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23
COPRODUCTS OF IDEAL MONADS
, 2004
"... The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by ..."
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Cited by 4 (1 self)
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The question of how to combine monads arises naturally in many areas with much recent interest focusing on the coproduct of two monads. In general, the coproduct of arbitrary monads does not always exist. Although a rather general construction was given by
Relating Two Approaches to Coinductive Solution of Recursive Equations
 Milius (Eds.), Proceedings of the 7th Workshop on Coalgebraic Methods in Computer Science, CMCS’04 (Barcelona, March 2004), Electron. Notes in Theoret. Comput. Sci
, 2004
"... This paper shows that the approach of [2,12] for obtaining coinductive solutions of equations on infinite terms is a special case of a more general recent approach of [4] using distributive laws. ..."
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Cited by 3 (2 self)
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This paper shows that the approach of [2,12] for obtaining coinductive solutions of equations on infinite terms is a special case of a more general recent approach of [4] using distributive laws.
On iterable endofunctors
 Category Theory and Computer Science 2002, number 69 in Elect. Notes in Theor. Comp. Sci
, 2003
"... Completely iterative monads of Elgot et al. are the monads such that every guarded iterative equation has a unique solution. Free completely iterative monads are known to exist on every iteratable endofunctor H, i. e., one with final coalgebras of all functors H ( ) + X. We show that conversely, if ..."
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Completely iterative monads of Elgot et al. are the monads such that every guarded iterative equation has a unique solution. Free completely iterative monads are known to exist on every iteratable endofunctor H, i. e., one with final coalgebras of all functors H ( ) + X. We show that conversely, if H generates a free completely iterative monad, then it is iteratable. Key words: monad, completely iterative, iterable 1
ELGOT ALGEBRAS †
, 2006
"... Abstract. Denotational semantics can be based on algebras with additional structure (order, metric, etc.) which makes it possible to interpret recursive specifications. It was the idea of Elgot to base denotational semantics on iterative theories instead, i.e., theories in which abstract recursive s ..."
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Abstract. Denotational semantics can be based on algebras with additional structure (order, metric, etc.) which makes it possible to interpret recursive specifications. It was the idea of Elgot to base denotational semantics on iterative theories instead, i.e., theories in which abstract recursive specifications are required to have unique solutions. Later Bloom and Ésik studied iteration theories and iteration algebras in which a specified solution has to obey certain axioms. We propose socalled Elgot algebras as a convenient structure for semantics in the present paper. An Elgot algebra is an algebra with a specified solution for every system of flat recursive equations. That specification satisfies two simple and well motivated axioms: functoriality (stating that solutions are stable under renaming of recursion variables) and compositionality (stating how to perform simultaneous recursion). These two axioms stem canonically from Elgot’s iterative theories: We prove that the
The essence of dataflow programming (short version
 Proc. of 3rd Asian Symp. on Programming Languages and Systems, APLAS 2005, v. 3780 of Lect. Notes in Comput. Sci
, 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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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
Coalgebraic semantics for logic programming
 18th Worshop on (Constraint) Logic Programming, WLP 2004, March 0406
, 2004
"... www.dis.uniroma1.it / ¢ majkic/ Abstract. General logic programs with negation have the 3valued minimal Herbrand models based on the Kripke’s fixpoint knowledge revision operator and on Clark’s completion. Based on these results we deifine a new algebra £¥ ¤, (with the relational algebra embedded ..."
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www.dis.uniroma1.it / ¢ majkic/ Abstract. General logic programs with negation have the 3valued minimal Herbrand models based on the Kripke’s fixpoint knowledge revision operator and on Clark’s completion. Based on these results we deifine a new algebra £¥ ¤, (with the relational algebra embedded in it), and present an algorithmic transformation of logic programs into the system of tuplevariable equations which is a £ ¤coalgebra. The solution of any such system of equations (a £ ¤coalgebra) corresponds to the unique homomorphism from this £¦ ¤coalgebra into the final £ ¤coalgebra, which is just the coalgebraic semantics for logic programs. It is shown that such unique solution corresponds to the minimal Herbrand model of annotated version of logic programs and is closely related to the encapsulation of multivalued logic programs into the 2valued annotated logic programs. 1
The Recursion Scheme from the Cofree Recursive Comonad
"... We instantiate the general comonadbased construction of recursion schemes for the initial algebra of a functor F to the cofree recursive comonad on F. Differently from the scheme based on the cofree comonad on F in a similar fashion, this scheme allows not only recursive calls on elements structura ..."
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We instantiate the general comonadbased construction of recursion schemes for the initial algebra of a functor F to the cofree recursive comonad on F. Differently from the scheme based on the cofree comonad on F in a similar fashion, this scheme allows not only recursive calls on elements structurally smaller than the given argument, but also subsidiary recursions. We develop a Mendler formulation of the scheme via a generalized Yoneda lemma for initial algebras involving strong dinaturality and hint a relation to circular proofs à la Cockett, Santocanale.
CMCS 2008 Comonadic Notions of Computation
"... We argue that symmetric (semi)monoidal comonads provide a means to structure contextdependent notions of computation such as notions of dataflow computation (computation on streams) and of tree relabelling as in attribute evaluation. We propose a generic semantics for extensions of simply typed lam ..."
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We argue that symmetric (semi)monoidal comonads provide a means to structure contextdependent notions of computation such as notions of dataflow computation (computation on streams) and of tree relabelling as in attribute evaluation. We propose a generic semantics for extensions of simply typed lambda calculus with contextdependent operations analogous to the Moggistyle semantics for effectful languages based on strong monads. This continues the work in the early 90s by Brookes, Geva and Van Stone on the use of computational comonads in intensional semantics.
Languages, Theory
"... Recently there has been a great deal of interest in higherorder syntax which seeks to extend standard initial algebra semantics to cover languages with variable binding by using functor categories. The canonical example studied in the literature is that of the untyped λcalculus which is handled as ..."
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Recently there has been a great deal of interest in higherorder syntax which seeks to extend standard initial algebra semantics to cover languages with variable binding by using functor categories. The canonical example studied in the literature is that of the untyped λcalculus which is handled as an instance of the general theory of binding algebras, cf. Fiore, Plotkin, Turi [8]. Another important syntactic construction is that of explicit substitutions. The syntax of a language with explicit substitutions does not form a binding algebra as an explicit substitution may bind an arbitrary number of variables. Nevertheless we show that the language given by a standard signature Σ and explicit substitutions is naturally modelled as the initial algebra of the endofunctor Id + FΣ ◦ + ◦ on a functor category. We also comment on the apparent lack of modularity in syntax with variable binding as compared to firstorder languages. Categories and Subject Descriptors
FINAL COALGEBRAS IN ACCESSIBLE CATEGORIES
, 905
"... Abstract. We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra in ..."
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Abstract. We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra in this case. On the other hand, there are interesting examples of final coalgebras beyond the realm of l.f.p. categories to which our results apply. We rely on ideas developed by Tom Leinster for the study of selfsimilar objects in topology. 1.