identity / functor / applicative / monad / zansh.in

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# identity functor / applicative / monad / maybe

3 min read

Mathlessly journey from a basic Identity Functor to a Maybe Monad with an Applicative in-between.

# identity functor / just

const Just = x => ({
  valueOf: () => x, 
  map: f => Just(f(x)) 
})

const run = () =>
  Just(['world', 'hello'])
    .map(x => x.reverse()) 
    .map(x => x.join(', ')) 
    .map(x => x + '!') 
    .valueOf()

# unary function

function unary(msg) {
  console.log(msg)
}

const run = () => unary("hello, world!");

# unary applicative

const Applicative = fn => ({
  ap: m => m.map(fn) 
})

const run = () =>
  Applicative(unary) 
    .ap(Just("hello, world!"));

# binary curried function

const reverse = first => second => {
  return [second, first] 
}

const run = () =>
  reverse('world')('hello')

# identity applicative

const Just = x => ({
  valueOf: () => x, 
  map: f => Just(f(x)), 
  ap: m => m.map(x) 
})

const reverse = first => second => {
  return [second, first] 
}

const run = () =>
  Just(reverse)
    .ap(Just('world')) 
    .ap(Just('hello')) 
    .map(x => x.join(', ')) 
    .map(x => x + '!') 
    .valueOf()

# identity monad

const Just = x => ({
  valueOf: () => x, 
  map: f => Just(f(x)), 
  ap: m => m.map(x), 
  chain: f => f(x) 
})

const reverse = first => second => {
  return [second, first] 
}

const run = () =>
  Just(reverse)
    .ap(Just('world')) 
    .ap(Just('hello')) 
    .map(x => x.join(', ')) 
    .chain(x => Just(x + '!')) 
    .valueOf()

# just + nothing

const Just = x => ({
  valueOf: () => x,
  map: f => Just(f(x)), 
  ap: m => m.map(x),
  chain: f => f(x)
})

const Nothing = () => ({
  valueOf: () => undefined,
  map: () => Nothing(), 
  ap: () => Nothing(),
  chain: () => Nothing()
})

const just = () =>
  Just("five boxing wizards").map(value =>
    console.log("Just: " + value) 
  );

const nothing = () =>
  Nothing('five boxing wizards').map(() =>
    console.log('Nothing?')
  )

# maybe / orElse()

const Just = x => ({
  valueOf: () => x, 
  map: f => Just(f(x)), 
  ap: m => m.map(x),
  chain: f => f(x),
  orElse: () => Just(x) 
})

const Nothing = () => ({
  valueOf: () => undefined,
  map: () => Nothing(), 
  ap: () => Nothing(),
  chain: () => Nothing(),
  orElse: f => f() 
})

function maybeDate(possibleDate) {
  const isDate =
    possibleDate instanceof Date &&
    !isNaN(possibleDate)

  return isDate
    ? Just(possibleDate) 
    : Nothing(); 
}

const parseDate = dateString =>
  maybeDate(new Date(dateString)) 
    .map(x => x.toLocaleDateString()) 
    .orElse(() => Just('Not a date')) 
    .valueOf()

# MakeMaybe

const MakeMaybe = predicate => value => {
  return predicate(value)
    ? Just(value) 
    : Nothing(); 
};

const maybeDate = MakeMaybe(
  x => x instanceof Date && !isNaN(x)
)

const parseDate = dateString =>
  maybeDate(new Date(dateString)) 
    .map(x => x.toLocaleDateString()) 
    .orElse(() => Just('Not a date')) 
    .valueOf()

# separate logic + runtime type-checking

const timeAndDate_logic =
  time => date => {
    const merged = new Date(date)
    merged.setHours(time.getHours())
    merged.setMinutes(time.getMinutes())
    merged.setSeconds(0, 0)
    return merged
  }

const timeAndDate = (time, date) =>
  Just(timeAndDate_logic)
    .ap(maybeDate(new Date(`99/01/01 ${time}`))) 
    .ap(maybeDate(new Date(date))) 
    .map(x => x.toLocaleString()) 
    .orElse(() => Just(`Bad arguments`)) 
    .valueOf();