reading the "The Typeclassopedia" by Brent Yorgey in Monad.Reader#13 ,and found that "the Functor hierachy" is interdependent of "the Category hierachy" as the Figure.1 shown. And according to the author, ArrowApply == Monad,…

在前面的讨论里我们提到自由数据结构就是产生某种类型的最简化结构,比如:free monoid, free monad, free category等等.我们也证明了List[A]是个free monoid.我们再看看free monad结构Free的定义:scalaz/Free.scala /** A free operational monad for some functor `S`. Binding is done using the heap instead of the stack,…

Arrow class Category a => Arrow a where arr :: (b -> c) -> a b c first :: a b c -> a (b,d) (c,d) first = (*** id) second :: a b c -> a (d,b) (d,c) second = (id ***) (***) :: a b c -> a b' c' -> a (b,b') (c,c') f *** g = first f >&g…

简单来说:Monad就是泛函编程中最概括通用的数据模型(高阶数据类型).它不但涵盖了所有基础类型(primitive types)的泛函行为及操作,而且任何高阶类或者自定义类一旦具备Monad特性就可以与任何类型的Monad实例一样在泛函编程中共同提供一套通用的泛函编程方式.所以有人把泛函编程视作Monadic Programming也不为过之.那么,具体什么是Monad呢? 在前面我们讨论过Monoid,我们说过它是一个特殊的范畴(Category),所有数据类型的Monoid实例都共同拥有一…

The point of Monad is composability. In the green category, T -> Monad<U> and U -> Monad<R> are not composable. flatMap turns a function of type T -> Monad<U> into a function of type Monad<T> -> Monad<U>, so that…

Category class Category cat where id :: cat a a (.) :: cat b c -> cat a b -> cat a c instance Category (->) where id = GHC.Base.id (.) = (GHC.Base..) (<<<) :: Category cat => cat b c -> cat a b -> cat a c (<<<) = (.) (&…

一个单子(Monad)说白了不过就是自函子范畴上的一个幺半群而已.这句话涉及到了几个概念:单子(Monad),自函子(Endo-Functor),幺半群(Monoid),范畴(category). 范畴 范畴的定义 范畴由三部分组成: 一组对象,是需要操作的数据的组合. 一组态射(morphisms).一组态射,是数据对象上的映射关系,比如f:A -> B,每个态射会绑定两个对象,假如f是从源对象A到目标对象B的态射,记作:f:A -> B. 态射组合.就是态射能够几个组合在一起形成一个新的态…

Before we introduce what is Monad, first let's recap what is a pointed functor: A pointed functor is a Functor with .of() method Why pointed Functor is imporant? here OK, now, let's continue to see some code: const mmo = Maybe.of(Maybe.of('nunchucks'…

I have been trying to teach myself Functional Programming since late 2013. Many of the concepts are very daunting because of their somewhat academic nature. Since I’m obviously not an expert, I intend this to be a very practical post. You will find m…

monad的特征: 类型转化+添加新的操作. monad  RACStream RACSignal RACSubject monad:单一体,(不可分的)个体 以计算为中心的封装. In functional programming, a monad is a design pattern that defines how functions, actions, inputs, and outputs can be used together to build generic types,[1]…