D. Miller. Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network of Excellence in Computational Logic, 2(2):63--67, 1995.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....this framework for checking mutual exclusion properties in concurrent systems. Keywords: Disjunctive Logic Programming, Linear Logic Programming, Abstract Interpretation, Petri Nets. APPIA GULP PRODE 2000 1 Introduction Disjunctive Logic Programming (DLP) 9] and Linear Logic Programming (LLP) [8] are among the more interesting extensions of the classical theory of Horn logic, underlying languages like Prolog. The motivations behind the introduction of these two paradigms look quite di erent. On one hand, disjunctive logic programming has been introduced in order to represent uncertain ....

....has been introduced in order to add a declarative notion of state to pure Prolog programs. A closer look at their formal de nition reveals however very interesting connections. Let us focus on the linear logic programming language LO [2] perhaps the rst proposal of linear extension of Prolog [8]. Both DLP and LO programs extend Horn programs allowing clauses with multiple heads. In fact, in DLP we nd clauses of the form p(X) q(X) r(X) t(X) whereas in LO we nd clauses of the form p(X) ....

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D. Miller. Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network of Excellence in Computational Logic, 2(2):63-67, 1995.

....for LO. We hope that our work will open interesting perspectives for the analysis and veri cation of linear logic programming languages. 1. INTRODUCTION In recent years a number of fragments of linear logic [16] have been proposed as a logical foundation for extensions of logic programming [28]. Several new programming languages like LO [4] ACL [24] Lolli [20] and Lygon [17] have been proposed with the aim of enriching traditional logic programming languages like Prolog with a well founded notion of state and with aspects of concurrency. The oper email:bozzano disi.unige.it y ....

D. Miller. A Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network in Computational Logic, 2(2):63-67, 1995.

....particularly well suited for this task. Linear Logic [Gir87] enriches the operational interpretation of classical logic in that formulas can be treated as resources. This idea has been incorporated in recent extensions of Logic Programming, the so called Linear Logic Programming (LLP) paradigm [Mil95] It has been successfully applied to formalize important programming aspects such as data management [HM94,BDM97] object orientation [AP90,DM95,BDLM96] statebased computations [Chi95] and aspects of concurrency [Mil93,MMP96] These features make LLP a suitable framework for specifying ....

D. Miller. Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network of Excellence in Computational Logic, 2(2):63--67, 1995.

....this framework for checking mutual exclusion properties in concurrent systems. Keywords: Disjunctive Logic Programming, Linear Logic Programming, Abstract Interpretation, Petri Nets. APPIA GULP PRODE 2000 1 Introduction Disjunctive Logic Programming (DLP) 9] and Linear Logic Programming (LLP) [8] are among the more interesting extensions of the classical theory of Horn logic, underlying languages like Prolog. The motivations behind the introduction of these two paradigms look quite different. On one hand, disjunctive logic programming has been introduced in order to represent uncertain ....

....in order to add a declarative notion of state to pure Prolog programs. A closer look at their formal definition reveals however very interesting connections. Let us focus on the linear logic programming language LO [2] Linear Objects) perhaps the first proposal of linear extension of Prolog [8]. Both DLP and LO programs extend Horn programs allowing clauses with multiple heads. In fact, in DLP we find clauses of the form p(X) q(X) r(X) t(X) whereas in LO we find clauses of the form p(X) ....

[Article contains additional citation context not shown here]

D. Miller. Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network of Excellence in Computational Logic, 2(2):63--67, 1995.

....around the principles of Lolli. See, for example, CP96] Harland and Pym have also approached the design of linear logic programming languages using the notion of goal directed search [HP91, HP92] A survey of various approaches to using linear logic in logic programming can be found in [Mil95]. 35 5.8 Exercises 1. Below is the specification of two predicates. The greaterEq is the same of in the problem above. Assume that the predicate (greaterEq N M) is provable (consuming no resources) if and only if N is greater than or equal to M. mx N. mx N o a M, greaterEq N M, mx N. sr ....

.... Proof search using linear logic and or Forum has been used to represent object oriented programming languages [DM95, BDLM96] Topics in concurrency have often been addresses as well: see, for example, AP90, AP91] BG96, Gug95, Gug96, Gug94] KY93] and [Mil93] See also the survey paper [Mil95]. 6.5 Exercises 1. The LO logic programming language is based on clauses of the following form. G : j j A j G 1 G 2 j G 1 . ....

Dale Miller. A survey of linear logic programming. Computational Logic: The Newsletter of the European Network in Computational Logic, 2(2):63 -- 67, December 1995. ftp://ftp.cis.upenn.edu/pub/papers/miller/ComputNet95/llsurvey.html.

....which allows one to use them as programming constructs inside an ideal interpreter for the considered logic language. This metaphor, proofs as computations, has been investigated from many different point of views in LL as shown by the works in [3, 2, 24, 27, 29, 18] The reader can refer to [1, 37] to have an extensive bibliography and survey on the topic. We will focus on a particular presentation of LL proof theory based on previous work on Logic Programming and non standard logics [39] 2.2 Forum: Higher Order Linear Logic Forum [36] can be considered as the point of convergence of ....

D. Miller. Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network of Excellence in Computational Logic, 2(2):63--67, 1995.

....database system which incorporates many of the most advanced technologies in the field. Our work is aimed at proposing a formalization of its computational contents by employing the language Ehhf [14] a rich linear logic programming and specification language which is a subset of Forum[34] (a presentation of linear logic in terms of an abstract logic programming language) We will show that the resulting specification captures the most important operational aspects of Chimera at the right level of abstraction, leaving room both for experiments and changes, and for possible ....

D. Miller. Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network of Excellence in Computational Logic, 2(2):63--67, 1995.

....in order to interpret them as description of computation in the target computational model. As described below the main objectives of this approach are: the development of new logic programming languages; the study of linear logic as a logical model for concurrency (the reader can refer to [7, 61] to have an extensive bibliography and survey on the topic) 1.1.1 Concurrency Among the seminal works in the field it is possible to find Kobayashi s and Yonezawa s ACL [48] The former is a presentation of Classical Linear Logic in terms of a model for concurrency. It is based on a one sided ....

D. Miller. Survey of Linear Logic Programming. Computational Logic: The Newsletter of the European Network of Excellence in Computational Logic, 2(2):63--67, 1995.

....calculus around the principles of Lolli. See, for example, CP96] Harland and Pym have also approached the design of linear logic programming languages using the notion of goal directed search [HP91, HP92] A survey of various approaches to using linear logic in logic programming can be found in [Mil95]. 6.8 Exercises 1. Below is the specification of two predicates. The greaterEq is the same of in the problem above. Assume that the predicate (greaterEq N M) is provable (consuming no resources) if and only if N is greater than or equal to M. mx N. mx N o a M, greaterEq N M, mx N. sr nil. sr ....

.... Proof search using linear logic and or Forum has been used to represent object oriented programming languages [DM95, BDLM96] Topics in concurrency have often been addresses as well: see, for example, AP90, AP91] BG96, Gug95, Gug96, Gug94] KY93] and [Mil93] See also the survey paper [Mil95]. 7.3 Exercises 1. The LO logic programming language is based on clauses of the following form. G : j j A j G 1 G 2 j G 1 . ....

Dale Miller. A survey of linear logic programming. Computational Logic: The Newsletter of the European Network in Computational Logic, 2(2):63 -- 67, December 1995. ftp://ftp.cis.upenn.edu/pub/ papers /miller/ComputNet95/llsurvey.html.

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