An introduction to (co)algebra and (co)induction

Jacobs, Bart; Rütten, Jan

doi:10.1017/cbo9780511792588.003

Cited by 144 publications

(184 citation statements)

References 67 publications

(51 reference statements)

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“…Another semantic theory for stream-based systems, alternative to Kahn, is the co-algebraic theory of streams (see for instance [8]). Basically, moving to coalgebraic streams would consist, in the stream programs shown in the paper, to remove the cases.…”

Section: Resultsmentioning

confidence: 99%

Actors without Directors: A Kahnian View of Heterogeneous Systems

Caspi

Benveniste

Lublinerman

et al. 2009

Hybrid Systems: Computation and Control

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Abstract. This paper aims to simplify recent efforts proposed by the Berkeley school in giving a formal semantics to the Ptolemy toolbox. We achieve this by developing a simple and elegant functional theory of deterministic tag systems that is a generalisation of Kahn Process Network theory (KPN). Our theory extends KPN by encompassing networks of processes labelled by tags from partially ordered sets and makes deeper use of Scott theory of Complete Partial Orders (CPO). Since CPO compose well under direct sums, heterogeneous systems are simply captured by direct sums of homogeneous systems, which are in turn constructed by connecting systems over different tag sets by means of tag conversion processes. For the (large) class of tag systems of "stream" type, we show how to define tag conversion processes and how to implement process communication. The resulting architecture is fully decentralised and does not require Ptolemy's directors. Last but not least, it provides distribution for free.

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Section: Resultsmentioning

confidence: 99%

Actors without Directors: A Kahnian View of Heterogeneous Systems

Caspi

Benveniste

Lublinerman

et al. 2009

Hybrid Systems: Computation and Control

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“…The final coalgebra for F gives, as we would expect, a sensible notion of infinitary terms (following e.g. [11]). This calculus also offers a convenient piece of syntactic sugar:…”

Section: Applications and Further Workmentioning

confidence: 96%

Generalised Name Abstraction for Nominal Sets

Clouston

2013

Lecture Notes in Computer Science

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Abstract. The Gabbay-Pitts nominal sets model provides a framework for reasoning with names in abstract syntax. It has appealing semantics for name binding, via a functor mapping each nominal set to the 'atomabstractions' of its elements. We wish to generalise this construction for applications where sets, lists, or other patterns of names are bound simultaneously. The atom-abstraction functor has left and right adjoint functors that can themselves be generalised, and their generalisations remain adjoints, but the atom-abstraction functor in the middle comes apart to leave us with two notions of generalised abstraction for nominal sets. We give new descriptions of both notions of abstraction that are simpler than those previously published. We discuss applications of the two notions, and give conditions for when they coincide.

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“…[2,18]). In this section we review the relevant concepts around the categorical approach to recursive types [23,25,21] and its application to program calculation [24,27,11,22,5]. The category-theoretic explanation of (recursive) types is based on the idea that types constitute objects of a category C, programs are modelled by arrows of the category, and type constructors are functors on C. In this setting, a datatype Tis understood as a solution (a fixed point) of a type equation X F X, for an appropriate endofunctor F : C ---+ C that captures the shape (or signature) of the type.…”

Section: Mathematical Frameworkmentioning

confidence: 99%

Generic Accumulations

Pardo

2003

Generic Programming

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Accumulations are recursive functions that keep intermediate results in additional parameters which are eventually used in later stages of the computation . We present a generic definition of accumulations obtained by the introduction of a new recursive operator on inductive types. We also show that the notion of downwards accumulation developed by Gibbons is subsumed by our notion of accumulation.

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An introduction to (co)algebra and (co)induction

Cited by 144 publications

References 67 publications

Actors without Directors: A Kahnian View of Heterogeneous Systems

Actors without Directors: A Kahnian View of Heterogeneous Systems

Generalised Name Abstraction for Nominal Sets

Generic Accumulations

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