`Option` vs non-`Option`

foo.md

Option vs non-Option

	Option<T>	non-Option (T | undefined)
accessing property	userOption.map(user => user.age)	userNullish?.age
calling a method	userOption.map(user => user.fn())	userNullish?.fn()
providing fallback	ageOption.getOrElse(0)	ageNullish ?? 0
filter	ageOption.filter(checkIsOddNumber)	ageNullish !== undefined && checkIsOddNumber(ageNullish) ? ageNullish : undefined
map	ageOption.map(add1)	ageNullish !== undefined ? add1(ageNullish) : undefined
flat map / chain	ageOption.flatMap(add1)	ageNullish !== undefined ? add1(ageNullish) : undefined
check for existence with predicate	ageOption.exists(checkIsOddNumber)	ageNullish !== undefined ? checkIsOddNumber(ageNullish) : false
check for existence with method	nameOption.exists(name => name.startsWith('bob'))	nameNullish?.startsWith('bob') ?? false
nesting	Option<Option<T>>	impossible
sequencing	sequence(fa, fb)	fa !== undefined ? fb !== undefined ? [fa, fb] : undefined : undefined
mapping multiple	sequence(fa, fb).map(add)	fa !== undefined ? fb !== undefined ? add([fa, fb]) : undefined : undefined

Comparison of advanced example

const age1 = userOption
  .flatMap(user => user.age)
  .map(plus1)
  .filter(checkIsOddNumber)
  .getOrElse(0);

const age2 =
  (user?.age !== undefined
    ? (() => {
        const agePlus1 = plus1(user.age);
        return checkIsOddNumber(agePlus1) ? agePlus1 : undefined;
      })()
    : undefined) ?? 0;

I'm wondering if you can comment no the static-land modules implemented for type Nilable<T> = T | undefined | null from nilable and option in hkts (an fp-ts port to deno).

	Option	Nilable
accessing property	userOption.map(user => user.age)	pipe(userNilable, N.map(user => user.age))
calling a method	userOption.map(user => user.fn())	pipe(userNilable, N.map(user => user.fn()))
providing fallback	ageOption.getOrElse(0)	pipe(userNilable, N.getOrElse(0))
filter	ageOption.filter(checkIsOddNumber)	N.Filterable.filter(checkIsOddNumber, userNilable)
map	ageOption.map(add1)	pipe(ageNilable, N.map(add1))
flat map / chain	ageOption.flatMap(add1)	pipe(ageNilable, N.chain(add1))
check for existence with predicate	ageOption.exists(checkIsOddNumber)	pipe(ageNilable, N.exists(checkIsOddNumber)) *unimplemented
check for existence with method	nameOption.exists(name => name.startsWith('bob'))	pipe(nameNilable, N.exists(name => name.startsWith('bob')) *unimplemented
nesting	Option<Option>	still impossible
sequencing	sequence(fa, fb)	N.sequenceTuple(ageNilable, nameNilable)
mapping multiple	sequence(fa, fb).map(add)	N.sequenceTuple(ageNilable1, ageNilable2).map(add)

Specifically, aside from being able to represent the different between [] and [undefined] when calling const head = <T>(ts: T[]): Nilable<T> => ts[0]; what are the type theoretical problems? (Even in this case the return value from head([]) and head([undefined]) are correct).

@baetheus I've also explored an approach like nilables before but ultimately the problem is that it does not satisfy FP laws.

@hasparus attempted something similar here https://github.com/hasparus/maybe-ts, and wrote about his learnings here: https://haspar.us/speaking/maybe-ts.

@OliverJAsh Which laws does it not satisfy? I've created some assert statements that test instances of Functor, Apply, Applicative, and Monad and have tested my monad with them. It seems to pass for the simple valued case I setup. I've even run through a proof outline myself:

// Identity: F.map(x => x, a) ≡ a
map(identity, 1)
= isNil(1) ? undefined : identity(1)
= identity(1)
= 1

map(identity, undefined)
= isNil(undefined) ? undefined : identity(undefined)
= undefined

Ok!

// Composition: F.map(x => f(g(x)), a) ≡ F.map(f, F.map(g, a))
map(x => String(parseInt(x)), "1")
= isNil("1") ? undefined : String(parseInt("1"))
= String(parseInt("1"))
= String(1)
= 1

map(String, map(parseInt, "1"))
= isNil(isNil("1") ? undefined : parseInt("1")) ? undefined : String(parseInt("1")) *not actual reduction
= isNil(parseInt("1")) ? undefined : String(parseInt("1"))
= String(parseInt("1"))
= String(1)
= 1

Ok!

map(x => String(parseInt(x)), undefined)
= isNil(undefined) ? undefined : String(parseInt(undefined))
= undefined

map(String, map(parseInt, "1"))
= isNil(isNil(undefined) ? undefined : parseInt(undefined)) ? undefined : String(parseInt(undefined)) *not actual reduction
= isNil(undefined) ? undefined : String(parseInt(undefined))
= undefined

Ok!

Albeit only for functor.

I see, for the case where you are mapping with a function f where f<T>(ta: Nilable<T>): Nilable<T> you lose information during composition. Effectively this is the case where undefined is meaningful as a value.