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Forum: A multipleconclusion specification logic
 Theoretical Computer Science
, 1996
"... The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higherorder program ..."
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Cited by 96 (12 self)
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The theory of cutfree sequent proofs has been used to motivate and justify the design of a number of logic programming languages. Two such languages, λProlog and its linear logic refinement, Lolli [15], provide for various forms of abstraction (modules, abstract data types, and higherorder programming) but lack primitives for concurrency. The logic programming language, LO (Linear Objects) [2] provides some primitives for concurrency but lacks abstraction mechanisms. In this paper we present Forum, a logic programming presentation of all of linear logic that modularly extends λProlog, Lolli, and LO. Forum, therefore, allows specifications to incorporate both abstractions and concurrency. To illustrate the new expressive strengths of Forum, we specify in it a sequent calculus proof system and the operational semantics of a programming language that incorporates references and concurrency. We also show that the meta theory of linear logic can be used to prove properties of the objectlanguages specified in Forum.
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 42 (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...
Linear Behaviour Of Term Graph Rewriting Programs
 Proc. ACM SAC `95
"... The generalised term graph rewriting computational model is exploited to implement concurrent languages based on Girard's Linear Logic (LL). In particular a fragment of LL is identified which is able to serve as a "process calculus" and on which the design of a number of languages can ..."
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Cited by 12 (12 self)
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The generalised term graph rewriting computational model is exploited to implement concurrent languages based on Girard's Linear Logic (LL). In particular a fragment of LL is identified which is able to serve as a "process calculus" and on which the design of a number of languages can be based. It is then shown how this fragment can be mapped onto equivalent sets of graph rewriting rules that both preserve the functionality of the LL connectives and also exploit the properties of linearity for efficient implementation on a distributed architecture. Notions such as channels, production and consumption of messages, and NtoN communication between agents, are interpreted in the world of (term) graph rewriting. This work serves two purposes: i) to extend the notion of Term Graph Rewriting as a generalised computational model for the case of linear concurrent languages, and ii) to act as an initial investigation towards a fully linear term graph rewriting model of computation able to be im...
Semanticspreserving translations between Linear Concurrent Constraint Programming and Constraint Handling Rules ∗
"... The Constraint Simplification Rules (CSR) subset of CHR and the flat subset of LCC, where agent nesting is restricted, are very close syntactically and semantically. The first contribution of this paper is to provide translations between CSR and flatLCC. The second contribution is a transformation ..."
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Cited by 5 (2 self)
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The Constraint Simplification Rules (CSR) subset of CHR and the flat subset of LCC, where agent nesting is restricted, are very close syntactically and semantically. The first contribution of this paper is to provide translations between CSR and flatLCC. The second contribution is a transformation from the full LCC language to flatLCC which preserves semantics. This transformation is similar to λlifting in functional languages. In conjunction with the equivalence between CHR and CSR with respect to original operational semantics, these results lead to semanticspreserving translations from full LCC to CHR and conversely. Immediate consequences of this work include new proofs for CHR linear logic and phase semantics, relying on corresponding results for LCC, plus an encoding of the λcalculus in CHR. 1.
A Survey of Linear Logic Programming
 Computational Logic
, 1995
"... Abstract. Logic programming can be given a foundation in sequent calculus, viewing computation as the process of building a cutfree sequent proof from the bottomup. Earliest accounts of logic programming were based in classical logic and then later in intuitionistic logic. The use of linear logic ..."
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Cited by 4 (0 self)
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Abstract. Logic programming can be given a foundation in sequent calculus, viewing computation as the process of building a cutfree sequent proof from the bottomup. Earliest accounts of logic programming were based in classical logic and then later in intuitionistic logic. The use of linear logic to design new logic programming languages was inevitable given that it allows for more dynamics in the way sequents change during the search for a proof and since it can account for logic programming in these other logics. We overview how linear logic has been used to design new logic programming languages and describe some applications and implementation issues for such languages. §1. Introduction. It is now common place to recognize the important role of logic in the foundations of computer science in general and programming languages more specifically. For this reason, when a major new advance is made in our understanding of logic, we can expect to see that advance ripple into other areas of computer science. Such rippling has been observed during the years
On connections between CHR and LCC
"... Abstract. Both CHR and LCC languages are based on the same model of concurrent computation, where agents communicate through a shared constraint store, with a synchronization mechanism based on constraint entailment. The Constraint Simplification Rules (CSR) subset of CHR and the flat subset of LCC, ..."
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Abstract. Both CHR and LCC languages are based on the same model of concurrent computation, where agents communicate through a shared constraint store, with a synchronization mechanism based on constraint entailment. The Constraint Simplification Rules (CSR) subset of CHR and the flat subset of LCC, where agent nesting is restricted, are very close syntactically and semantically. The first contribution of this paper is to provide translations between CSR and flatLCC and back. The second contribution is a transformation from the full LCC language to flatLCC which preserves semantics. This transformation is similar to λlifting in functional languages. In conjunction with the equivalence between CHR and CSR with respect to naive operational semantics, these results lead to semanticspreserving translations from full LCC to CHR and conversely. Immediate consequences of this work include new proofs for CHR linear logic and phase semantics, relying on corresponding results for LCC, plus an encoding of the λcalculus in CHR. 1
Targeted Communication in Linear Objects
, 1994
"... Linear Objects (LO) of Andreoli and Pareschi is the first proposal to integrate objectoriented programming into logic programming based on Girard's Linear Logic (LL). In LO each object is represented by a separate open node of a proof tree. This "insulates" objects from one another w ..."
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Linear Objects (LO) of Andreoli and Pareschi is the first proposal to integrate objectoriented programming into logic programming based on Girard's Linear Logic (LL). In LO each object is represented by a separate open node of a proof tree. This "insulates" objects from one another which allows the attributes of an object to be represented as a multiset of atoms and thus facilitates easy retrieval and update of attributes. However this separation hinders communication between objects. Communication in LO is achieved through broadcasting to all objects which in our opinion is infeasible from a computational viewpoint. This paper proposes a refined communication mechanism for LO which uses explicit communication channels specified by the programmer. We name it TCLO which stands for "Targeted Communication in LO". Although channel specification puts some burden on the programmer, we demonstrate that the language is expressive enough by redoing some of the examples given for LO. Broadcast...