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Higherorder logic programming
 HANDBOOK OF LOGIC IN AI AND LOGIC PROGRAMMING, VOLUME 5: LOGIC PROGRAMMING. OXFORD (1998
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ACL  A Concurrent Linear Logic Programming Paradigm
 Proceedings of the 1993 International Logic Programming Symposium
, 1993
"... We propose a novel concurrent programming framework called ACL. ACL is a variant of linear logic programming, where computation is described in terms of bottomup proof search of some formula in linear logic. The whole linear sequent calculus is too nondeterministic to be interpreted as an operatio ..."
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Cited by 46 (4 self)
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We propose a novel concurrent programming framework called ACL. ACL is a variant of linear logic programming, where computation is described in terms of bottomup proof search of some formula in linear logic. The whole linear sequent calculus is too nondeterministic to be interpreted as an operational semantics for a realistic programming language. We restrict formulas and accordingly refine inference rules for those formulas, hence overcoming this problem. Don't care interpretation of nondeterminism in the resulting system yields a very clean and powerful concurrent programming paradigm based on messagepassing style communication. It is remarkable that each ACL inference rule has an exact correspondence to some operation in concurrent computation and that nondeterminism in proof search just corresponds to an inherent nondeterminism in concurrent computation, namely, nondeterminism on message arrival order. We demonstrate the power of our ACL framework by showing several programm...
Applications of Linear Logic to Computation: An Overview
, 1993
"... This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, li ..."
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Cited by 41 (3 self)
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This paper is an overview of existing applications of Linear Logic (LL) to issues of computation. After a substantial introduction to LL, it discusses the implications of LL to functional programming, logic programming, concurrent and objectoriented programming and some other applications of LL, like semantics of negation in LP, nonmonotonic issues in AI planning, etc. Although the overview covers pretty much the stateoftheart in this area, by necessity many of the works are only mentioned and referenced, but not discussed in any considerable detail. The paper does not presuppose any previous exposition to LL, and is addressed more to computer scientists (probably with a theoretical inclination) than to logicians. The paper contains over 140 references, of which some 80 are about applications of LL. 1 Linear Logic Linear Logic (LL) was introduced in 1987 by Girard [62]. From the very beginning it was recognized as relevant to issues of computation (especially concurrency and stat...
HigherOrder Concurrent Linear Logic Programming
 In Theory and Practice of Parallel Programming
, 1995
"... . We propose a typed, higherorder, concurrent linear logic programming called higherorder ACL, which uniformly integrates a variety of mechanisms for concurrent computation based on asynchronous message passing. Higherorder ACL is based on a proof search paradigm according to the principle, p ..."
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Cited by 30 (8 self)
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. We propose a typed, higherorder, concurrent linear logic programming called higherorder ACL, which uniformly integrates a variety of mechanisms for concurrent computation based on asynchronous message passing. Higherorder ACL is based on a proof search paradigm according to the principle, proofs as computations, formulas as processes in linear logic. In higherorder ACL, processes as well as functions, and other values can be communicated via messages, which provides high modularity of concurrent programs. Higherorder ACL can be viewed as an asynchronous counterpart of Milner's higherorder, polyadic  calculus. Moreover, higherorder ACL is equipped with an elegant MLstyle type system that ensures (1) well typed programs can never cause type mismatch errors, and (2) there is a type inference algorithm which computes a most general typing for an untyped term. We also demonstrate a power of higherorder ACL by showing several examples of "higherorder concurrent prog...
Automated Protocol Verification in Linear Logic
, 2002
"... In this paper we investigate the applicability of a bottomup evaluation strategy for a first order fragment of linear logic [7] for the purposes of automated validation of authentication protocols. Following [11], we use multiconclusion clauses to represent the behaviour of agents in a protocol ..."
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Cited by 15 (1 self)
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In this paper we investigate the applicability of a bottomup evaluation strategy for a first order fragment of linear logic [7] for the purposes of automated validation of authentication protocols. Following [11], we use multiconclusion clauses to represent the behaviour of agents in a protocol session, and we adopt the DolevYao intruder model and related message and cryptographic assumptions. Also, we use universal quantification to provide a logical and clean way to express creation of nonces. Our approach is well suited to verify properties which can be specified by means of minimality conditions. Unlike traditional approaches based on modelchecking, we can reason about parametric, infinitestate systems, thus we do not pose any limitation on the number of parallel runs of a given protocol. Furthermore, our approach can be used both to find attacks and to prove correctness of protocols. We present some preliminary experiments which we have carried out using the above approach.
Static Analysis of Linear Logic Programming
 NEW GENERATION COMPUTING
, 1997
"... Linear Logic is gaining momentum in computer science because it offers a unified framework and a common vocabulary for studying and analyzing different aspects of programming and computation. We focus here on models where computation is identified with proof search in the sequent system of Linear ..."
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Cited by 13 (3 self)
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Linear Logic is gaining momentum in computer science because it offers a unified framework and a common vocabulary for studying and analyzing different aspects of programming and computation. We focus here on models where computation is identified with proof search in the sequent system of Linear Logic. A proof normalization procedure, called "focusing", has been proposed to make the problem of proof search tractable. Correspondingly,
Specifying RealTime FiniteState Systems in Linear Logic
 In 2nd International Workshop on Constraint Programming for TimeCritical Applications and MultiAgent Systems (COTIC
, 1998
"... Realtime finitestate systems may be specified in linear logic by means of linear implications between conjunctions of fixed finite length. In this setting, where time is treated as a dense linear ordering, safety properties may be expressed as certain provability problems. These provability proble ..."
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Cited by 12 (4 self)
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Realtime finitestate systems may be specified in linear logic by means of linear implications between conjunctions of fixed finite length. In this setting, where time is treated as a dense linear ordering, safety properties may be expressed as certain provability problems. These provability problems are shown to be in pspace. They are solvable, with some guidance, by finite proof search in concurrent logic programming environments based on linear logic and acting as sort of modelcheckers. One advantage of our approach is that either it provides unsafe runs or it actually establishes safety. 1 Introduction There are a number of formalisms for expressing realtime processes, including [1, 6, 7, 3, 4, 5, 50, 44, 45, 38]. Many of these realtime formalisms are based on temporal logic or its variations [46, 38, 33] or on timed process algebras [14, 42, 43, 23, 12], or on Buchi automata [52, 3]. In some cases exact complexitytheoretic information is available, such as [51, 3, 5], while ...
An Effective Fixpoint Semantics for Linear Logic Programs
 THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2002
"... In this paper we investigate the theoretical foundation of a new bottomup semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically ..."
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Cited by 11 (3 self)
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In this paper we investigate the theoretical foundation of a new bottomup semantics for linear logic programs, and more precisely for the fragment of LinLog (Andreoli, 1992) that consists of the language LO (Andreoli & Pareschi, 1991) enriched with the constant 1. We use constraints to symbolically and finitely represent possibly infinite collections of provable goals. We define a fixpoint semantics based on a new operator in the style of TP working over constraints. An application of the fixpoint operator can be computed algorithmically. As sufficient conditions for termination, we show that the fixpoint computation is guaranteed to converge for propositional LO. To our knowledge, this is the first attempt to define an effective fixpoint semantics for linear logic programs. As an application of our framework, we also present a formal investigation of the relations between LO and Disjunctive Logic Programming (Minker et al., 1991). Using an approach based on abstract interpretation, we show that DLP fixpoint semantics can be viewed as an abstraction of our semantics for LO. We prove that the resulting abstraction is correct and complete (Cousot & Cousot, 1977; Giacobazzi & Ranzato, 1997) for an interesting class of LO programs encoding Petri Nets.
Concurrent Constraint Programming and NonCommutative Linear Logic (Extended Abstract)
, 1996
"... This paper presents a precise connection between a noncommutative version of intuitionistic linear logic (INLL) and concurrent constraint programming (cc). The contribution of this paper is twofold: ffl on the one hand, we refine existing logical characterizations of operational aspects of concu ..."
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Cited by 9 (5 self)
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This paper presents a precise connection between a noncommutative version of intuitionistic linear logic (INLL) and concurrent constraint programming (cc). The contribution of this paper is twofold: ffl on the one hand, we refine existing logical characterizations of operational aspects of concurrent constraint programming, by providing a logical interpretation of finer observable properties of cc programs, namely successes and suspensions. ffl on the other ha...
Logical, Testing, and Observation Equivalence for Processes in a Linear Logic Programming
, 1993
"... Linear logic programming has recently been proposed and shown to be able to integrate a wide range of mechanisms for concurrent computation uniformly in terms of proof search. This paper introduces several process equivalence relations for linear logic programming and investigate relationships betwe ..."
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Cited by 9 (1 self)
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Linear logic programming has recently been proposed and shown to be able to integrate a wide range of mechanisms for concurrent computation uniformly in terms of proof search. This paper introduces several process equivalence relations for linear logic programming and investigate relationships between them in order to establish foundations for program transformation in linear logic programming. We also introduce unfold/fold transformation procedure for linear logic programming and prove its soundness with respect to a testing equivalence. 1 Introduction Linear logic programming, where computation is described in terms of a bottomup proof search in linear logic[5], has recently been investigated as frameworks for novel concurrent programming languages[3][2][6][7][8][12]. The general goal of this paper is to investigate several equivalence relations for processes in linear logic programming, by which establishing foundations for program transformation in linear logic programming. In th...