J. Zobel. Derivation of polymorphic types for Prolog programs. In Logic Programming, ICLP 1987, pages 817--838, 1987. 16  Home/Search   Document Not in Database   Summary   Related Articles   Check

....programs severely by imposing a mode discipline. Moreover, it is an open problem whether his type checking discipline is decidable. Another direction of the syntactic approach investigates type inference for logic programs in the complete absence of programmer provided type declarations [Mis84, Zob87] The semantic approach, to which this thesis contributes, bases logic programming with types on logics that account for sorts. Consequently, the computational mechanisms may change, which typically shows up in the unification procedure. One direction, which appeared with Eqlog [GM86] takes ....

J. Zobel. Derivation of polymorphic types for prolog programs. In Proceedings of the 4th International Conference on Logic Programming, pages 817--838, Cambridge, Mass., 1987. MIT Press.

....calculus. As a consequence, logic programming languages have traditionally been untyped. Nonetheless, it has been shown that types play an important role in the programmer s intended meaning of a logic program [74] Early work on types in logic programming concentrated on descriptive type systems [11, 68, 106, 112]. A descriptive type system is one which does not seek to distinguish between well typed and ill typed programs; instead, it seeks to simply approximate the structure of a program for use by an optimising compiler. The Mycroft O Keefe [70] prescriptive type system integrated the essence of the ....

Justin Zobel. Derivation of polymorphic types for Prolog programs. In Proceedings of the 4th Internation Conference on Logic Programming, pages 817-838, May 1987. 174

....equation 2.1 for T above. In a similar work, logic programs are analysed using nite height [RRS95] or more generally, possessing the nite ascending chain property [GDL95] constraint domains. 2.2. 1 Regular Unary Logic Programs Types for logic programs have been studied by many researchers [Mis84, Zob87, YS91, JB92, HCC94, GdW94]. Any information about the possible types taken by a program at runtime is considered as descriptive typing as opposed to prescriptive typing where programs are checked against type de nitions for compliance. The former typing mechanism is closer to the concept of approximation and thus is the ....

J. Zobel. Derivation of polymorphic types for Prolog programs. In Proceedings of the Fourth International Conference on Logic Programming, pages 817-838. MIT Press, 1987.

....vast literature on prescriptive types is not further discussed here. In the context of descriptive typing some preliminary ideas on the issue of parametric polymorphism are discussed already in (Mishra, 1984) as a possible extension of the presented type checking method for non directional types. (Zobel, 1987) presents a method for deriving syntactic polymorphic types. These types are not directional. They are clearly related to term grammars but the paper does not explain the relationship. Our techniques focus on directional types and are based on semantic considerations. Polymorphic directional ....

Zobel, J. (1987). Derivation of polymorphic types for Prolog programs. Pages 817-- 838 of: Lassez, J-L. (ed), Proceedings of the Fourth International Conference on Logic Programming. MIT Press.

.... write programs without having to define or mention types; rather, the compiler automatically infers types and checks for type correctness [Red88] Given that recognition in the benefit of type checking, the design of type systems for logic programming languages has been studied extensively (cf. [Klu87, Mis84, MO83, Red88, XW88, Zob87]) The basis for descriptive type systems for logic programs was proposed by Mishra [Mis84] a formula that fails may be considered erroneous. Thus, the type of a predicate describes all the terms for which the predicate may succeed. Such types can be called optimistic types [Red88] A type of a ....

....With such rules one can easily simulate Turing machines [Sha84] Thus, improper unary predicate programs can define all recursively enumerable sets of terms. In contrast, as we shall see, proper unary predicate programs define regular sets of terms. Such sets are often used to describe types, cf. [HJ90a, Mis84, YS87, Zob87], though often only a proper subclass of the class of regular term sets is used. 4 Type Inference and Type Checking Our goal in this section is to characterize the complexity of type inference and type checking for types described by unary predicate programs. As a first step we convert proper ....

J. Zobel. Derivation of polymorphic types for Prolog programs. In Proc. 4th International Conference on Logic Programming, pages 817--838, Melbourne, Australia, May 1987. MIT Press. 21

....loops, controlling the depth of the search tree. For each program (to which an oracle predicate is associated) the set of solutions is compared with the set of solutions of a correct program. Several improvements can be made to this domain module, such as the inference of argument types and modes [FD92, Zob87]. Another improvement could be the identification of classes of problems with denotational semantics that support methods for evaluating program equivalence, using techniques similar to those used for proving integrity in deductive databases [Lev91] 5.4 Assembly programming Assembly programming ....

J. Zobel. Derivation of polymorphic types for prolog programs. In Proceedings 4th International Conference on Logic Programming, 1987. 9

....checking comes with the type inferencing done automatically to at least some degree. The purpose of this paper is to study the problem of complete type inferencing for polymorphic ordersorted logic programs. However, among the different approaches to type inferencing in logic programming (e.g. [9, 15, 14, 13, 8]) there are only a few dealing with type inferencing in an polymorphic order sorted setting. Of the cited work, only [13] and [8] explicitly address this topic. However, there are problems with both approaches. As is already pointed out in [12, 13] the type inferencing algorithm presented there is ....

J. Zobel. Derivation of polymorphic types for Prolog programs. In J.-L. Lassez, editor, Proceedings of the Fourth International Conference on Logic Programming, pages 817--838, Melbourne, May 1987. MIT PRESS.

....paradigm, set based analysis involves computing an upper approximation of the success set of a program. This approach could be related to the notion of typing defined in [Mis84] and [MR85] Unlike other works concerning type systems based on the extension of the logical language [MO84] [Zob87], the type of a logic program is simply defined as a recursive (regular) superset of its logical consequences. The intuitive interpretation is that this superset contains the atoms that may succeed for the considered program. For logic programming, set based analysis of a logic program is defined ....

J. Zobel. Derivation of polymorphic types for prolog programs. In Proceedings of the 4 th Int. Conf. on Logic Programming, 1987.

....in its effect to the abstract interpretation method. This applies also to the construction proposed by Fruhwirth et al. to derive a regular program from a uniform one. The phrase type inference was used (in a non standard way) by several authors when speaking of regular approximations. Zobel [32] and Reddy [25] defined algorithms that infer descriptions of success types . Comparison of their results with ours suggests that their results are often less precise, in spite of including parameterised types ( polymorphic types) and are somewhat limited in their handling of mutual recursion. ....

J. Zobel. Derivation of polymorphic types for Prolog programs. In R.A. Kowalski and K. Bowen, editors, Proceedings of the 5th International Conference and Symposium on Logic Programming, MIT Press, 1988.

....Prolog with type systems in the forms of type checking systems [4, 18, 39] and type analysis systems. Type analysis systems infer types from the text of a program. Some type analysis systems infer a type for the program and the type is meant to denote a superset of the success set of the program [1, 2, 10, 16, 19, 20, 37, 42, 48, 49, 50]. Other type analysis systems infer types for procedure calls and successes [6, 22, 24, 27, 28] There are three main approaches to inferring types [20] The first approach obtains from a program P a system of formulae which describes set theoretic relationships between the atoms appearing in P. A ....

....to inferring types [20] The first approach obtains from a program P a system of formulae which describes set theoretic relationships between the atoms appearing in P. A type is then defined to be a distinguished model of the system of formulae. Examples of this approach are to be found in [1, 16, 37, 42, 48, 49, 50]. The second approach uses an abstract immediate consequence operator to approximate the immediate consequence operator T P associated with P [46] A type is defined as a fixed point of the abstract immediate consequence operator. An example of this approach appears in [49] Heintze and Jaffar ....

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J. Zobel. Derivation of polymorphic types for Prolog programs. In J.-L. Lassez, editor, Logic Programming: Proceedings of the fourth international conference, pages 817--838, Australia, 1987.

....would represent the traces as clauses in a logic program, and then compute an approximation that could generate the traces. 6 Related Work and Conclusion The procedure in this paper can be compared to methods for inferring regular descriptions or types for the predicates of logic programs [19], 15] 8] Our method differs in that it is a bottom up fixed point computation. This makes it more precise for some programs, such as looping definitions. For instance, the program fp(x) p(x)g would get an empty approximation using the procedure in this paper, whereas apparently other methods ....

....is successively broken down during the computation. Although [18] contains a definition of an abstraction of the T P operator in order to define a type, similar in spirit to T R P in this paper, it could not used as a means of constructing an approximation. Other methods such as those in [15] and [19] include polymorphism, which our method does not. This gives extra precision where we would obtain any(x) in some cases, since polymorphism captures structure sharing information that cannot be represented in regular structures. The fixed point computation can be expensive for larger programs, ....

J. Zobel. Derivation of polymorphic types for prolog programs. In Proceedings of the 5th International Conference and Symposium on Logic Programming, MIT Press, 1988.

....of logic programs, called regular unary logic programs, and show the equivalence between them. They represent regular types by Deterministic Finite Automata (DFA) and use tuple distributive closure for types as defined by Mishra [18] We adopted their formalism for describing sets of terms. In [23], Zobel presents an approach similar to the one in [18] A syntactic type inference based on a specialisation of the unification algorithm is presented. No type declarations are required. The clauses are explored only once, to ensure termination, so type information is rather imprecise in the case ....

J. Zobel. Derivation of polymorphic types for Prolog programs. In R.A. Kowalski and K. Bowen, editors, Proceedings of the 5th International Conference and Symposium on Logic Programming, MIT Press, 1988.

....This need has arisen mainly in the context of program development, where the detection of such a clause could indicate a bug, since that clause contributes nothing to the program s computation. Such a clause might be considered badly typed . Related topics are discussed in [17] 29] 19] and [30]. Normally a programmer would try not to write useless clauses and so their detection is regarded as debugging. However useless clauses arise more frequently in programs that are generated by transforming some other program. In such cases removal of useless clauses is an important part of the ....

J. Zobel. Derivation of polymorphic types for Prolog programs. In Proceedings of the 5th International Conference and Symposium on Logic Programming. MIT Press, 1988.

....languages are what might be called type languages: the expressions in them denote sets of terms and therefore correspond to types. The description of such languages has generally been complemented by the development of rules for inferring type annotations for the predicates that appear in programs [15, 16, 24, 25, 30]. The idea of descriptive types have several potential uses. The types that are inferred for the predicates in a program may, for instance, constitute useful information for a compiler. Inferred types may similarly be utilized as a form of documentation for a program and may also provide the ....

Zobel, J. Derivation of polymorphic types for Prolog programs. Proceedings of the Fourth International Conference on Logic Programming, Melbourne, 1987, MIT Press, 817 -- 838.

....Normally a programmer would try not to write a program containing useless clauses, but if such useless clauses exist, it could indicate a bug, since these clauses contribute nothing to successful computations. Such clauses might also be considered badly typed . Related topics are discussed in [79, 71, 110, 111]. Useless clauses arise more frequently in programs generated by transformation systems. In the previous chapter our aim was to transform a program into an equivalent program, but with the different instances of inference rules separated out into different clauses. If this is not done, one ....

J. Zobel. Derivation of polymorphic types for Prolog programs. In Proceedings of the 5th International Conference and Symposium on Logic Programming. MIT Press, 1988.

....and flexibility of logic programming, since it requires every predicate symbol to be annotated with a type. Mishra [Mis84] was the first one to show that the idea of type inference that is widely used in functional languages is applicable to logic programs as well. This work was then followed by [MR85, KH85, Zob87, Azz88, Fru88, PR89], where various inference based approaches were studied. The idea of type inference is to let the compiler infer the types of predicates automatically, with little or no declarations supplied by the user. With type inference, the compiler normally cannot detect type errors, since types are ....

....declarations are represented as regular trees and satisfy the well typing principle according to which the inferred typing must cover all atoms that can be successfully derived from the program. This principle is widely accepted in the logic programming community, and several other researchers [Zob87, Azz88, PR89] further extended Mishra s work by proposing different type inference algorithms. In this subsection we explain how T PC captures the notion of Mishra s regular trees and show that his well typing principle is consistent with the notion of type correctness in T PC. In particular, this means that ....

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J. Zobel. Derivation of polymorphic types for Prolog programs. In Proceedings of the Fourth International Logic Programming Conference, Australia, 1987.

....ground type term. 2 3.7 Discussion A notion of regular types has been introduced to logic programming by Mishra [Mis84] The basic idea is to describe a (possibly infinite) set of ground terms using finite representation. Regular types have been used by many authors later. See for instance [YS91, FSVY91, DZ92, PR89, Zob87]. Regular types can be defined by (non parametric) regular term grammars [DZ92] or by restricted class of logic programs [FSVY91, YS91, GdW92, GdW94] They are both equivalent to deterministic root to frontier tree automata [GS97] In most cases regular types obey tuple distributivity restriction. ....

....it seems that tuple distributive regular types are expressive enough to describe commonly used data structures. Another issue is how regular sets of terms are used in the context of typing in logic programming. Often they are used to denote a superset of declarative semantics of the program [YS91, FSVY91, DZ92, Zob87]. They are also used to describe modes [RNP92] and directional types [Boy96] 5 Problem of correctness and completeness of this algorithm is left in [DZ92] as an open question. Chapter 4 Constructing regular approximations of CLP programs Inferring descriptive types means computing an ....

[Article contains additional citation context not shown here]

J. Zobel. Derivation of polymorphic types for Prolog programs. In J-L. Lassez, editor, Proceedings of the Fourth International Conference on Logic Programming, pages 817--838. MIT Press, 1987.

....application has occurred mainly in the context of program development, where the detection of such a clause could indicate a bug, since that clause contributes nothing to the program s computation. Such a clause might be considered badlytyped . Related topics are discussed in [16] 26] 19] [27]. Definition 4.1 useless clause Let P be a normal program and let C 2 P be a clause. Then C is useless if for all goals G, C is not used in any refutation of P [ fGg. A stronger notion of uselessness is obtained by considering particular computations. Definition 4.2 useless clause with respect to ....

J. Zobel. Derivation of polymorphic types for prolog programs. In Proceedings of the 5th International Conference and Symposium on Logic Programming, MIT Press, 1988.

....emptiness, prescriptive type 1 Introduction Types play an important role in programming languages [6] They make programs easier to understand and help detect errors. Types have been introduced into logic programming in the forms of type checking and inference [5,9,12,26,32] or type analysis [25,33,17,19,13,22,7,23] or typed languages [16,21,28,31] Recent logic programming systems allow the programmer to declare types for predicates and type errors are then detected either at compile time or at run time. The reader is referred to [27] for more details on types in logic programming. A type is a possibly ....

....union and complement operations. The decision problems such as the emptiness of a type, inclusion of a type in another and equivalence of two types should be decidable. Regular term languages [14,8] called regular types, satisfy these conditions and have been used widely used as types [29,25,33,9,17,21,28,31,12,32,19,13,22,7,23]. Most type systems use tuple distributive regular types which are strictly less powerful than regular types [29,25,33,17,21,28,31,12,32,19,13,22,7,23] Tuple distributive regular types are regular types closed under tuple distributive closure. Intuitively, the tuple distributive closure of a ....

[Article contains additional citation context not shown here]

J. Zobel. Derivation of polymorphic types for Prolog programs. In J.-L. Lassez, editor, Logic Programming: Proceedings of the fourth international conference, pages 817--838. The MIT Press, 1987.

....paradigm, set based analysis involves computing an upper approximation of the success set of a program. This approach could be related to the notion of typing defined in [Mis84] and [MR85] Unlike other works concerning type systems based on the extension of the logical language [MO84] [Zob87], the type of a logic program is simply defined as a recursive (regular) superset of its logical consequences. The intuitive interpretation is that this superset contains the atoms that may succeed for the considered program. For logic programming, set based analysis of a logic program is defined ....

J. Zobel. Derivation of polymorphic types for prolog programs. In Proceedings of the 4 th Int. Conf. on Logic Programming, 1987.

....to handle more general classes of logic programs and type systems. These works generally fall into two categories: those extending the prescriptive theory of Mycroft and O Keefe (e.g. 7, 17, 31, 12, 16, 10, 27, 13] and those inspired by the descriptive type inference system of Mishra [22, 18, 39, 1, 9, 26, 36, 37, 15, 11]. In the prescriptive approach, Mycroft and O Keefe [23] adopted Milner s slogan that welltyped programs do not go wrong , meaning that if a logic program and a query is well typed, then any SLD derivation of the query with respect to the program will remain well typed. This, however, bases a ....

J. Zobel. Derivation of polymorphic types for Prolog programs. In Proceedings of the Fourth International Logic Programming Conference, pages 817--838, Melbourne, Australia, 1987. MIT Press.

....of assertions this can be formalized as follows: negex(isort(X; Y ) integer list(Y ) not sorted(Y ) The negative existential assertions generalize NO answers to existential queries. It is worth noticing that various notions of types for logic programs discussed in the literature e.g. (Zobel 1987), Mycroft and O Keefe 1984) Nilsson 1983) can be related to negative existential assertions (if an argument in an atom is of a wrong type then the atom should be unsatisfiable ) At every stage of development the program As(IP ) should describe the intended model. A necessary condition for ....

Zobel, J., Derivation of Polymorphic Types for Prolog Programs, in: Lassez, J.L.,(ed), Proceedings of the Fourth International Conference on Logic Programming, Melbourne 1987 : 817-838.

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J. Zobel. Derivation of polymorphic types for Prolog programs. In Logic Programming, ICLP 1987, pages 817--838, 1987. 16

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Justin Zobel. Derivation of polymorphic types for prolog programs. In Proc. of the 1987 International Conference on Logic Programming, pages 817--838, 1987.

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J. Zobel, Derivation of polymorphic types for Prolog programs, Proc. 4th International Conference on Logic Programming, Melbourne, Australia, May 1987, pp. 817--838. 22

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