' anchez, A.Gil-Luezas, F.L' opez-Fraguas. Combining Lazy Narrowing with Disequality Constraints, Procs. PLILP'94, Springer LNCS 844, pp. 385-399, 1994.

....sense of, e.g. 18] in the same way that CLP (X ) extended traditional logic programming. There are other proposals for CFLP (see e.g. 17] for commented references) but, as far as we know, they have not fructified in the development of concrete, practical languages, maybe with the exception of [1] where a lazy FLP language is extended to cope with disequality constraints over syntactic terms (see [17] for a thorough exposition of that language and the CFLP (X ) scheme) We have recently known of a work [4] still in quite an early stage of development, where the functional logic language ....

....the ETC translation the technique introduced by Cheong for implementing sharing 3 by means of Prolog variables. There are still many sources for optimizing the translation. For instance, the occur check scheme performs redundant work in many occasions. A more efficient version similar to that in [1, 17] could be implemented. 5 Conclusions We have presented CFLP (R) a functional logic programming language enhanced with the possibility of using real arithmetic constraints. By means of examples we have shown the interest of the language for a wide range of problems which include all CLP (R) ....

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Arenas-S'anchez P., Gil-Luezas A., L'opez-Fraguas F.J.: Combining Lazy Narrowing with Disequality Constraints. Procs. of PLILP'94, Springer LNCS 844, 385--399, 1994.

....of concrete, practical languages. In this paper we describe the language CFLP (R) which incorporates real arithmetic constraints to a higher order lazy nondeterministic functional logic language in the spirit of [7, 8] The language incorporates also syntactic disequality constraints in the way of [2]. The language has been implemented in the system TOY(R) http: mozart.mat.ucm.es incoming comprimidos toyr.tar.gz) which is an extension of the FLP system TOY (http: mozart.mat. ucm.es incoming comprimidos toy.tar.gz) The rest of the paper is organized as follows: in Sect. 2 we shortly ....

....CLP (R) philosophy: non linear constraints are delayed. For the non real case, and = are interpreted as strict equality and disequality. Such constraints are transformed into some kind of solved forms. For instance, X= Y; Z] which covers infinite positive cases) is a solved form (see [2, 19] for details) Goals take the form 1 ; k . Solving a goal means obtaining conditions (a mixture of substitution and constraints) over their variables ensuring the satisfiability of the goal. To give a complete semantic characterization of CFLP (R) is far out of the scope of this ....

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Arenas-S'anchez P., Gil-Luezas A., L'opez-Fraguas F.J.: Combining Lazy Narrowing with Disequality Constraints. Procs. of PLILP'94, Springer LNCS 844, 385--399, 1994.

....1, the type condition tail(X) nelist(ff) in the rule for second, allows to deduce head(tail(X) ff. However there are not any environment allowing to deducing it. For terms, environments are enough. 2. 1 Typed Programs Typed programs consist of a set of conditional rewriting rules [MoRo92] [AGL94] with data and type conditions working as constraints for the rule applicability. Definition 5 (Program Rule) A program rule has the form: f(t 1 ; t n ) r ( CD2C T where f(t 1 ; t n ) is called head, r is called body and CD2C T is called rule condition (CD is called data ....

P. Arenas-S' anchez, A. Gil-Luezas, F. L' opez-Fraguas. Combining Lazy Narrowing with Disequality Constraints, Proc. PLILP'94, LNCS 844, 385-399, 1994.

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