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Towards a Mathematical Operational Semantics
 In Proc. 12 th LICS Conf
, 1997
"... We present a categorical theory of `wellbehaved' operational semantics which aims at complementing the established theory of domains and denotational semantics to form a coherent whole. It is shown that, if the operational rules of a programming language can be modelled as a natural transforma ..."
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Cited by 142 (9 self)
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We present a categorical theory of `wellbehaved' operational semantics which aims at complementing the established theory of domains and denotational semantics to form a coherent whole. It is shown that, if the operational rules of a programming language can be modelled as a natural transformation of a suitable general form, depending on functorial notions of syntax and behaviour, then one gets both an operational model and a canonical, internally fully abstract denotational model for free; moreover, both models satisfy the operational rules. The theory is based on distributive laws and bialgebras; it specialises to the known classes of wellbehaved rules for structural operational semantics, such as GSOS.
On Generalised Coinduction and Probabilistic Specification Formats: Distributive Laws in Coalgebraic Modelling
, 2004
"... ..."
On the Foundations of Final Coalgebra Semantics: nonwellfounded sets, partial orders, metric spaces
, 1998
"... ..."
A Coalgebraic Foundation for Linear Time Semantics
 In Category Theory and Computer Science
, 1999
"... We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for nondeterministic choice. In Set , this gives a category with ordinary transition systems as objects and with morphisms characterised ..."
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Cited by 14 (1 self)
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We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for nondeterministic choice. In Set , this gives a category with ordinary transition systems as objects and with morphisms characterised in terms of a linear notion of bisimulation. The final object in this category is the canonical abstract model for trace equivalence and can be obtained by extending the final coalgebra of the deterministic action behaviour to the Kleisli category of the nonempty powerset monad. The corresponding final coalgebra semantics is fully abstract with respect to trace equivalence.
GSOS for probabilistic transition systems (Extended Abstract)
, 2002
"... We introduce probabilistic GSOS, an operator specification format for (reactive) probabilistic transition systems which arises as an adaptation of the known GSOS format for labelled (nondeterministic) transition systems. Like the standard one, the format is well behaved in the sense that on all mode ..."
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We introduce probabilistic GSOS, an operator specification format for (reactive) probabilistic transition systems which arises as an adaptation of the known GSOS format for labelled (nondeterministic) transition systems. Like the standard one, the format is well behaved in the sense that on all models bisimilarity is a congruence and the uptocontext proof principle is valid. Moreover, every specification has a final model which can be shown to offer unique solutions for guarded recursive equations. The format covers operator specifications from the literature, so that the wellbehavedness results given for those arise as instances of our general one.
Bialgebraic Operational Semantics and Modal Logic (extended abstract)
"... A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by Structural Operational Semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived fr ..."
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A novel, general approach is proposed to proving the compositionality of process equivalences on languages defined by Structural Operational Semantics (SOS). The approach, based on modal logic, is inspired by the simple observation that if the set of formulas satisfied by a process can be derived from the corresponding sets for its subprocesses, then the logical equivalence is a congruence. Striving for generality, SOS rules are modeled categorically as bialgebraic distributive laws for some notions of process syntax and behaviour, and modal logics are modeled via coalgebraic polyadic modal logic. Compositionality is proved by providing a suitable notion of behaviour for the logic together with a dual distributive law, reflecting the one modeling the SOS specification. Concretely, the dual laws may appear as SOSlike rules where logical formulas play the role of processes, and their behaviour models logical decomposition over process syntax. The approach can be used either to proving compositionality for specific languages or for defining SOS congruence formats.
Abstract A Coalgebraic Foundation for Linear Time Semantics
"... We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for nondeterministic choice. In Set, this gives a category with ordinary transition systems as objects and with morphisms characterised i ..."
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We present a coalgebraic approach to trace equivalence semantics based on lifting behaviour endofunctors for deterministic action to Kleisli categories of monads for nondeterministic choice. In Set, this gives a category with ordinary transition systems as objects and with morphisms characterised in terms of a linear notion of bisimulation. The final object in this category is the canonical abstract model for trace equivalence and can be obtained by extending the final coalgebra of the deterministic action behaviour to the Kleisli category of the nonempty powerset monad. The corresponding final coalgebra semantics is fully abstract with respect to trace equivalence.
Guarded Recursion and Mathematical Operational Semantics
"... Operational semantics gives meaning to terms in a programming language by defining a transition relation which represents execution steps. In structural operational semantics (SOS) this transition relation is given by a set of rules defined on the structure of the terms of the language. But, when is ..."
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Operational semantics gives meaning to terms in a programming language by defining a transition relation which represents execution steps. In structural operational semantics (SOS) this transition relation is given by a set of rules defined on the structure of the terms of the language. But, when is a collection of rules satisfactory, in the sense that it defines a wellbehaved operational semantics? Before the introduction of Mathematical Operational Semantics by Turi [2], there were many attempts to conceive a theory of operational semantics in the form of syntactic rule formats. These results were specific to a particular type of transition relation, strongly syntactic, and therefore difficult to generalize and adapt to other settings. Turi stripped operational semantics to its bare bones, ignoring concrete syntax to focus on its structure and, as a result, giving us a clean categorical reformulation of SOS. Under this interpretation, the SOS of a language is given by a distributive law of syntax over behaviour. If the operations in the language are given by a signature functor Σ and the behaviour