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Monads and Effects
 IN INTERNATIONAL SUMMER SCHOOL ON APPLIED SEMANTICS APPSEM’2000
, 2000
"... A tension in language design has been between simple semantics on the one hand, and rich possibilities for sideeffects, exception handling and so on on the other. The introduction of monads has made a large step towards reconciling these alternatives. First proposed by Moggi as a way of structu ..."
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Cited by 47 (6 self)
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A tension in language design has been between simple semantics on the one hand, and rich possibilities for sideeffects, exception handling and so on on the other. The introduction of monads has made a large step towards reconciling these alternatives. First proposed by Moggi as a way of structuring semantic descriptions, they were adopted by Wadler to structure Haskell programs, and now offer a general technique for delimiting the scope of effects, thus reconciling referential transparency and imperative operations within one programming language. Monads have been used to solve longstanding problems such as adding pointers and assignment, interlanguage working, and exception handling to Haskell, without compromising its purely functional semantics. The course will introduce monads, effects and related notions, and exemplify their applications in programming (Haskell) and in compilation (MLj). The course will present typed metalanguages for monads and related categorica...
Container Types Categorically
, 2000
"... A program derivation is said to be polytypic if some of its parameters are data types. Often these data types are container types, whose elements store data. Polytypic program derivations necessitate a general, noninductive definition of `container (data) type'. Here we propose such a definition: a ..."
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Cited by 12 (0 self)
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A program derivation is said to be polytypic if some of its parameters are data types. Often these data types are container types, whose elements store data. Polytypic program derivations necessitate a general, noninductive definition of `container (data) type'. Here we propose such a definition: a container type is a relator that has membership. It is shown how this definition implies various other properties that are shared by all container types. In particular, all container types have a unique strength, and all natural transformations between container types are strong. Capsule Review Progress in a scientific dicipline is readily equated with an increase in the volume of knowledge, but the true milestones are formed by the introduction of solid, precise and usable definitions. Here you will find the first generic (`polytypic') definition of the notion of `container type', a definition that is remarkably simple and suitable for formal generic proofs (as is amply illustrated in t...
Multilevel modelling via stochastic multilevel multiset rewriting, draft submitted to
 Mathematical Structures in Computer Science
, 2011
"... Abstract. We present a simple stochastic rulebased approach to multilevel modelling for computational systems biology. Populations are modelled using multilevel multisets; these contain both species and agents, with the latter possibly containing further such multisets. Rules are pairs of such mult ..."
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Cited by 6 (1 self)
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Abstract. We present a simple stochastic rulebased approach to multilevel modelling for computational systems biology. Populations are modelled using multilevel multisets; these contain both species and agents, with the latter possibly containing further such multisets. Rules are pairs of such multisets, but now allowing variables to occur (as well as species and agents), together with an associated stochastic rate. We give two illustrative examples. The first is an extracellular model of virus infection, coupled with an intracellular model of viral reproduction; this model can demonstrate successive waves of infection. The second is a model of cell division in which a repressor protein is diluted in successive generations, when repression no longer occurs. The multilevel multiset approach can also be seen in terms of stochastic term rewriting for the theory of a commutative monoid, equipped with extra constants (for the species) and unary operations (for the agents). We further discuss the relationship of this approach with two others: Krivine et al.’s stochastic bigraphs, restricted to Milner’s place graphs, and Coppo et al.’s Stochastic Calculus of Wrapped Compartments. These various relationships provide evidence for the fundamental nature of the approach. 1.
TYPES AND COALGEBRAIC STRUCTURE
"... We relate weak limit preservation properties of coalgebraic type functors F to structure theoretic properties of the class of all Fcoalgebras. ..."
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Cited by 6 (4 self)
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We relate weak limit preservation properties of coalgebraic type functors F to structure theoretic properties of the class of all Fcoalgebras.
From Tcoalgebras to filter structures and transition systems
 Algebra and Coalgebra in Computer Science
, 2005
"... Abstract. For any setendofunctor T: Set → Set there exists a largest subcartesian transformation µ to the filter functor F: Set → Set. Thus we can associate with every Tcoalgebra A a certain filtercoalgebra AF. Precisely, when T weakly preserves preimages, µ is natural, and when T weakly preserve ..."
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Cited by 4 (2 self)
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Abstract. For any setendofunctor T: Set → Set there exists a largest subcartesian transformation µ to the filter functor F: Set → Set. Thus we can associate with every Tcoalgebra A a certain filtercoalgebra AF. Precisely, when T weakly preserves preimages, µ is natural, and when T weakly preserves intersections, µ factors through the covariant powerset functor P, thus providing for every Tcoalgebra A a Kripke structure AP. The paper characterizes weak preservation of preimages, of intersections, and preservation of both preimages and intersections by a functor T via the existence of transformations from T to either F or P. Moreover, we define for arbitrary Tcoalgebras A a nexttime operator ○A with associated modal operators ✷ and ✸ and relate their properties to weak limit preservation properties of T. In particular, for any Tcoalgebra A there is a transition system K with ○A = ○K if and only if T weakly preserves intersections. 1.
ON MINIMAL COALGEBRAS
"... Abstract. We define an outdegree for Fcoalgebras and show that the coalgebras of outdegree at most κ form a covariety. As a subcategory of all Fcoalgebras, this class has a terminal object, which for many problems can stand in for the terminal Fcoalgebra, which need not exist in general. As exam ..."
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Cited by 4 (1 self)
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Abstract. We define an outdegree for Fcoalgebras and show that the coalgebras of outdegree at most κ form a covariety. As a subcategory of all Fcoalgebras, this class has a terminal object, which for many problems can stand in for the terminal Fcoalgebra, which need not exist in general. As examples, we derive structure theoretic results about minimal coalgebras, showing that, for instance minimization of coalgebras is functorial, that products of finitely many minimal coalgebras exist and are given by their largest common subcoalgebra, that minimal subcoalgebras have no inner endomorphisms and show how minimal subcoalgebras can be constructed from Mooreautomata. Since the elements of minimal subcoalgebras must correspond uniquely to the formulae of any logic characterizing observational equivalence, we give in the last section a straightforward and selfcontained account of the coalgebraic logic of D. Pattinson and L. Schröder, which we believe is simpler and more direct than the original exposition. For every automaton A there exists a minimal automaton ∇(A), which displays
Monad Transformers as Monoid Transformers
"... The incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a preexisting monad. A complication of this approach is that the operations associated to the preexisting monad need to be lifted to the new monad. In a compa ..."
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Cited by 2 (0 self)
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The incremental approach to modular monadic semantics constructs complex monads by using monad transformers to add computational features to a preexisting monad. A complication of this approach is that the operations associated to the preexisting monad need to be lifted to the new monad. In a companion paper by Jaskelioff, the lifting problem has been addressed in the setting of system F ω. Here, we recast and extend those results in a categorytheoretic setting. We abstract and generalize from monads to monoids (in a monoidal category), and from monad transformers to monoid transformers. The generalization brings more simplicity and clarity, and opens the way for lifting of operations with applicability beyond monads. Key words: Monad, Monoid, Monoidal Category
BarQL: Collaborating Through Change
"... Applications such as Google Docs, Office 365, and Dropbox show a growing trend towards incorporating multiuser collaboration functionality into web applications. These collaborative applications share a need to efficiently express shared state, typically through a shared log abstraction. Extensive ..."
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Cited by 1 (1 self)
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Applications such as Google Docs, Office 365, and Dropbox show a growing trend towards incorporating multiuser collaboration functionality into web applications. These collaborative applications share a need to efficiently express shared state, typically through a shared log abstraction. Extensive research efforts on log abstractions by the database, programming languages, and distributed systems communities have identified a variety of analysis techniques based on the algebraic properties of updates (i.e., pairwise commutativity, subsumption, and idempotence). Although these techniques have been applied to specific application domains, to the best of our knowledge, no attempt has been made to create a general framework for such analyses in the context of a nontrivial update language. In this paper, we introduce monadic logs, a semantically rich state abstraction that provides a powerful, expressive framework for reasoning about a variety of application state properties. We also define BarQL, a general purpose stateupdate language, and show how the monadic log abstraction allows us to reason about the properties of updates expressed in BarQL. Finally, we show how such analyses can be expressed declaratively using the SPARQL graph query language. 1.