نتایج جستجو برای: monad theory

تعداد نتایج: 783100  

1995
Zhenjiang Hu Hideya Iwasaki

Monads are becoming an increasingly important tool for structural functional programming, because they provide a uniform framework for describing a wide range of programming language features. To facilitate program transformation, Fokkinga derived a su cient assumption under which there is a kind of socalled monadic catamorphisms which satisfy several general laws useful for the transformation ...

Journal: :Theor. Comput. Sci. 2003
Peter Aczel Jirí Adámek Stefan Milius Jiri Velebil

In#nite trees form a free completely iterative theory over any given signature—this fact, proved by Elgot, Bloom and Tindell, turns out to be a special case of a much more general categorical result exhibited in the present paper. We prove that whenever an endofunctor H of a category has #nal coalgebras for all functors H ( ) + X , then those coalgebras, TX , form a monad. This monad is complet...

Journal: :Electr. Notes Theor. Comput. Sci. 2005
Markus Michelbrink Anton Setzer

We introduce the notion of state dependent interactive programs for Martin-Löf Type Theory. These programs are elements of coalgebras of an endofunctor on the presheaf category S → Set. We prove the existence of final coalgebras for these functors. This shows as well the consistency of type theory plus rules expressing the existence of weakly final coalgebras for these functors, which represent...

2009
Gordon D. Plotkin Matija Pretnar

We present an algebraic treatment of exception handlers and, more generally, introduce handlers for other computational effects representable by an algebraic theory. These include nondeterminism, interactive input/output, concurrency, state, time, and their combinations; in all cases the computation monad is the free-model monad of the theory. Each such handler corresponds to a model of the the...

In this work, we describe an adjunction between the comma category of Set-based monads under the V -powerset monad and the category of associative lax extensions of Set-based monads to the category of V -relations. In the process, we give a general construction of the Kleisli extension of a monad to the category of V-relations.

2008
ALAIN BRUGUIÈRES

The center Z(C) of an autonomous category C is monadic over C (if certain coends exist in C). The notion of Hopf monad naturally arises if one tries to reconstruct the structure of Z(C) in terms of its monad Z: we show that Z is a quasitriangular Hopf monad on C and Z(C) is isomorphic to the braided category ZC of Z-modules. More generally, let T be a Hopf monad on an autonomous category C. We ...

Journal: :CoRR 2017
Tobias Fritz Paolo Perrone

We define a monad on the category of complete metric spaces with short maps, which assigns to each space the space of Radon probability measures on it with finite first moment, equipped with the Kantorovich–Wasserstein distance. It is analogous to the Giry monad on the category of Polish spaces, and it extends a construction due to van Breugel for compact and for 1bounded complete metric spaces...

2006
Feng Wu

The physical foundation of the main mathematical concepts in the nonstandard analysis theory of turbulence are presented and discussed. The basic fact is that there does not exist the absolute zero fluid-volume. Therefore, the corresponding physical object to the absolute point is just the uniform fluid-particle. The fluid-particle, in general, corresponds to the monad. The uniform fluid-partic...

2001
Martin Hyland Gordon Plotkin John Power

We begin to develop a unified account of modularity for computational effects. We use the notion of enriched Lawvere theory, together with its relationship with strong monads, to reformulate Moggi’s paradigm for modelling computational effects; we emphasise the importance here of the operations that induce computational effects. Effects qua theories are then combined by appropriate bifunctors (...

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