Results 1 
8 of
8
Ypnos: Declarative, Parallel Structured Grid Programming
 In Proc. of the 5th ACM SIGPLAN workshop on Declarative Aspects of Multicore Programming
, 2010
"... A fully automatic, compilerdriven approach to parallelisation can result in unpredictable time and space costs for compiled code. On the other hand, a fully manual approach to parallelisation can be long, tedious, prone to errors, hard to debug, and often architecturespecific. We present a declarat ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
(Show Context)
A fully automatic, compilerdriven approach to parallelisation can result in unpredictable time and space costs for compiled code. On the other hand, a fully manual approach to parallelisation can be long, tedious, prone to errors, hard to debug, and often architecturespecific. We present a declarative domainspecific language, Ypnos, for expressing structured grid computations which encourages manual specification of causally sequential operations but then allows a simple, predictable, static analysis to generate optimised, parallel implementations. We introduce the language and provide some discussion on the theoretical aspects of the language semantics, particularly the structuring of computations around the category theoretic notion of a comonad. Categories and Subject Descriptors D [3]: 2—Applicative (functional) languages, Concurrent, distributed, and parallel languages, Specialised application languages; D [3]: 3—Concurrent programming structures General Terms
Freyd is Kleisli, for arrows
 In C. McBride, T. Uustalu, Proc. of Wksh. on Mathematically Structured Programming, MSFP 2006, Electron. Wkshs. in Computing. BCS
, 2006
"... Arrows have been introduced in functional programming as generalisations of monads. They also generalise comonads. Fundamental structures associated with (co)monads are Kleisli categories and categories of (EilenbergMoore) algebras. Hence it makes sense to ask if there are analogous structures for ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Arrows have been introduced in functional programming as generalisations of monads. They also generalise comonads. Fundamental structures associated with (co)monads are Kleisli categories and categories of (EilenbergMoore) algebras. Hence it makes sense to ask if there are analogous structures for Arrows. In this short note we shall take first steps in this direction, and identify for instance the Freyd
Structural Operational Semantics and Modal Logic, Revisited
"... A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is reexamined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal l ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
A previously introduced combination of the bialgebraic approach to structural operational semantics with coalgebraic modal logic is reexamined and improved in some aspects. Firstly, a more abstract, conceptual proof of the main compositionality theorem is given, based on an understanding of modal logic as a study of coalgebras in slice categories of adjunctions. Secondly, a more concrete understanding of the assumptions of the theorem is provided, where proving compositionality amounts to finding a syntactic distributive law between two collections of predicate liftings. Keywords: structural operational semantics, modal logic, coalgebra 1
MFPS 2014 Coalgebraic
"... Lenses are mathematical structures used in the context of bidirectional transformations. In this paper, we introduce update lenses as a refinement of ordinary (asymmetric) lenses in which we distinguish between views and updates. In addition to the set of views, there is a monoid of updates and an a ..."
Abstract
 Add to MetaCart
Lenses are mathematical structures used in the context of bidirectional transformations. In this paper, we introduce update lenses as a refinement of ordinary (asymmetric) lenses in which we distinguish between views and updates. In addition to the set of views, there is a monoid of updates and an action of the monoid on the set of views. Decoupling updates from views allows for other ways of changing the source than just merging a view into the source. We also consider a yet finer dependently typed version of update lenses. We give a number of characterizations of update lenses in terms of bialgebras and coalgebras, including analogs to O’Connor’s coalgebraic and Johnson, Rosebrugh and Wood’s algebraic characterizations of ordinary lenses. We consider conversion of views and updates, a tensor product of update lenses and composition of update lenses.
BACHUKI MESABLISHVILI, TBILISI AND
, 710
"... Abstract. The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal c ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal categories which in a certain sense follow the classical trace. Here we do not pose any conditions on our base category but we do refer to the monoidal
Bimonads and Hopf monads on categories
, 2008
"... The purpose of the paper is to develop a theory of bimonads and Hopf monads on arbitrary categories A thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. The basic tools are distributive laws between monads and comonads ..."
Abstract
 Add to MetaCart
(Show Context)
The purpose of the paper is to develop a theory of bimonads and Hopf monads on arbitrary categories A thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. The basic tools are distributive laws between monads and comonads (entwinings) on A. Double entwinings satisfying the YangBaxter equation provide a kind of local braidings for a bimonad and allow to extend the theory of classical braided Hopf algebras. In particular, in this case the existence of an antiode implies that the comparison functor is an equivalence provided idempotents split in A. 1
BIMONADS AND HOPF MONADS ON CATEGORIES BACHUKI MESABLISHVILI, TBILISI AND
, 710
"... Abstract. The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal c ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal categories which in a certain sense follow the classical trace. Here we do not pose any conditions on our base category but we do refer to the monoidal
3. Actions on functors and Galois fun...
"... Abstract. The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal c ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary categories thus providing the possibility to transfer the essentials of the theory of Hopf algebras in vector spaces to more general settings. There are several extensions of this theory to monoidal categories which in a certain sense follow the classical trace. Here we do not pose any conditions on our base category but we do refer to the monoidal