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The Essence of Multitasking
 Proceedings of the 11th International Conference on Algebraic Methodology and Software Technology, volume 4019 of Lecture Notes in Computer Science
, 2006
"... Abstract. This article demonstrates how a powerful and expressive abstraction from concurrency theory—monads of resumptions—plays a dual rôle as a programming tool for concurrent applications. The article demonstrates how a wide variety of typical OS behaviors may be specified in terms of resumption ..."
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Abstract. This article demonstrates how a powerful and expressive abstraction from concurrency theory—monads of resumptions—plays a dual rôle as a programming tool for concurrent applications. The article demonstrates how a wide variety of typical OS behaviors may be specified in terms of resumption monads known heretofore exclusively in the literature of programming language semantics. We illustrate the expressiveness of the resumption monad with the construction of an exemplary multitasking kernel in the pure functional language Haskell. 1
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.
Build, augment and destroy. Universally
 In Asian Symposium on Programming Languages, Proceedings
, 2004
"... Abstract. We give a semantic footing to the fold/build syntax of programming with inductive types, covering shortcut deforestation, based on a universal property. Specifically, we give a semantics for inductive types based on limits of algebra structure forgetting functors and show that it is equiva ..."
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Abstract. We give a semantic footing to the fold/build syntax of programming with inductive types, covering shortcut deforestation, based on a universal property. Specifically, we give a semantics for inductive types based on limits of algebra structure forgetting functors and show that it is equivalent to the usual initial algebra semantics. We also give a similar semantic account of the augment generalization of build and of the unfold/destroy syntax of coinductive types. 1
Coalgebras and Monads in the Semantics of Java
 Theoretical Computer Science
, 2002
"... This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at th ..."
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This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at the University of Nijmegen. It is shown how the monadic perspective gives rise to the relevant computational structure in Java (composition, extension and repetition), and how the coalgebraic perspective o#ers an associated program logic (with invariants, bisimulations, and Hoare logics) for reasoning about the computational structure provided by the monad.
Traces for Coalgebraic Components
 MATH. STRUCT. IN COMP. SCIENCE
, 2010
"... This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, statebased modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of sta ..."
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This paper contributes a feedback operator, in the form of a monoidal trace, to the theory of coalgebraic, statebased modelling of components. The feedback operator on components is shown to satisfy the trace axioms of Joyal, Street and Verity. We employ McCurdy’s tube diagrams, an extension of standard string diagrams for monoidal categories, for representing and manipulating component diagrams. The microcosm principle then yields a canonical “inner” traced monoidal structure on the category of resumptions (elements of final coalgebras / components). This generalises an observation by Abramsky, Haghverdi and Scott.
Chapter 1 Generalizing the AUGMENT Combinator
"... Abstract: The usual initial algebra semantics of inductive types provides a clear and uniform explanation for the FOLD combinator. In an APLAS 2004 paper [1], we described an alternative equivalent semantics of inductive types as limits of algebra structure forgetting functors. This gave us an elega ..."
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Abstract: The usual initial algebra semantics of inductive types provides a clear and uniform explanation for the FOLD combinator. In an APLAS 2004 paper [1], we described an alternative equivalent semantics of inductive types as limits of algebra structure forgetting functors. This gave us an elegant universal property based account of the BUILD and AUGMENT combinators, which form the core of the shortcut deforestation program transformation method by Gill et al. [2, 3]. Here we present further evidence for the flexibility of our approach by showing that a useful AUGMENTlike combinator is definable for a far wider class of parameterized inductive types than free monads, namely for all monads arising from a parameterized monad via an initial algebra construction. 1.1
Abstract Coalgebras and Monads in the Semantics of Java ⋆
"... This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at th ..."
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This paper describes the basic structures in the denotational and axiomatic semantics of sequential Java, both from a monadic and a coalgebraic perspective. This semantics is an abstraction of the one used for the verification of (sequential) Java programs using proof tools in the LOOP project at the University of Nijmegen. It is shown how the monadic perspective gives rise to the relevant computational structure in Java (composition, extension and repetition), and how the coalgebraic perspective offers an associated program logic (with invariants, bisimulations, and Hoare logics) for reasoning about the computational structure provided by the monad.