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22
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 135 (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.
Distributive laws for the coinductive solution of recursive equations
 Information and Computation
"... This paper illustrates the relevance of distributive laws for the solution of recursive equations, and shows that one approach for obtaining coinductive solutions of equations via infinite terms is in fact a special case of a more general approach using an extended form of coinduction via distributi ..."
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Cited by 12 (1 self)
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This paper illustrates the relevance of distributive laws for the solution of recursive equations, and shows that one approach for obtaining coinductive solutions of equations via infinite terms is in fact a special case of a more general approach using an extended form of coinduction via distributive laws. 1
Categorical Modelling of Structural Operational Rules  Case Studies
, 1997
"... . This paper aims at substantiating a recently introduced categorical theory of `wellbehaved' operational semantics. A variety of concrete examples of structural operational rules is modelled categorically illustrating the versatility and modularity of the theory. Further, a novel functorial n ..."
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Cited by 8 (4 self)
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. This paper aims at substantiating a recently introduced categorical theory of `wellbehaved' operational semantics. A variety of concrete examples of structural operational rules is modelled categorically illustrating the versatility and modularity of the theory. Further, a novel functorial notion of guardedness is introduced which allows for a general and formal treatment of guarded recursive programs. Introduction The predominant approach to operational semantics is Plotkin's SOS [13], which is based on structural rules. One finds in the literature various formats of structural rules which guarantee a good behaviour such as having adequate denotational models and behavioural equivalence (eg bisimulation) being a congruence. In [17], it is shown that the rules in the best known of these formats, namely GSOS [5], are in 11 correspondence with natural transformations of a suitable type, depending on specific functorial notions of syntax and behaviour. This led to studying abstract ...
Algebraic model structures
"... Abstract. We define a new notion of an algebraic model structure, in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads, and prove “algebraic ” analogs of classical results. Using a modified version of Quillen’s small object argument, we show that e ..."
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Cited by 7 (5 self)
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Abstract. We define a new notion of an algebraic model structure, in which the cofibrations and fibrations are retracts of coalgebras for comonads and algebras for monads, and prove “algebraic ” analogs of classical results. Using a modified version of Quillen’s small object argument, we show that every cofibrantly generated model structure in the usual sense underlies a cofibrantly generated algebraic model structure. We show how to pass a cofibrantly generated algebraic model structure across an adjunction, and we characterize the algebraic Quillen adjunction that results. We prove that pointwise algebraic weak factorization systems on diagram categories are cofibrantly generated if the original ones are, and we give an algebraic generalization of the projective model structure. Finally, we prove that certain fundamental comparison maps present in any cofibrantly generated model category are cofibrations when the cofibrations are monomorphisms, a conclusion that does not seem to be provable in the classical, nonalgebraic, theory. Contents
Distributivity for a Monad and a Comonad
"... We give a systematic treatment of distributivity for a monad and a comonad as arises in incorporating category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2categor ..."
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Cited by 6 (0 self)
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We give a systematic treatment of distributivity for a monad and a comonad as arises in incorporating category theoretic accounts of operational and denotational semantics, and in giving an intensional denotational semantics. We do this axiomatically, in terms of a monad and a comonad in a 2category, giving accounts of the EilenbergMoore and Kleisli constructions. We analyse the eight possible relationships, deducing that two pairs are isomorphic, but that the other pairs are all distinct. We develop those 2categorical definitions necessary to support this analysis. 1 Introduction In recent years, there has been an ongoing attempt to incorporate operational semantics into a category theoretic treatment of denotational semantics. The denotational semantics is given by starting with a signature 6 for a language without variable binding, and considering the category 6Alg of 6algebras [4]. The programs of the language form the initial 6algebra. For operational semantics, one starts ...
Symmetric monoidal completions and the exponential principle among labeled combinatorial structures
 THEORY AND APPLICATIONS OF CATEGORIES
, 2003
"... We generalize Dress and Müller's main result in [5]. We observe that their result can be seen as a characterization of free algebras for certain monad on the category of species. This perspective allows to formulate a general exponential principle in a symmetric monoidal category. We show th ..."
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Cited by 4 (2 self)
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We generalize Dress and Müller's main result in [5]. We observe that their result can be seen as a characterization of free algebras for certain monad on the category of species. This perspective allows to formulate a general exponential principle in a symmetric monoidal category. We show that for any groupoid G, the !G of presheaves on the symmetric monoidal completion !G of G satisfies the exponential principle. The main result in [5] reduces to the case G = 1. We discuss two notions of functor between categories satisfying the exponential principle and express some well known combinatorial identities as instances of the preservation properties of these functors. Finally, we give a characterization of G as a subcategory of !G.
Wellbehaved translations between structural operational semantics
 quasiupper set, 52 readinessaware relation, 53 ready CONCEPT INDEX 149 equivalence
, 2002
"... We examine two versions of maps between distributive laws as candidates for wellbehaved translations between structural operational semantics, and validate that by using simple coalgebraic arguments. We give some concrete examples of wellbehaved translations that are maps between distributive laws. ..."
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Cited by 4 (0 self)
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We examine two versions of maps between distributive laws as candidates for wellbehaved translations between structural operational semantics, and validate that by using simple coalgebraic arguments. We give some concrete examples of wellbehaved translations that are maps between distributive laws. The modelling of structural operational semantics uses Turi and Plotkin's categorical models of GSOS. These maps between distributive laws come from the previous work on 2categories of distributive laws. 1
Structural Operational Semantics and Modal Logic, Revisited
"... A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is reexamined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal l ..."
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Cited by 3 (1 self)
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A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is reexamined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal logic as a study of coalgebras in slice categories of adjunctions. Secondly, a more concrete understanding of the assumptions of the theorem is provided, where proving compositionality amounts to finding a syntactic distributive law between two collections of predicate liftings. Keywords: structural operational semantics, modal logic, coalgebra 1
Pretorsors and Galois comodules over mixed distributive laws, arXiv:0806.1212
"... Abstract. We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (socalled) regular arrow in Street’s bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equi ..."
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Cited by 2 (0 self)
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Abstract. We study comodule functors for comonads arising from mixed distributive laws. Their Galois property is reformulated in terms of a (socalled) regular arrow in Street’s bicategory of comonads. Between categories possessing equalizers, we introduce the notion of a regular adjunction. An equivalence is