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A Brief Guide to Linear Logic
, 1993
"... An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation. ..."
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Cited by 53 (8 self)
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An overview of linear logic is given, including an extensive bibliography and a simple example of the close relationship between linear logic and computation.
Domain theory for concurrency
, 2003
"... Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey. ..."
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Cited by 23 (6 self)
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Concurrent computation can be given an abstract mathematical treatment very similar to that provided for sequential computation by domain theory and denotational semantics of Scott and Strachey.
The essence of dataflow programming
 In APLAS
, 2005
"... Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure ..."
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Cited by 18 (3 self)
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Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure contextdependent computation. In particular, we develop a generic comonadic interpreter of languages for contextdependent computation and instantiate it for streambased computation. We also discuss distributive laws of a comonad over a monad as a means to structure combinations of effectful and contextdependent computation. We apply the latter to analyse clocked dataflow (partial stream based) computation. 1
Axiomatic Domain Theory
 in Categories of Partial Maps. Distinguished Dissertation Series
, 1995
"... The denotational semantics approach to the semantics of programming languages interprets the language constructions by assigning elements of mathematical structures to them. The structures form socalled categories of domains and the study of their closure properties is the subject of domain theory ..."
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Cited by 16 (2 self)
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The denotational semantics approach to the semantics of programming languages interprets the language constructions by assigning elements of mathematical structures to them. The structures form socalled categories of domains and the study of their closure properties is the subject of domain theory [Sco70, Sco82, Plo83, GS90, AJ94]. Typically, categories of domains consist of suitably complete partially ordered sets together with continuous maps. But, what is a category of domains? The main aim of axiomatic domain theory is to answer this question by axiomatising the structure needed on a mathematical universe so that it can be considered a category of domains. Criteria required from categories of domains can be of the most varied sort. For example, we could ask them to * have a rich collection of type constructors: sums, products, exponentials, powerdomains, dependent types, polymorphic types, etc; * have fixedpoint operators for programs and type constructors; * have only computable maps [Sco76, Smy77, Mul81, McC84, Ros86, Pho90, Lon95]; * have a Stone dual providing a logic of observable properties [Abr87, Vic89, Zha91]. An additional aim of the axiomatic approach is to relate these mathematical criteria with computational criteria. As we indicate below an axiomatic treatment of various of the above aspects is now available but much research remains to be done.
Linear Logic and Computation: A Survey
 Proof and Computation, Proceedings Marktoberdorf Summer School
, 1993
"... . This is a survey of computational aspects of linear logic related to proof search. Keywords. Linear logic, cut free proof search, logic programming, complexity. 1 Introduction Linear logic, introduced by Girard [14, 36, 32], is a refinement of classical logic. While the central notions of truth ..."
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Cited by 16 (6 self)
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. This is a survey of computational aspects of linear logic related to proof search. Keywords. Linear logic, cut free proof search, logic programming, complexity. 1 Introduction Linear logic, introduced by Girard [14, 36, 32], is a refinement of classical logic. While the central notions of truth (emphasized in classical logic) and proof construction (emphasized in intuitionistic logic) remain important in linear logic, it might be said that the emphasis in linear logic is on state. Linear logic is sometimes described as being resource sensitive because it provides an intrinsic and natural accounting of process states, events, and resources. Linear logic also sheds new light on classical logic and its relationship to intuitionistic logic, see Girard [15, 16] and Danos et al. [11]. An evocative semantic paradigm for linear logic by means of games is proposed by Blass [7] and by Abramsky and Jagadeesan [2]. As an intuitive motivation, let us consider reading logical deductions so tha...
Relating StateBased and ProcessBased Concurrency through Linear Logic
, 2006
"... This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, mu ..."
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Cited by 12 (1 self)
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This paper has the purpose of reviewing some of the established relationships between logic and concurrency, and of exploring new ones. Concurrent and distributed systems are notoriously hard to get right. Therefore, following an approach that has proved highly beneficial for sequential programs, much effort has been invested in tracing the foundations of concurrency in logic. The starting points of such investigations have been various idealized languages of concurrent and distributed programming, in particular the wellestablished statetransformation model inspired to Petri nets and multiset rewriting, and the prolific processbased models such as the πcalculus and other process algebras. In nearly all cases, the target of these investigations has been linear logic, a formal language that supports a view of formulas as consumable resources. In the first part of this paper, we review some of these interpretations of concurrent languages into linear logic. In the second part of the paper, we propose a completely new approach to understanding concurrent and distributed programming as a manifestation of logic, which yields a language that merges those two main paradigms of concurrency. Specifically, we present a new semantics for multiset rewriting founded on an alternative view of linear logic. The resulting interpretation is extended with a majority of linear connectives into the language of ωmultisets. This interpretation drops the distinction between multiset elements and rewrite rules, and considerably enriches the expressive power of standard multiset rewriting with embedded rules, choice, replication, and more. Derivations are now primarily viewed as open objects, and are closed only to examine intermediate rewriting states. The resulting language can also be interpreted as a process algebra. For example, a simple translation maps process constructors of the asynchronous πcalculus to rewrite operators, while the structural equivalence corresponds directly to logicallymotivated structural properties of ωmultisets (with one exception).
Logical Predicates for Intuitionistic Linear Type Theories
 In Typed Lambda Calculi and Applications (TLCA'99), Lecture Notes in Computer Science 1581
, 1999
"... We develop a notion of Kripkelike parameterized logical predicates for two fragments of intuitionistic linear logic (MILL and DILL) in terms of their categorytheoretic models. Such logical predicates are derived from the categorical glueing construction combined with the free symmetric monoidal co ..."
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Cited by 11 (4 self)
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We develop a notion of Kripkelike parameterized logical predicates for two fragments of intuitionistic linear logic (MILL and DILL) in terms of their categorytheoretic models. Such logical predicates are derived from the categorical glueing construction combined with the free symmetric monoidal cocompletion. As applications, we obtain full completeness results of translations between linear type theories.
Parametricity as a Notion of Uniformity in Reflexive Graphs
, 2002
"... data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information. ..."
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Cited by 11 (3 self)
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data types embody uniformity in the form of information hiding. Information hiding enforces the uniform treatment of those entities that dier only on hidden information.
Enrichment and Representation Theorems for Categories of Domains and Continuous Functions
, 1996
"... This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that Research supported b ..."
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Cited by 7 (5 self)
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This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that Research supported by SERC grant RR30735 and EC project Programming Language Semantics and Program Logics grant SC1000 795 they explain the ordertheoretic structure). Our aim is 1. to provide a justification of Scott's original consideration of ordered structures, and 2. to deepen our understanding of the notion of passage to the limit