diff --git a/readme.md b/readme.md index 0492162..74cafc3 100644 --- a/readme.md +++ b/readme.md @@ -155,16 +155,9 @@ Points-free function definitions look just like normal assignments without `func --- -## Container Type -> A data structure that can have any other type, function, or data structure in it. - -Array in JavaScript is a container type. - ---- - ## Functor -> A container type that can be mapped over and returns the same kind of container. +> An object with a `map` function. `Map` runs a function on values in an object and returns a new object. Simplest functor in javascript is an `Array` @@ -173,9 +166,21 @@ Simplest functor in javascript is an `Array` ``` --- +## Pointed Functor +> A functor with an `of` method. `Of` puts _any_ single value into a functor. + +Array Implementation: +```js + Array.prototype.of = (v) => [v]; + + [].of(1) // [1] +``` + +--- + ## Lift -> Lift takes a function with n arguments and returns one that can be run on n containers of the same type. +> Lift is like `map` except it can be applied to multiple functors. Map is the same as a lift over a one-argument function: @@ -186,7 +191,6 @@ Unlike map lift can be used to combine values from multiple arrays: ``` lift((a, b) => a * b)([1, 2], [3]); // [3, 6] ``` -Lift can apply to any [Applicative Functor](#applicative-functor). --- @@ -269,44 +273,19 @@ The identity value is empty array `[]` ## Monad -> A monad is a container type that provides two functions, [chain](#chain) and `of`. Monads provide an interface for executing a common sequence of commands on a particular kind of value, often one you want to avoid acting on directly. One of the most common monads is the "maybe" or optional value monad, which wraps a value that could be either nothing or something. By using a monad instead of the raw value, you can protect your code from exposure to null values. Likewise, a "state" monad can be used in a parser to algorithmically consume an input string using a repeatable sequence of steps that preserves the current state of the input from operation to operation. Also, since a monad is, by definition, a special kind of functor that also returns a monad, they can be chained together to describe any sequence of operations. In functional languages with lazy evaluation, monads are used where sequence of evaluation is important, such as in I/O. Due to this sequencing utility, they are sometimes referred to as "programmable semicolons." - -The simplest monad is the Identity monad. It simply wraps a value. +> A monad is an object with [`of`](#pointed-functor) and `chain` functions. `Chain` is like [map](#functor) except it unnests the resulting nested object. ```js -let Identity = v => ({ - val: v, - chain: transform => transform(this.val), - of: v => this.val -}) +['cat,dog','fish,bird'].chain(a => a.split(',')) // ['cat','dog','fish','bird'] -// Function that increments value and then wraps with Identity. -let increment = v => Identity(v + 1) - -// Use chain to apply function to wrapped values -let incrementIdentity = id => id.chain(increment) - -incrementIdentity(Identity(1)) // Identity(2) - -//Contrast to using a map, where increment would cause nested Identities -id.map(increment) // Identity(Identity(2)) +//Contrast to map +['cat,dog','fish,bird'].map(a => a.split(',')) // [['cat','dog'], ['fish','bird']] ``` - ---- - -## Chain - -> A chain is a container type that implements a chain function. The chain function takes another function to run on the contained value and returns a value in the same container. The passed function must also return a value in the same container. This is also known as bind, or flatmap in other languages. - -```js -['cat,dog','fish,bird'].chain((a) => a.split(',')) // ['cat','dog','fish','bird'] -``` - --- ## Comonad -> A container type that has `extract` and `extend` functions. +> An object that has `extract` and `extend` functions. ```js let CoIdentity = v => ({ @@ -316,7 +295,7 @@ let CoIdentity = v => ({ }) ``` -Extract takes a value out of a container. Essentially it's the opposite of `of`. +Extract takes a value out of a functor. ```js CoIdentity(1).extract() // 1 ``` @@ -329,7 +308,7 @@ CoIdentity(1).extend(co => co.extract() + 1) // CoIdentity(2) ## Applicative Functor -> An applicative functor is a container type that can have functions put in it. A function often called `ap` is available on the type which applies a function in the container to a value in another container of the same type. +> An applicative functor is an object with an `ap` function. `Ap` applies a function in the object to a value in another object of the same type. ```js [(a)=> a + 1].ap([1]) // [2] @@ -339,14 +318,18 @@ CoIdentity(1).extend(co => co.extract() + 1) // CoIdentity(2) ## Morphism +> A transformation function. + --- -## Isomorphic +## Isomorphism -> Two objects are Isomorphic is they satisfy the condition: `compose(to, from) == identity` and `compose(from, to) == identity` +> A pair of transformations between 2 types of objects that is structural in nature and no data is lost. +For example, 2D coordinates could be stored as an array `[2,3]` or object `{x: 2, y: 3}`. ```js -const pairToCoords = (arr) => ({x: arr[0], y: arr[1]}) +// Providing functions to convert in both directions makes them isomorphic. +const pairToCoords = (pair) => ({x: pair[0], y: pair[1]}) const coordsToPair = (coords) => [coords.x, coords.y]