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Bialgebraic Methods and Modal Logic in Structural Operational Semantics
 Electronic Notes in Theoretical Computer Science
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various ..."
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational semantics (SOS). An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this paper, bialgebraic semantics is combined with a coalgebraic approach to modal logic in a novel, general approach to proving the compositionality of process equivalences for languages defined by structural operational semantics. To prove compositionality, one provides a notion of behaviour for logical formulas, and defines an SOSlike specification of modal operators which reflects the original SOS specification of the language. This approach can be used to define SOS congruence formats as well as to prove compositionality for specific languages and equivalences. Key words: structural operational semantics, coalgebra, bialgebra, modal logic, congruence format 1
Presenting distributive laws
 In CALCO
, 2013
"... Abstract. Distributive laws of a monad T over a functor F are categorical tools for specifying algebracoalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of wellbehaved structural operational semantics and, more recently, also fo ..."
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Abstract. Distributive laws of a monad T over a functor F are categorical tools for specifying algebracoalgebra interaction. They proved to be important for solving systems of corecursive equations, for the specification of wellbehaved structural operational semantics and, more recently, also for enhancements of the bisimulation proof method. If T is a free monad, then such distributive laws correspond to simple natural transformations. However, when T is not free it can be rather difficult to prove the defining axioms of a distributive law. In this paper we describe how to obtain a distributive law for a monad with an equational presentation from a distributive law for the underlying free monad. We apply this result to show the equivalence between two different representations of contextfree languages. 1
Bialgebraic methods in structural operational semantics
 ENTCS
, 2007
"... Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational specifications. An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various k ..."
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Cited by 5 (1 self)
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Bialgebraic semantics, invented a decade ago by Turi and Plotkin, is an approach to formal reasoning about wellbehaved structural operational specifications. An extension of algebraic and coalgebraic methods, it abstracts from concrete notions of syntax and system behaviour, thus treating various kinds of operational descriptions in a uniform fashion. In this talk, the current state of the art in the area of bialgebraic semantics is presented, and its prospects for the future are sketched. In particular, a combination of basic bialgebraic techniques with a categorical approach to modal logic is described, as an abstract approach to proving compositionality by decomposing modal logics over structural operational specifications. Keywords:
The expression lemma ⋆
"... Abstract. Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in objectoriented (OO) programming, recursive hierarchies of objec ..."
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Abstract. Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in objectoriented (OO) programming, recursive hierarchies of object types with virtual methods play a central role for the same reason. There is a semantical correspondence between these two situations which we reveal and formalize categorically. To this end, we assume a coalgebraic model of OO programming with functional objects. The development may be helpful in deriving refactorings that turn sufficiently disciplined functional programs into OO programs of a designated shape and vice versa. Key words: expression lemma, expression problem, functional object, catamorphism, fold, the composite design pattern, program calculation, distributive law, free monad, cofree comonad. 1
Information and Computation 207 (2009) 258–283 Contents lists available at ScienceDirect
"... Information and Computation journal homepage: www.elsevier.com/locate/ic ..."
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1st Year Transfer Report
, 2006
"... This document is a summary of the work I have done during my first year whilst researching on the modularity of structural operational semantics. I discuss why modularity is important in semantics and the shortcomings of structural operational semantics in this regard. I review the related literat ..."
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This document is a summary of the work I have done during my first year whilst researching on the modularity of structural operational semantics. I discuss why modularity is important in semantics and the shortcomings of structural operational semantics in this regard. I review the related literature and explain what I have achieved so far. Also, I outline some possible directions for future work. 1
Sliced bananas on opaque data ⋆ The expression lemma
"... Abstract. Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in objectoriented (OO) programming, recursive hierarchies of objec ..."
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Abstract. Algebraic data types and catamorphisms (folds) play a central role in functional programming as they allow programmers to define recursive data structures and operations on them uniformly by structural recursion. Likewise, in objectoriented (OO) programming, recursive hierarchies of object types with virtual methods play a central role for the same reason. There is a semantical correspondence between these two situations which we reveal and formalize categorically. To this end, we assume a coalgebraic model of OO programming with functional objects. In practical terms, the development prepares for refactorings that turn sufficiently disciplined functional folds into OO programs of a designated shape (and v.v.). Key words: expression lemma, expression problem, functional object, catamorphism, fold, composite, program calculation, distributive law, free monad, cofree comonad. 1
Biinductive Structural Semantics (Extended Abstract)
"... We propose a simple ordertheoretic generalization of settheoretic inductive definitions. This generalization covers inductive, coinductive and biinductive definitions and is preserved by abstraction. This allows the structural operational semantics to describe simultaneously the finite/terminati ..."
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We propose a simple ordertheoretic generalization of settheoretic inductive definitions. This generalization covers inductive, coinductive and biinductive definitions and is preserved by abstraction. This allows the structural operational semantics to describe simultaneously the finite/terminating and infinite/diverging behaviors of programs. This is illustrated on the structural bifinitary small/bigstep trace/relational/operational semantics of the callbyvalue λcalculus.