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@ -119,22 +119,22 @@ executions with the the same input parameters.
--- ---
## Points-Free ## Point-Free Style
> A function whose definition does not include information regarding its arguments. > Writing functions where the definition does not explicitly define arguments. This style usually requires [currying](#currying) or other [Higher-Order functions](#higher-order-functions-hof). A.K.A Tacit programming.
```js ```js
// Given // Given
let combine = curry((fn, initialVal, list) => list.reduce(fn, initialVal)); let map = fn => list => list.map(fn);
let add = (a, b) => a + b; let add = (a, b) => a + b;
// Then // Then
// Not points-free // Not points-free - `numbers` is an explicit parameter
let total1 = (numbers) => combine(add, 0, numbers); let incrementAll = (numbers) => map(add(1))(numbers);
// Points-free // Points-free - The array is an implicit parameter
let total2 = combine(add, 0); let incrementAll2 = map(add(1));
``` ```
`total1` lists and uses the parameter `numbers`, so it is not points-free. `total2` is written just by combining functions and values, making no mention of its arguments. It __is__ points-free. `total1` lists and uses the parameter `numbers`, so it is not points-free. `total2` is written just by combining functions and values, making no mention of its arguments. It __is__ points-free.
@ -155,9 +155,16 @@ It is easy to recognize points-free function definitions; they are the ones that
--- ---
## 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 ## Functor
> Structure that can be mapped over. > A container type that can be mapped over and returns the same kind of container.
Simplest functor in javascript is an `Array` Simplest functor in javascript is an `Array`
@ -168,17 +175,25 @@ Simplest functor in javascript is an `Array`
## Lift ## Lift
> Lift takes a function and runs it on values in a container type. Map is a lift over a one-argument function, but the same principal can be used to combine multiple containers of the same type. > Lift takes a function with n arguments and returns one that can be run on n containers of the same type.
Map is the same as a lift over a one-argument function:
```js ```js
lift(n => n * 2)([2,3,4]); // [4,6,8] lift(n => n * 2)([2,3,4]); // [4,6,8]
```
Unlike map lift can be used to combine values from multiple arrays:
```
lift((a, b) => a * b)([1, 2], [3]); // [3, 6] lift((a, b) => a * b)([1, 2], [3]); // [3, 6]
``` ```
Lift can apply to any [Applicative Functor](#applicative-functor).
---
## Referential Transparency ## Referential Transparency
> An expression that can be replaced with its value without changing the > An expression that can be replaced with its value without changing the
behavior of the program is said to be referential transparent. behavior of the program is said to be referentially transparent.
Say we have function greet: Say we have function greet:
@ -187,7 +202,7 @@ let greet = () => "Hello World!";
``` ```
Any invocation of `greet()` can be replaced with `Hello World!` hence greet is Any invocation of `greet()` can be replaced with `Hello World!` hence greet is
referential transparent. referentially transparent.
--- ---
@ -259,7 +274,7 @@ The identity value is empty array `[]`
The simplest monad is the Identity monad. It simply wraps a value. The simplest monad is the Identity monad. It simply wraps a value.
```js ```js
let Identity = v => ({ bind: transform => transform(v) }) let Identity = v => ({ chain: transform => transform(v) })
``` ```
--- ---
@ -288,11 +303,16 @@ let Identity = v => ({ bind: transform => transform(v) })
--- ---
## Morphism ## Morphism
--- ---
## Isomorphic
> <del>When the same code runs on the client and the server</del> **[Wrong](https://www.youtube.com/watch?v=5gDn28kghdQ)**
---
## Setoid ## Setoid
--- ---
@ -301,10 +321,6 @@ let Identity = v => ({ bind: transform => transform(v) })
--- ---
## Chain
---
## Foldable ## Foldable
--- ---