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monad
monad (ˈmɒnæd) Also 7 monade. [a. L. monad-, monas unit, ad. Gr. µονάς unit, f. µόνος alone. Cf. F. monade, Sp., Pg. monada, It. monade.] 1. a. The number one, unity; an arithmetical unit. Now only Hist. with reference to the Pythagorean or other Greek philosophies, in which numbers were regarded as...
Oxford English Dictionary
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Monad
Monad may refer to:
Philosophy
Monad (philosophy), a term meaning "unit"
Monism, the concept of "one essence" in the metaphysical and theological theory Monad (Gnosticism), the most primal aspect of God in Gnosticism
Great Monad, an older name for the taijitu symbol
Monadologia Physica, by Immanuel
wikipedia.org
en.wikipedia.org
Monad - HaskellWiki
Oct 22, 2022For more information, including an intuitive explanation of why the monad laws should be satisfied, see Monad laws.. As of GHC 7.10, the Applicative typeclass is a superclass of Monad, and the Functor typeclass is a superclass of Applicative.This means that all monads are applicatives, all applicatives are functors, and therefore all monads are also functors.
wiki.haskell.org
The Result Monad • Adam Bennett
The Result Monad. May 15, 2020. android kotlin functional development. 15 min read. Recently I've come to really appreciate the kotlin-result library as we've integrated it more and more deeply into the Cuvva Android stack. In this post, I'll explain why we needed it, how it works and what problems it solves, and show some examples of how ...
adambennett.dev
Monad (music)
In music, a monad is a single note or pitch. The Western chromatic scale, for example, is composed of twelve monads.
wikipedia.org
en.wikipedia.org
Monad as not trivial adjunctions It is well known that a monad $(T, \mu, \eta)$ can be factorized in multiple ways as adjunctions, and that in some sense, Kleisli is the initial factorization while Eilenberg-Moore is ...
Identity monad on $\mathrm{Set}$ factors in many different ways.
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State Monad - HaskellWiki
It's a simple string parsing algorithm. module StateGame where import Control.Monad.State -- Example use of State monad -- Passes a string of dictionary {a,b,c} -- Game is to produce a number from the string. -- By default the game is off, a C toggles the -- game on and off. A 'a' gives +1 and a b gives -1.
wiki.haskell.org
Monad transformer
Typically, a monad transformer is created by generalising an existing monad; applying the resulting monad transformer to the identity monad yields a monad Given any monad , the option monad transformer (where denotes the option type) is defined by:
The exception monad transformer
Given any monad , the
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en.wikipedia.org
Monad laws - HaskellWiki
Feb 1, 2024The three laws. All instances of the Monad typeclass should satisfy the following laws: Here, p ≡ q simply means that you can replace p with q and vice-versa, and the behaviour of your program will not change: p and q are equivalent. Using eta-expansion, the associativity law can be re-written for clarity as:
wiki.haskell.org
Epimorphisms and Algebras Just a quick question. Suppose a monad on $\mathbf{Set}$ (in particular monad's endofunctor preserves epimorphisms), are epimorphisms in the category of algebras also surjective? Thanks
What is true is that, for any monad on $\mathbf{Set}$, the _regular_ epimorphisms in the category of algebras are precisely the surjective homomorphisms
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What is this Monad/comonad? Last year I asked about Monads and comonands. At the bottom of the accepted answer, someone tried to give me an example of a (co)monad on Set. They said, given any monoid M, the endofuncto...
Clearly these assignments satisfy the definition of a monad. An algebra for thid monad is simply an $M$-set, in other words an action of $M$ on $X$.
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Permutation monad Given a set $S$, say $S= \\{a,b\\}$, the set of permuations of $S$ is $\\{[a,b],[b,a]\\}$ (these are supposed to be lists like $ab$ and $ba$). Can we define a monad that captures this? This monad wou...
Note that you have only defined $P$ on objects. There isn't a nice way of extending $P$ to a functor $\mathbf{Set} \to \mathbf{Set}$, however there _is_ another category where your definition of $P$ does extend nicely. Namely, let $\mathbf{B}$ be the category of sets and _bijections_ ; then you can ...
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The Lawvere Theory and Monad for the category of Symmetric groups Take the category of Symmetric groups. Each object is the group of all permutations for some set. Is there a Lawvere theory for this category? What is ...
There is no Lawvere theory whose category of models is the category of symmetric groups. This is immediate, for instance, from the fact that the category of models of any Lawvere theory is complete and cocomplete, but the category of symmetric groups has very few limits or colimits (for instance, it...
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图解 Monad - 阮一峰的网络日志 - 阮一峰的个人网站
图解 Monad. 作者： 阮一峰. 日期： 2015年7月16日. 函数式编程有一个重要概念，叫做 Monad 。. 网上有很多解释（ 这里 和 这里 ），但都很抽象，不容易看懂。. 我尝试了好多次，还是不明白Monad到底是什么。. 昨天，我读到了 Aditya Bhargava 的文章，他画了很多图 ...
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