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Combining algebraic effects with continuations
, 2007
"... We consider the natural combinations of algebraic computational effects such as sideeffects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor ext ..."
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Cited by 17 (4 self)
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We consider the natural combinations of algebraic computational effects such as sideeffects, exceptions, interactive input/output, and nondeterminism with continuations. Continuations are not an algebraic effect, but previously developed combinations of algebraic effects given by sum and tensor extend, with effort, to include commonly used combinations of the various algebraic effects with continuations. Continuations also give rise to a third sort of combination, that given by applying the continuations monad transformer to an algebraic effect. We investigate the extent to which sum and tensor extend from algebraic effects to arbitrary monads, and the extent to which Felleisen et al.’s C operator extends from continuations to its combination with algebraic effects. To do all this, we use Dubuc’s characterisation of strong monads in terms of enriched large Lawvere theories.
Generic trace theory
 International Workshop on Coalgebraic Methods in Computer Science (CMCS 2006), volume 164 of Elect. Notes in Theor. Comp. Sci
, 2006
"... Trace semantics has been defined for various nondeterministic systems with different input/output types, or with different types of “nondeterminism ” such as classical nondeterminism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms ..."
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Cited by 14 (5 self)
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Trace semantics has been defined for various nondeterministic systems with different input/output types, or with different types of “nondeterminism ” such as classical nondeterminism (with a set of possible choices) vs. probabilistic nondeterminism. In this paper we claim that these various forms of “trace semantics” are instances of a single categorical construction, namely coinduction in a Kleisli category. This claim is based on our main technical result that an initial algebra in
The Structure of CallbyValue
, 2000
"... To my parents Understanding procedure calls is crucial in computer science and everyday programming. Among the most common strategies for passing procedure arguments (‘evaluation strategies’) are ‘callbyname’, ‘callbyneed’, and ‘callbyvalue’, where the latter is the most commonly used. While ..."
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Cited by 12 (3 self)
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To my parents Understanding procedure calls is crucial in computer science and everyday programming. Among the most common strategies for passing procedure arguments (‘evaluation strategies’) are ‘callbyname’, ‘callbyneed’, and ‘callbyvalue’, where the latter is the most commonly used. While reasoning about procedure calls is simple for callbyname, problems arise for callbyneed and callbyvalue, because it matters how often and in which order the arguments of a procedure are evaluated. We shall classify these problems and see that all of them occur for callbyvalue, some occur for callbyneed, and none occur for callbyname. In that sense, callbyvalue is the ‘greatest common denominator ’ of the three evaluation strategies. Reasoning about callbyvalue programs has been tackled by Eugenio Moggi’s ‘computational lambdacalculus’, which is based on a distinction between ‘values’
Recursive Types in Kleisli Categories
 Preprint 2004. MFPS Tutorial, April 2007 Classical Domain Theory 75/75
, 1992
"... We show that an enriched version of Freyd's principle of versality holds in the Kleisli category of a commutative strong monad with fixedpoint object. This gives a general categorical setting in which it is possible to model recursive types involving the usual datatype constructors. ..."
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Cited by 8 (2 self)
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We show that an enriched version of Freyd's principle of versality holds in the Kleisli category of a commutative strong monad with fixedpoint object. This gives a general categorical setting in which it is possible to model recursive types involving the usual datatype constructors.
Enrichment and Representation Theorems for Categories of Domains and Continuous Functions
, 1996
"... This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that Research supported b ..."
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Cited by 8 (5 self)
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This paper studies the notions of approximation and passage to the limit in an axiomatic setting. Our axiomatisation is subject to the following criteria: the axioms should be natural (so that they are available in as many contexts as possible) and nonordertheoretic (so that Research supported by SERC grant RR30735 and EC project Programming Language Semantics and Program Logics grant SC1000 795 they explain the ordertheoretic structure). Our aim is 1. to provide a justification of Scott's original consideration of ordered structures, and 2. to deepen our understanding of the notion of passage to the limit
Complete iterativity for algebras with effects
 In Algebra and Coalgebra in Computer Science (Proc. Third International Conference
"... Abstract. Completely iterative algebras (cias) are those algebras in which recursive equations have unique solutions. In this paper we study complete iterativity for algebras with computational effects (described by a monad). First, we prove that for every analytic endofunctor on Set there exists a ..."
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Abstract. Completely iterative algebras (cias) are those algebras in which recursive equations have unique solutions. In this paper we study complete iterativity for algebras with computational effects (described by a monad). First, we prove that for every analytic endofunctor on Set there exists a canonical distributive law over any commutative monad M, hence a lifting of that endofunctor to the Kleisli category ofM. Then, for an arbitrary distributive law λ of an endofunctor H on Set over a monad M we introduce λcias. The cias for the corresponding lifting ofH (called Kleislicias) form a full subcategory of the category of λcias. For various monads of interest we prove that free Kleislicias coincide with free λcias, and these free algebras are given by free algebras for H. Finally, for three concrete examples of monads we prove that Kleislicias and λcias coincide and give a characterisation of those algebras. Key words: iterative algebra, monad, distributive law, initial algebra, terminal coalgebra 1
Relational databases and Bell’s theorem
 In Search of Elegance in the Theory and Practice of Computation: Essays Dedicated to Peter Buneman
, 2013
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Free Products of Higher Operad Algebras
, 909
"... Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray’s little brother, ..."
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Cited by 4 (4 self)
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Abstract. One of the open problems in higher category theory is the systematic construction of the higher dimensional analogues of the Gray tensor product of 2categories. In this paper we continue the developments of [3] and [2] by understanding the natural generalisations of Gray’s little brother, the funny tensor product of categories. In fact we exhibit for any higher categorical structure definable by an noperad in the sense of Batanin [1], an analogous tensor product which forms a symmetric monoidal closed structure
Lifting as a KZdoctrine
 Proceedings of the 6 th International Conference, CTCS'95, volume 953 of Lecture Notes in Computer Science
, 1995
"... this paper, is the analysis of notions of approximation aiming at explaining and justifying (ordertheoretic) properties of categories of domains. For example, in [Fio94c, Fio94a], while studying the interaction between partiality and orderenrichment we considered contextual approximation which, in ..."
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Cited by 3 (2 self)
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this paper, is the analysis of notions of approximation aiming at explaining and justifying (ordertheoretic) properties of categories of domains. For example, in [Fio94c, Fio94a], while studying the interaction between partiality and orderenrichment we considered contextual approximation which, in the framework we were working in, coincided with the specialisation preorder . But in the applications carried out in [FP94, Fio94a] we had to work with an axiomatised notion of approximation, instead of the aforementioned one, for the following two reasons: first, the specialisation preorder is not appropriate in categories of domains and stable functions (see [Fio94c]) and, second, we do not know of nonordertheoretic axioms making the specialisation preorder !complete. To overcome these drawbacks another notion of approximation was to be considered. And, it was the second problem that motivated the intensional notion of approximation provided by the path relation. In fact, it is shown in [Fio94b] that under suitable axioms the path relation can be equipped with a canonical passagetothelimit operator appropriate for fixedpoint computations; stronger axioms make this operator be given by lubs of !chains
Units of equivariant ring spectra
 Algebr. Geom. Topol
, 2011
"... It is well known that very special –spaces and grouplike E1–spaces both model connective spectra. Both these models have equivariant analogues in the case when the group acting is finite. Shimakawa defined the category of equivariant –spaces and showed that special equivariant –spaces determine p ..."
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Cited by 3 (0 self)
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It is well known that very special –spaces and grouplike E1–spaces both model connective spectra. Both these models have equivariant analogues in the case when the group acting is finite. Shimakawa defined the category of equivariant –spaces and showed that special equivariant –spaces determine positive equivariant spectra. Costenoble and Waner [7] showed that grouplike equivariant E1–spaces determine connective equivariant spectra.