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Generalised Coinduction
, 2001
"... We introduce the lambdacoiteration schema for a distributive law lambda of a functor T over a functor F. Under certain conditions it can be shown to uniquely characterise functions into the carrier of a final Fcoalgebra, generalising the basic coiteration schema as given by finality. The duals of ..."
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Cited by 17 (3 self)
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We introduce the lambdacoiteration schema for a distributive law lambda of a functor T over a functor F. Under certain conditions it can be shown to uniquely characterise functions into the carrier of a final Fcoalgebra, generalising the basic coiteration schema as given by finality. The duals of primitive recursion and courseofvalue iteration, which are known extensions of coiteration, arise as instances of our framework. One can furthermore obtain schemata justifying recursive specifications that involve operators such as addition of power series, regular operators on languages, or parallel and sequential composition of processes. Next...
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:
Abstract
"... Comparing hierarchies of types in models of linear logic PaulAndré Melliès 1 We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F: C ⇄ D: G and transformations IdC ..."
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Comparing hierarchies of types in models of linear logic PaulAndré Melliès 1 We show that two models M and N of linear logic collapse to the same extensional hierarchy of types, when (1) their monoidal categories C and D are related by a pair of monoidal functors F: C ⇄ D: G and transformations IdC ⇒ GF and IdD ⇒ F G, and
Abstract SOS 2006 Preliminary Version Bialgebraic Methods in Structural Operational Semantics (Invited Talk)
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DISTRIBUTIVE LAWS IN PROGRAMMING STRUCTURES
, 2009
"... Generalised Distributive laws in Computer Science are rules governing the transformation of one programming structure into another. In programming, they are programs satisfying certain formal conditions. Their importance has been to date documented in several isolated cases by diverse formal approac ..."
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Generalised Distributive laws in Computer Science are rules governing the transformation of one programming structure into another. In programming, they are programs satisfying certain formal conditions. Their importance has been to date documented in several isolated cases by diverse formal approaches. These applications have always meant leaps in understanding the nature of the subject. However, distributive laws have not yet been given the attention they deserve. One of the reasons for this omission is certainly the lack of a formal notion of distributive laws in their full generality. This hinders the discovery and formal description of occurrences of distributive laws, which is the precursor of any formal manipulation. In this thesis, an approach to formalisation of distributive laws is presented based on the functorial approach to formal Category Theory pioneered by Lawvere and others, notably Gray. The proposed formalism discloses a rather simple nature of distributive laws of the kind found in programming structures based on lax 2naturality and Gray’s tensor product of 2categories. It generalises the existing more specific notions of distributive