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Removed blockquotes #11
Removed superflous <hr/>s Added gitignore for build directory
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jethro larson
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node_modules
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readme.md
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readme.md
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@ -4,7 +4,7 @@ The goal of this document is to define jargon from functional programming in pla
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*This is a WIP; please feel free to send a PR ;)*
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> Where applicable, this document uses terms defined in the [Fantasy Land spec](https://github.com/fantasyland/fantasy-land)
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Where applicable, this document uses terms defined in the [Fantasy Land spec](https://github.com/fantasyland/fantasy-land)
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<!-- RM(noparent,notop) -->
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@ -48,7 +48,7 @@ The goal of this document is to define jargon from functional programming in pla
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## Arity
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> 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).
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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).
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```js
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const sum = (a, b) => a + b;
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@ -59,11 +59,9 @@ console.log(arity); // 2
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// The arity of sum is 2
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```
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---
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## Higher-Order Functions (HOF)
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> A function which takes a function as an argument and/or returns a function.
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A function which takes a function as an argument and/or returns a function.
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```js
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const filter = (pred, xs) => {
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@ -78,7 +76,7 @@ const filter = (pred, xs) => {
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```
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```js
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const is = type => x => Object(x) instanceof type;
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const is = (type) => (x) => Object(x) instanceof type;
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```
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```js
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@ -87,7 +85,7 @@ filter(is(Number), [0, '1', 2, null]); // [0, 2]
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## Partial Application
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> The process of getting a function with lesser arity compared to the original
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The process of getting a function with lesser arity compared to the original
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function by fixing the number of arguments is known as partial application.
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```js
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@ -100,11 +98,9 @@ let partial = sum.bind(null, 40);
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partial(2); // 42
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```
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---
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## Currying
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> The process of converting a function that takes multiple arguments into a function that takes them one at a time.
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The process of converting a function that takes multiple arguments into a function that takes them one at a time.
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Each time the function is called it only accepts one argument and returns a function that takes one argument until all arguments are passed.
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@ -121,23 +117,19 @@ add2(10) // 12
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```
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---
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## Function Composition
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> The act of putting two functions together to form a third function where the the output of one function is the input of the other.
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The act of putting two functions together to form a third function where the the output of one function is the input of the other.
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```js
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const compose = (f, g) => a => f(g(a)) // Definition
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const compose = (f, g) => (a) => f(g(a)) // Definition
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const floorAndToString = compose((val) => val.toString(), Math.floor) // Usage
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floorAndToString(121.212121) // "121"
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```
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---
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## Purity
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> A function is pure if the return value is only determined by its
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A function is pure if the return value is only determined by its
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input values, and does not produce side effects.
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```js
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@ -159,21 +151,17 @@ greet(); // "Hi, Brianne"
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```
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---
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## Side effects
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> A function or expression is said to have a side effect if apart from returning a value, it modifies some state or has an observable interaction with external functions.
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A function or expression is said to have a side effect if apart from returning a value, it modifies some state or has an observable interaction with external functions.
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```js
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console.log("IO is a side effect!");
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```
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---
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## Idempotent
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> A function is idempotent if reapplying it to its result does not produce a different result.
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A function is idempotent if reapplying it to its result does not produce a different result.
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```js
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f(f(x)) = f(x)
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@ -187,16 +175,14 @@ Math.abs(Math.abs(10))
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sort(sort(sort([2,1])))
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```
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---
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## Point-Free Style
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> Writing functions where the definition does not explicitly identify the arguments used. This style usually requires [currying](#currying) or other [Higher-Order functions](#higher-order-functions-hof). A.K.A Tacit programming.
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Writing functions where the definition does not explicitly identify the arguments used. This style usually requires [currying](#currying) or other [Higher-Order functions](#higher-order-functions-hof). A.K.A Tacit programming.
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```js
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// Given
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let map = fn => list => list.map(fn);
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let add = a => b => a + b;
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let map = (fn) => (list) => list.map(fn);
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let add = (a) => (b) => a + b;
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// Then
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@ -211,25 +197,23 @@ let incrementAll2 = map(add(1));
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Points-free function definitions look just like normal assignments without `function` or `=>`.
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---
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## Contracts
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---
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TODO
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## Guarded Functions
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---
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TODO
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## Categories
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> Objects with associated functions that adhere to certain rules. E.g. [Monoid](#monoid)
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---
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Objects with associated functions that adhere to certain rules. E.g. [Monoid](#monoid)
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## Value
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> Anything that can be assigned to a variable.
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Anything that can be assigned to a variable.
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```js
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5
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@ -239,11 +223,9 @@ Object.freeze({name: 'John', age: 30}) // The `freeze` function enforces immutab
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undefined
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```
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---
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## Constant
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> A variable that cannot be reassigned once defined.
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A variable that cannot be reassigned once defined.
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```js
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const five = 5
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@ -258,52 +240,48 @@ With the above two constants the following expression will always return `true`.
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john.age + five === ({name: 'John', age: 30}).age + (5)
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```
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---
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## Functor
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> An object with a `map` function that adheres to certain rules. `Map` runs a function on values in an object and returns a new object.
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An object with a `map` function that adheres to certain rules. `Map` runs a function on values in an object and returns a new object.
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A common functor in javascript is `Array`
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```js
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[2, 3, 4].map(n => n * 2); // [4, 6, 8]
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[2, 3, 4].map((n) => n * 2); // [4, 6, 8]
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```
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If `func` is 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:
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```js
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// identity
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func.map(x => x) === func
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func.map((x) => x) === func
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```
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and
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```js
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// composition
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func.map(x => f(g(x))) === func.map(g).map(f)
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func.map((x) => f(g(x))) === func.map(g).map(f)
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```
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We can now see that `Array` is a functor because it adheres to the functor rules.
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```js
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[1, 2, 3].map(x => x); // = [1, 2, 3]
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[1, 2, 3].map((x) => x); // = [1, 2, 3]
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```
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and
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```js
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let f = x => x + 1;
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let g = x => x * 2;
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let f = (x) => x + 1;
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let g = (x) => x * 2;
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[1, 2, 3].map(x => f(g(x))); // = [3, 5, 7]
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[1, 2, 3].map((x) => f(g(x))); // = [3, 5, 7]
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[1, 2, 3].map(g).map(f); // = [3, 5, 7]
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```
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---
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## Pointed Functor
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> A functor with an `of` function that puts _any_ single value into that functor.
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A functor with an `of` function that puts _any_ single value into that functor.
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Array Implementation:
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@ -313,16 +291,14 @@ Array.prototype.of = (v) => [v];
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[].of(1) // [1]
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```
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---
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## Lift
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> Lift is like `map` except it can be applied to multiple functors.
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Lift is like `map` except it can be applied to multiple functors.
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Map is the same as a lift over a one-argument function:
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```js
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lift(n => n * 2)([2, 3, 4]); // [4, 6, 8]
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lift((n) => n * 2)([2, 3, 4]); // [4, 6, 8]
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```
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Unlike map lift can be used to combine values from multiple arrays:
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@ -331,11 +307,9 @@ Unlike map lift can be used to combine values from multiple arrays:
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lift((a, b) => a * b)([1, 2], [3]); // [3, 6]
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```
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---
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## Referential Transparency
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> An expression that can be replaced with its value without changing the
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An expression that can be replaced with its value without changing the
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behavior of the program is said to be referentially transparent.
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Say we have function greet:
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@ -347,17 +321,13 @@ let greet = () => "Hello World!";
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Any invocation of `greet()` can be replaced with `Hello World!` hence greet is
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referentially transparent.
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---
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## Equational Reasoning
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> When an application is composed of expressions and devoid of side effects, truths about the system can be derived from the parts.
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---
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When an application is composed of expressions and devoid of side effects, truths about the system can be derived from the parts.
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## Lazy evaluation
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> Lazy evaluation is a call-by-need evaluation mechanism that delays the evaluation of an expression until its value is needed. In functional languages, this allows for structures like infinite lists, which would not normally be available in an imperative language where the sequencing of commands is significant.
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Lazy evaluation is a call-by-need evaluation mechanism that delays the evaluation of an expression until its value is needed. In functional languages, this allows for structures like infinite lists, which would not normally be available in an imperative language where the sequencing of commands is significant.
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```js
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let rand = function*() {
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@ -372,11 +342,9 @@ let randIter = rand();
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randIter.next(); // Each execution gives a random value, expression is evaluated on need.
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```
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---
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## Monoid
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> A monoid is some data type and a two parameter function that "combines" two values of the type, where an identity value that does not affect the result of the function also exists.
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A monoid is some data type and a two parameter function that "combines" two values of the type, where an identity value that does not affect the result of the function also exists.
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One very simple monoid is numbers and addition:
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@ -413,36 +381,32 @@ The identity value is empty array `[]`
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If identity and compose functions are provided, functions themselves form a monoid:
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```js
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var identity = a => a;
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var compose = (f, g) => x => f(g(x));
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var identity = (a) => a;
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var compose = (f, g) => (x) => f(g(x));
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compose(foo, identity) ≍ compose(identity, foo) ≍ foo
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```
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---
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## Monad
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> 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.
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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.
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```js
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['cat,dog', 'fish,bird'].chain(a => a.split(',')) // ['cat', 'dog', 'fish', 'bird']
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['cat,dog', 'fish,bird'].chain((a) => a.split(',')) // ['cat', 'dog', 'fish', 'bird']
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//Contrast to map
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['cat,dog', 'fish,bird'].map(a => a.split(',')) // [['cat', 'dog'], ['fish', 'bird']]
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['cat,dog', 'fish,bird'].map((a) => a.split(',')) // [['cat', 'dog'], ['fish', 'bird']]
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```
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`of` is also known as `return` in other functional languages.
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`chain` is also known as `flatmap` and `bind` in other languages.
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---
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## Comonad
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> An object that has `extract` and `extend` functions.
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An object that has `extract` and `extend` functions.
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```js
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const CoIdentity = v => ({
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const CoIdentity = (v) => ({
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val: v,
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extract() { return this.val },
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extend(f) { return CoIdentity(f(this)) }
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@ -458,30 +422,24 @@ CoIdentity(1).extract() // 1
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Extend runs a function on the comonad. The function should return the same type as the comonad.
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```js
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CoIdentity(1).extend(co => co.extract() + 1) // CoIdentity(2)
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CoIdentity(1).extend((co) => co.extract() + 1) // CoIdentity(2)
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```
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---
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## Applicative Functor
|
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|
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> 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.
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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.
|
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|
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```js
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[(a) => a + 1].ap([1]) // [2]
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```
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---
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|
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## Morphism
|
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|
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> A transformation function.
|
||||
|
||||
---
|
||||
A transformation function.
|
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|
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## Isomorphism
|
||||
|
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> A pair of transformations between 2 types of objects that is structural in nature and no data is lost.
|
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A pair of transformations between 2 types of objects that is structural in nature and no data is lost.
|
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|
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For example, 2D coordinates could be stored as an array `[2,3]` or object `{x: 2, y: 3}`.
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|
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|
|
@ -496,16 +454,16 @@ coordsToPair(pairToCoords([1, 2])) // [1, 2]
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|||
pairToCoords(coordsToPair({x: 1, y: 2})) // {x: 1, y: 2}
|
||||
```
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|
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---
|
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|
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|
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## Setoid
|
||||
|
||||
> An object that has an `equals` function which can be used to compare other objects of the same type.
|
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An object that has an `equals` function which can be used to compare other objects of the same type.
|
||||
|
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Make array a setoid:
|
||||
|
||||
```js
|
||||
Array.prototype.equals = arr => {
|
||||
Array.prototype.equals = (arr) => {
|
||||
var len = this.length
|
||||
if (len != arr.length) {
|
||||
return false
|
||||
|
|
@ -522,36 +480,30 @@ Array.prototype.equals = arr => {
|
|||
[1, 2].equals([0]) // false
|
||||
```
|
||||
|
||||
---
|
||||
|
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## Semigroup
|
||||
|
||||
> An object that has a `concat` function that combines it with another object of the same type.
|
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An object that has a `concat` function that combines it with another object of the same type.
|
||||
|
||||
```js
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[1].concat([2]) // [1, 2]
|
||||
```
|
||||
|
||||
---
|
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|
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## Foldable
|
||||
|
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> An object that has a `reduce` function that can transform that object into some other type.
|
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An object that has a `reduce` function that can transform that object into some other type.
|
||||
|
||||
```js
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let sum = list => list.reduce((acc, val) => acc + val, 0);
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let sum = (list) => list.reduce((acc, val) => acc + val, 0);
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sum([1, 2, 3]) // 6
|
||||
```
|
||||
|
||||
---
|
||||
|
||||
## Traversable
|
||||
|
||||
---
|
||||
TODO
|
||||
|
||||
## Type Signatures
|
||||
|
||||
> Often functions will include comments that indicate the types of their arguments and return types.
|
||||
Often functions will include comments that indicate the types of their arguments and return types.
|
||||
|
||||
There's quite a bit of variance across the community but they often follow the following patterns:
|
||||
|
||||
|
|
@ -559,24 +511,24 @@ There's quite a bit of variance across the community but they often follow the f
|
|||
// functionName :: firstArgType -> secondArgType -> returnType
|
||||
|
||||
// add :: Number -> Number -> Number
|
||||
let add = x => y => x + y
|
||||
let add = (x) => (y) => x + y
|
||||
|
||||
// increment :: Number -> Number
|
||||
let increment = x => x + 1
|
||||
let increment = (x) => x + 1
|
||||
```
|
||||
|
||||
If a function accepts another function as an argument it is wrapped in parenthesis.
|
||||
|
||||
```js
|
||||
// call :: (a -> b) -> a -> b
|
||||
let call = f => x => f(x)
|
||||
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`.
|
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|
||||
```js
|
||||
// map :: (a -> b) -> [a] -> [b]
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||||
let map = f => list => list.map(f)
|
||||
let map = (f) => (list) => list.map(f)
|
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```
|
||||
|
||||
## Union type
|
||||
|
|
|
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Reference in a new issue