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23
The essence of dataflow programming
 In APLAS
, 2005
"... Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure ..."
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Cited by 18 (3 self)
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Abstract. We propose a novel, comonadic approach to dataflow (streambased) computation. This is based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads and on the intuition that comonads in general must be a good means to structure contextdependent computation. In particular, we develop a generic comonadic interpreter of languages for contextdependent computation and instantiate it for streambased computation. We also discuss distributive laws of a comonad over a monad as a means to structure combinations of effectful and contextdependent computation. We apply the latter to analyse clocked dataflow (partial stream based) computation. 1
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
Contextfree languages via coalgebraic trace semantics
 International Conference on Algebra and Coalgebra in Computer Science (CALCO’05), volume 3629 of Lect. Notes Comp. Sci
, 2005
"... Abstract. We show that, for functors with suitable mild restrictions, the initial algebra in the category of sets and functions gives rise to the final coalgebra in the (Kleisli) category of sets and relations. The finality principle thus obtained leads to the finite trace semantics of nondeterminis ..."
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Cited by 11 (8 self)
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Abstract. We show that, for functors with suitable mild restrictions, the initial algebra in the category of sets and functions gives rise to the final coalgebra in the (Kleisli) category of sets and relations. The finality principle thus obtained leads to the finite trace semantics of nondeterministic systems, which extends the trace semantics for coalgebras previously introduced by the second author. We demonstrate the use of our technical result by giving the first coalgebraic account on contextfree grammars, where we obtain generated contextfree languages via the finite trace semantics. Additionally, the constructions of both finite and possibly infinite parse trees are shown to be monads. Hence our extension of the application domain of coalgebras identifies several new mathematical constructions and structures. 1
Recursive coalgebras from comonads
 Inform. and Comput
, 2006
"... The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his work on categorical set theory to discuss the relationship between wellfounded induction and recursively specified functions. In this paper, we motivate the use of recursive coalgebras as a paradigm of struct ..."
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Cited by 10 (3 self)
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The concept of recursive coalgebra of a functor was introduced in the 1970s by Osius in his work on categorical set theory to discuss the relationship between wellfounded induction and recursively specified functions. In this paper, we motivate the use of recursive coalgebras as a paradigm of structured recursion in programming semantics, list some basic facts about recursive coalgebras and, centrally, give new conditions for the recursiveness of a coalgebra based on comonads, comonadcoalgebras and distributive laws of functors over comonads. We also present an alternative construction using countable products instead of cofree comonads.
The category theoretic solution of recursive program schemes
 Proc. First Internat. Conf. on Algebra and Coalgebra in Computer Science (CALCO 2005), Lecture Notes in Computer Science
, 2006
"... Abstract. This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the categorytheoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: worki ..."
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Cited by 7 (2 self)
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Abstract. This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the categorytheoretic version of the classical area of algebraic semantics. The overall assumptions needed are small indeed: working only in categories with “enough final coalgebras ” we show how to formulate, solve, and study recursive program schemes. Our general theory is algebraic and so avoids using ordered, or metric structures. Our work generalizes the previous approaches which do use this extra structure by isolating the key concepts needed to study substitution in infinite trees, including secondorder substitution. As special cases of our interpreted solutions we obtain the usual denotational semantics using complete partial orders, and the one using complete metric spaces. Our theory also encompasses implicitly defined objects which are not usually taken to be related to recursive program schemes. For example, the classical Cantor twothirds set falls out as an interpreted
Signals and comonads
 Journ. of Universal Comp. Sci
, 2005
"... Abstract: We propose a novel discipline for programming stream functions and for the semantic description of stream manipulation languages based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads. This seems to be a promising applica ..."
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Cited by 5 (2 self)
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Abstract: We propose a novel discipline for programming stream functions and for the semantic description of stream manipulation languages based on the observation that both general and causal stream functions can be characterized as coKleisli arrows of comonads. This seems to be a promising application for the old, but very little exploited idea that if monads abstract notions of computation of a value, comonads ought to be useable as an abstraction of notions of value in a context. We also show that causal partialstream functions can be described in terms of a combination of a comonad and a monad.
Explicit Substitutions and HigherOrder Syntax (Extended Abstract)
 in Proc. of 2nd ACM SIGPLAN Wksh. on Mechanized Reasoning about Languages with Variable Binding, MERLIN'03
, 2003
"... Neil Ghani Dept. of Math. and Comp. Sci. ..."
On coalgebra based on classes
 Theor. Comp. Science
, 2004
"... Abstract. The category Class of classes and functions is proved to have a number of properties suitable for algebra and coalgebra: every endofunctor has an initial algebra and a terminal coalgebra, the categories of algebras and coalgebras are complete and cocomplete, and every endofunctor generates ..."
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Cited by 5 (1 self)
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Abstract. The category Class of classes and functions is proved to have a number of properties suitable for algebra and coalgebra: every endofunctor has an initial algebra and a terminal coalgebra, the categories of algebras and coalgebras are complete and cocomplete, and every endofunctor generates a free completely iterative monad. A description of a terminal coalgebra for the powerset functor is provided.
On covarietes of coalgebras
 In preparation
"... Abstract. A survey of parts of General Coalgebra is presented with applications to the theory of systems. Stress is laid on terminal coalgebras and coinduction as well as ..."
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Cited by 5 (1 self)
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Abstract. A survey of parts of General Coalgebra is presented with applications to the theory of systems. Stress is laid on terminal coalgebras and coinduction as well as
Generalizing Substitution
, 2003
"... It is well known that, given an endofunctor H on a category C, the initial (A + H−)algebras (if existing), i.e., the algebras of (wellfounded) Hterms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Mo ..."
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Cited by 4 (1 self)
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It is well known that, given an endofunctor H on a category C, the initial (A + H−)algebras (if existing), i.e., the algebras of (wellfounded) Hterms over different variable supplies A, give rise to a monad with substitution as the extension operation (the free monad induced by the functor H). Moss [17] and Aczel, Adámek, Milius and Velebil [2] have shown that a similar monad, which even enjoys the additional special property of having iterations for all guarded substitution rules (complete iterativeness), arises from the inverses of the final (A + H−)coalgebras (if existing), i.e., the algebras of nonwellfounded Hterms. We show that, upon an appropriate generalization of the notion of substitution, the same can more generally be said about the initial T ′ (A, −)algebras resp. the inverses of the final T ′ (A, −)coalgebras for any endobifunctor T ′ on any category C such that the functors T ′ (−,X) uniformly carry a monad structure.