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13
Generic trace semantics via coinduction
 Logical Methods in Comp. Sci
, 2007
"... Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace ..."
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Cited by 34 (10 self)
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Abstract. Trace semantics has been defined for various kinds of statebased systems, notably with different forms of branching such as nondeterminism vs. probability. In this paper we claim to identify one underlying mathematical structure behind these “trace
Coalgebraic Components in a ManySorted Microcosm
"... Abstract. The microcosm principle, advocated by Baez and Dolan and formalized for Lawvere theories lately by three of the authors, has been applied to coalgebras in order to describe compositional behavior systematically. Here we further illustrate the usefulness of the approach by extending it to a ..."
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Cited by 8 (2 self)
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Abstract. The microcosm principle, advocated by Baez and Dolan and formalized for Lawvere theories lately by three of the authors, has been applied to coalgebras in order to describe compositional behavior systematically. Here we further illustrate the usefulness of the approach by extending it to a manysorted setting. Then we can show that the coalgebraic component calculi of Barbosa are examples, with compositionality of behavior following from microcosm structure. The algebraic structure on these coalgebraic components corresponds to variants of Hughes’ notion of arrow, introduced to organize computations in functional programming. 1
Involutive categories and monoids, with a GNScorrespondence
 In Quantum Physics and Logic (QPL
, 2010
"... This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of EilenbergMoore algebras of involutive monads are involutive, with conjugation for modules and vecto ..."
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Cited by 7 (5 self)
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This paper develops the basics of the theory of involutive categories and shows that such categories provide the natural setting in which to describe involutive monoids. It is shown how categories of EilenbergMoore algebras of involutive monads are involutive, with conjugation for modules and vector spaces as special case. The core of the socalled GelfandNaimarkSegal (GNS) construction is identified as a bijective correspondence between states on involutive monoids and inner products. This correspondence exists in arbritrary involutive symmetric monoidal categories. 1
A Rule Format for Associativity
"... Abstract. We propose a rule format that guarantees associativity of binary operators with respect to all notions of behavioral equivalence that are defined in terms of (im)possibility of transitions, e.g., the notions below strong bisimilarity in van Glabbeek’s spectrum. The initial format is a subs ..."
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Abstract. We propose a rule format that guarantees associativity of binary operators with respect to all notions of behavioral equivalence that are defined in terms of (im)possibility of transitions, e.g., the notions below strong bisimilarity in van Glabbeek’s spectrum. The initial format is a subset of the De Simone format. We show that all trivial generalizations of our format are bound for failure. We further extend the format in a few directions and illustrate its application to several formalisms in the literature. A subset of the format is studied to obtain associativity with respect to graph isomorphism. 1
Traces for Coalgebraic Components
 MATH. STRUCT. IN COMP. SCIENCE
, 2010
"... This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, statebased modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of sta ..."
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Cited by 2 (1 self)
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This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, statebased modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of standard string diagrams for monoidal categories, for representing and manipulating component diagrams. The microcosm principle then yields a canonical “inner” traced monoidal structure on the category of resumptions (elements of final coalgebras / components). This generalises an observation by Abramsky, Haghverdi and Scott.
Traces, Executions and Schedulers,
"... Abstract. A theory of traces of computations has emerged within the field of coalgebra, via finality in Kleisli categories. In concurrency theory, traces are traditionally obtained from executions, by projecting away states. These traces and executions are sequences and will be called “thin”. The co ..."
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Abstract. A theory of traces of computations has emerged within the field of coalgebra, via finality in Kleisli categories. In concurrency theory, traces are traditionally obtained from executions, by projecting away states. These traces and executions are sequences and will be called “thin”. The coalgebraic approach gives rise to both “thin ” and “fat” traces/executions, where in the “fat ” case the structure of computations is preserved. This distinction between thin and fat will be introduced first. It is needed for a theory of schedulers in a coalgebraic setting, of which we only present the very basic definitions and results. 1
Pseudo Functorial Semantics
"... Categories with algebraic structure—the most prominent example being monoidal categories—satisfy equational axioms only upto coherent isomorphisms. Therefore they are pseudo algebras. We extend Lawvere’s functorial semantics to such pseudo structure: in contrast to standard strict algebras which ar ..."
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Categories with algebraic structure—the most prominent example being monoidal categories—satisfy equational axioms only upto coherent isomorphisms. Therefore they are pseudo algebras. We extend Lawvere’s functorial semantics to such pseudo structure: in contrast to standard strict algebras which are identified with productpreserving functors, pseudo algebras are productpreserving pseudo functors. This identification paves a way to a uniform theory of pseudo algebras. To demonstrate its use we prove a lifting result of pseudo algebraic structure to a category of coalgebras, a result that is crucial in our coalgebraic study of software components with the microcosm principle. 1
1.1 Structural Operational Semantics and Its Bialgebraic Modeling
"... Abstract. In the previous work by Jacobs, Sokolova and the author, synchronous parallel composition of coalgebras—yielding a coalgebra—and parallel composition of behaviors—yielding a behavior, where behaviors are identified with states of the final coalgebra—were observed to form an instance of th ..."
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Abstract. In the previous work by Jacobs, Sokolova and the author, synchronous parallel composition of coalgebras—yielding a coalgebra—and parallel composition of behaviors—yielding a behavior, where behaviors are identified with states of the final coalgebra—were observed to form an instance of the microcosm principle. The microcosm principle, a term by Baez and Dolan, refers to the general phenomenon of nested algebraic structures such as a monoid in a monoidal category. Suitable organization of these two levels of parallel composition led to a general compositionality theorem: the behavior of the composed system relies only on the behaviors of its constituent parts. In the current paper this framework is extended so that it accommodates any process operator—not restricted to parallel composition—whose meaning is specified by means of GSOS rules. This generalizes Turi and Plotkin’s bialgebraic modeling of GSOS, by allowing a process operator to act as a connector between components as coalgebras.