نتایج جستجو برای: monad theory

تعداد نتایج: 783100  

Journal: :Mathematics 2021

The main goal of this publication is to show that the basic constructions in theories fuzzy sets, soft hesitant sets or intuitionistic have a common background, based on theory monads categories. It proven ad hoc defined concepts individual theories, such as power set structures these relations approximation operators by are only special examples applications monad This makes it possible, one h...

2004
Peter Hancock Anton Setzer

We introduce concepts for representing interactive programs in dependent type theory. The representation uses a monad, as in Haskell. We consider two versions, one, in which the interface with the real world is fixed, and another one, in which the interface varies depending on previous interactions. We then generalise the monadic construction to polynomial functors. Then we look at rules needed...

2000
Alex K. Simpson Gordon D. Plotkin

We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One re...

The paper sets forth in detail categorically-algebraic or catalg foundations for the operations of taking the image and preimage of (fuzzy) sets called forward and backward powerset operators. Motivated by an open question of S. E. Rodabaugh, we construct a monad on the category of sets, the algebras of which generate the fixed-basis forward powerset operator of L. A. Zadeh. On the next step, w...

Journal: :Theoretical Computer Science 2003

Journal: :The Art, Science, and Engineering of Programming 2019

Journal: :J. Symb. Log. 1992
Renling Jin

In an !1{saturated nonstandard universe a cut is an initial segment of the hyperintegers, which is closed under addition. Keisler and Leth in [KL] introduced, for each given cut U , a corresponding U{topology on the hyperintegers by letting O be U open if for any x 2 O there is a y greater than all the elements in U such that the interval [x y; x+y] O. Let U be a cut in a hyper nite time lineH,...

Journal: :Electr. Notes Theor. Comput. Sci. 2001
Martin Hyland John Power

We introduce the notion of pseudo-commutative monad together with that of pseudoclosed 2-category, the leading example being given by the 2-monad on Cat whose 2-category of algebras is the 2-category of small symmetric monoidal categories. We prove that for any pseudo-commutative 2-monad on Cat, its 2-category of algebras is pseudo-closed. We also introduce supplementary definitions and results...

2001
Nikolaos S. Papaspyrou

Resumptions are a valuable tool in the analysis and design of semantic models for concurrent programming languages, in which computations consist of sequences of atomic steps that may be interleaved. In this paper we consider a general notion of resumption, parameterized by the kind of computations that take place in the atomic steps. We define a monad transformer which, given a monad M that re...

2016
Jay A. McCarthy Burke Fetscher Max S. New Daniel Feltey Robert Bruce Findler

This paper presents a Coq library that lifts an abstract yet precise notion of running-time into the type of a function. Our library is based on a monad that counts abstract steps, controlled by one of the monadic operations. The monad’s computational content, however, is simply that of the identity monad so programs written in our monad (that recur on the natural structure of their arguments) ...

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