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Initial Algebra and Final Coalgebra Semantics for Concurrency
, 1994
"... The aim of this paper is to relate initial algebra semantics and final coalgebra semantics. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial ..."
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Cited by 55 (9 self)
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The aim of this paper is to relate initial algebra semantics and final coalgebra semantics. It is shown how these two approaches to the semantics of programming languages are each others dual, and some conditions are given under which they coincide. More precisely, it is shown how to derive initial semantics from final semantics, using the initiality and finality to ensure their equality. Moreover, many facts about congruences (on algebras) and (generalized) bisimulations (on coalgebras) are shown to be dual as well.
A Coinduction Principle for Recursive Data Types Based on Bisimulation
, 1996
"... This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programmin ..."
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Cited by 37 (3 self)
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This paper provides foundations for a reasoning principle (coinduction) for establishing the equality of potentially infinite elements of selfreferencing (or circular) data types. As it is wellknown, such data types not only form the core of the denotational approach to the semantics of programming languages [SS71], but also arise explicitly as recursive data types in functional programming languages like Standard ML [MTH90] or Haskell [HPJW92]. In the latter context, the coinduction principle provides a powerful technique for establishing the equality of programs with values in recursive data types (see examples herein and in [Pit94]).
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.
Final Semantics for untyped λcalculus
 IN LNCS, VOLUME 902
, 1995
"... Proof principles for reasoning about various semantics of untyped λcalculus are discussed. The semantics are determined operationally by fixing a particular reduction strategy on terms and a suitable set of values, and by taking the corresponding observational equivalence on terms. These principl ..."
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Cited by 2 (0 self)
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Proof principles for reasoning about various semantics of untyped λcalculus are discussed. The semantics are determined operationally by fixing a particular reduction strategy on terms and a suitable set of values, and by taking the corresponding observational equivalence on terms. These principles arise naturally as coinduction principles, when the observational equivalences are shown to be induced by the unique mapping into a final Fcoalgebra, for a suitable functor F . This is achieved either by induction on computation steps or exploiting the properties of some, computationally adequate, inverse limit denotational model. The final F coalgebras cannot be given, in general, the structure of a "denotational" λmodel. Nevertheless the "final semantics" can count as compositional in that it induces a congruence. We utilize the intuitive categorical setting of hypersets and functions. The importance of the principles introduced in this paper lies in the fact that they often allow...