diff --git a/package.json b/package.json new file mode 100644 index 0000000..e77e457 --- /dev/null +++ b/package.json @@ -0,0 +1,23 @@ +{ + "name": "functional-programming-jargons", + "version": "1.0.0", + "description": "Jargon from the functional programming world in simple terms!", + "main": "index.js", + "scripts": { + "test": "echo \"Error: no test specified\" && exit 1", + "toc": "roadmarks" + }, + "repository": { + "type": "git", + "url": "git+https://github.com/hemanth/functional-programming-jargon.git" + }, + "author": "hemanth", + "license": "MIT", + "bugs": { + "url": "https://github.com/hemanth/functional-programming-jargon/issues" + }, + "homepage": "https://github.com/hemanth/functional-programming-jargon#readme", + "devDependencies": { + "roadmarks": "^1.6.3" + } +} diff --git a/readme.md b/readme.md index 12d287c..e890efb 100644 --- a/readme.md +++ b/readme.md @@ -6,6 +6,43 @@ The goal of this document is to define jargon from functional programming in pla > Where applicable, this document uses terms defined in the [Fantasy Land spec](https://github.com/fantasyland/fantasy-land) + + +* [Arity](#arity) +* [Higher-Order Functions (HOF)](#higher-order-functions-hof) +* [Partial Application](#partial-application) +* [Currying](#currying) +* [Composition](#composition) +* [Purity](#purity) +* [Side effects](#side-effects) +* [Idempotency](#idempotency) +* [Point-Free Style](#point-free-style) +* [Contracts](#contracts) +* [Guarded Functions](#guarded-functions) +* [Categories](#categories) +* [Value](#value) +* [Constant](#constant) +* [Functor](#functor) +* [Pointed Functor](#pointed-functor) +* [Lift](#lift) +* [Referential Transparency](#referential-transparency) +* [Equational Reasoning](#equational-reasoning) +* [Lazy evaluation](#lazy-evaluation) +* [Monoid](#monoid) +* [Monad](#monad) +* [Comonad](#comonad) +* [Applicative Functor](#applicative-functor) +* [Morphism](#morphism) +* [Isomorphism](#isomorphism) +* [Setoid](#setoid) +* [Semigroup](#semigroup) +* [Foldable](#foldable) +* [Traversable](#traversable) +* [Type Signatures](#type-signatures) + + + + ## Arity > The number of arguments a function takes. From words like unary, binary, ternary, etc. This word has the distinction of being composed of two suffixes, "-ary" and "-ity." Addition, for example, takes two arguments, and so it is defined as a binary function or a function with an arity of two. Such a function may sometimes be called "dyadic" by people who prefer Greek roots to Latin. Likewise, a function that takes a variable number of arguments is called "variadic," whereas a binary function must be given two and only two arguments, currying and partial application notwithstanding (see below). @@ -14,10 +51,11 @@ The goal of this document is to define jargon from functional programming in pla const sum = (a, b) => a + b; const arity = sum.length; -console.log(arity); -// => 2 +console.log(arity); // 2 + // The arity of sum is 2 ``` + --- ## Higher-Order Functions (HOF) @@ -26,13 +64,13 @@ console.log(arity); ```js const filter = (pred, xs) => { - const result = []; - for (var idx = 0; idx < xs.length; idx += 1) { - if (pred(xs[idx])) { - result.push(xs[idx]); + const result = []; + for (var idx = 0; idx < xs.length; idx++) { + if (pred(xs[idx])) { + result.push(xs[idx]); + } } - } - return result; + return result; }; ``` @@ -41,7 +79,7 @@ const is = type => x => Object(x) instanceof type; ``` ```js -filter(is(Number), [0, '1', 2, null]); //=> [0, 2] +filter(is(Number), [0, '1', 2, null]); // [0, 2] ``` ## Partial Application @@ -56,7 +94,7 @@ let sum = (a, b) => a + b; let partial = sum.bind(null, 40); // Invoking it with `b` -partial(2); //=> 42 +partial(2); // 42 ``` --- @@ -72,20 +110,17 @@ let curriedSum = (a) => (b) => a + b; curriedSum(40)(2) // 42. ``` + --- -## Composition +## Function Composition -> A function which combines two values of a given type (usually also some kind of functions) into a third value of the same type. - -The most well-known type of composition is normal function composition. -It allows you to combines functions that accept and return a single value. +> The act of putting two two functions together to form a third function so that the output of one function is the input of the other. ```js const compose = (f, g) => a => f(g(a)) // Definition -const floorAndToString = compose((val)=> val.toString(), Math.floor) //Usage +const floorAndToString = compose((val) => val.toString(), Math.floor) // Usage floorAndToString(121.212121) // "121" - ``` --- @@ -98,9 +133,9 @@ input values, and does not produce side effects. ```js let greet = "yo"; -greet.toUpperCase(); // YO; +greet.toUpperCase(); // "YO" -greet // yo; +greet // "yo" ``` As opposed to: @@ -122,17 +157,24 @@ numbers // [] ```js console.log("IO is a side effect!"); ``` + --- ## Idempotent > A function is idempotent if reapplying it to its result does not produce a different result. -`f(f(x)) = f(x)` +```js +f(f(x)) = f(x) +``` -`Math.abs(Math.abs(10))` +```js +Math.abs(Math.abs(10)) +``` -`sort(sort(sort([2,1])))` +```js +sort(sort(sort([2,1]))) +``` --- @@ -143,7 +185,7 @@ console.log("IO is a side effect!"); ```js // Given let map = fn => list => list.map(fn); -let add = (a, b) => a + b; +let add = a => b => a + b; // Then @@ -170,7 +212,7 @@ Points-free function definitions look just like normal assignments without `func ## Categories -> Objects with associated functions that adhere certain rules. E.g. [monoid](#monoid) +> Objects with associated functions that adhere to certain rules. E.g. [Monoid](#monoid) --- @@ -185,6 +227,7 @@ Object.freeze({name: 'John', age: 30}) // The `freeze` function enforces immutab [1] undefined ``` + --- ## Constant @@ -195,13 +238,15 @@ undefined const five = 5 const john = {name: 'John', age: 30} ``` + Constants are [referentially transparent](#referential-transparency). That is, they can be replaced with the values that they represent without affecting the result. + In other words with the above two constants the expression: ```js john.age + five === ({name: 'John', age: 30}).age + (5) - ``` + Should always return `true`. --- @@ -213,7 +258,7 @@ Should always return `true`. A common functor in javascript is `Array` ```js -[2,3,4].map( n => n * 2 ); // [4,6,8] +[2, 3, 4].map(n => n * 2); // [4, 6, 8] ``` Let `func` be an object implementing a `map` function, and `f`, `g` be arbitrary functions, then `func` is said to be a functor if the map function adheres to the following rules: @@ -231,11 +276,13 @@ func.map(x => f(g(x))) == func.map(g).map(f) ``` We can now see that `Array` is a functor because it adheres to the functor rules. + ```js [1, 2, 3].map(x => x); // = [1, 2, 3] ``` and + ```js let f = x => x + 1; let g = x => x * 2; @@ -243,16 +290,18 @@ let g = x => x * 2; [1, 2, 3].map(x => f(g(x))); // = [3, 5, 7] [1, 2, 3].map(g).map(f); // = [3, 5, 7] ``` + --- ## Pointed Functor > A functor with an `of` function that puts _any_ single value into that functor. Array Implementation: -```js - Array.prototype.of = (v) => [v]; - [].of(1) // [1] +```js +Array.prototype.of = (v) => [v]; + +[].of(1) // [1] ``` --- @@ -264,11 +313,13 @@ Array Implementation: Map is the same as a lift over a one-argument function: ```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] + +```js +lift((a, b) => a * b)([1, 2], [3]); // [3, 6] ``` --- @@ -301,15 +352,17 @@ referentially transparent. ```js let rand = function*() { - while(1<2) { + while (1 < 2) { yield Math.random(); } } ``` + ```js let randIter = rand(); -randIter.next(); // Each exectuion gives a random value, expression is evluated on need. +randIter.next(); // Each execution gives a random value, expression is evaluated on need. ``` + --- ## Monoid @@ -347,6 +400,7 @@ The identity value is empty array `[]` ```js [1, 2].concat([]); // [1, 2] ``` + If identity and compose functions are provided, functions themselves form a monoid: ```js @@ -356,18 +410,17 @@ var compose = (f, g) => x => f(g(x)); compose(foo, identity) ≍ compose(identity, foo) ≍ foo ``` - --- ## Monad -> A monad is an object with [`of`](#pointed-functor) and `chain` functions. `Chain` is like [map](#functor) except it unnests the resulting nested object. +> A monad is an object with [`of`](#pointed-functor) and `chain` functions. `chain` is like [`map`](#functor) except it un-nests the resulting nested object. ```js -['cat,dog','fish,bird'].chain(a => a.split(',')) // ['cat','dog','fish','bird'] +['cat,dog', 'fish,bird'].chain(a => a.split(',')) // ['cat', 'dog', 'fish', 'bird'] //Contrast to map -['cat,dog','fish,bird'].map(a => a.split(',')) // [['cat','dog'], ['fish','bird']] +['cat,dog', 'fish,bird'].map(a => a.split(',')) // [['cat', 'dog'], ['fish', 'bird']] ``` `of` is also known as `return` in other functional languages. @@ -388,22 +441,25 @@ let CoIdentity = v => ({ ``` Extract takes a value out of a functor. + ```js CoIdentity(1).extract() // 1 ``` -Extend runs a function on the comonad. The function should return the same type as the Comonad. +Extend runs a function on the comonad. The function should return the same type as the comonad. + ```js CoIdentity(1).extend(co => co.extract() + 1) // CoIdentity(2) ``` + --- ## Applicative Functor -> 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. +> 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] +[(a) => a + 1].ap([1]) // [2] ``` --- @@ -419,6 +475,7 @@ CoIdentity(1).extend(co => co.extract() + 1) // CoIdentity(2) > 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 // Providing functions to convert in both directions makes them isomorphic. const pairToCoords = (pair) => ({x: pair[0], y: pair[1]}) @@ -436,7 +493,8 @@ pairToCoords(coordsToPair({x: 1, y: 2})) // {x: 1, y: 2} > An object that has an `equals` function which can be used to compare other objects of the same type. -Make array a setoid. +Make array a setoid: + ```js Array.prototype.equals = arr => { var len = this.length @@ -459,7 +517,7 @@ Array.prototype.equals = arr => { ## Semigroup -An object that has a `concat` function that combines it with another object of the same type. +> An object that has a `concat` function that combines it with another object of the same type. ```js [1].concat([2]) // [1, 2] @@ -469,7 +527,7 @@ An object that has a `concat` function that combines it with another object of t ## Foldable -> An object that has a reduce function that can transform that object into some other type. +> An object that has a `reduce` function that can transform that object into some other type. ```js let sum = list => list.reduce((acc, val) => acc + val, 0); @@ -481,11 +539,13 @@ sum([1, 2, 3]) // 6 ## Traversable --- + ## Type Signatures > Often functions will include comments that indicate the types of their arguments and return types. -There's quite a bit variance across the community but they often follow the following patterns: +There's quite a bit of variance across the community but they often follow the following patterns: + ```js // functionName :: firstArgType -> secondArgType -> returnType @@ -502,8 +562,13 @@ If a function accepts another function as an argument it is wrapped in parenthes // call :: (a -> b) -> a -> b let call = f => x => f(x) ``` -The letters `a`, `b`, `c`, `d` are used to signify that the argument can be of any type. For this map it takes a function that transforms a value of some type `a` into another type `b`, an array of values of type `a`, and returns an array of values of type `b`. + +The letters `a`, `b`, `c`, `d` are used to signify that the argument can be of any type. For this `map` it takes a function that transforms a value of some type `a` into another type `b`, an array of values of type `a`, and returns an array of values of type `b`. + ```js // map :: (a -> b) -> [a] -> [b] -let map = f => list => list.map(f) +let map = f => list => list.map(f) ``` +--- + +__P.S:__ Without the wonderful [contributions](https://github.com/hemanth/functional-programming-jargon/graphs/contributors) this repo would be meaningless!