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feat: Add PartialEqUnary and Improve doc and test (#228)
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import { assertEquals } from "../deps.ts"; | ||
import { Array, Compose, Func, Identity, Option, Zipper } from "../mod.ts"; | ||
import { | ||
applicative, | ||
comonad, | ||
type Coyoneda, | ||
coyoneda, | ||
distributive, | ||
foldRT, | ||
functor, | ||
hoist, | ||
lower, | ||
monad, | ||
partialEq, | ||
partialEqUnary, | ||
traversable, | ||
unCoyoneda, | ||
} from "./coyoneda.ts"; | ||
import type { Apply2Only } from "./hkt.ts"; | ||
import { strict } from "./type-class/partial-eq.ts"; | ||
|
||
Deno.test("hoist", () => { | ||
const getFirst = <A>(arr: readonly A[]): Option.Option<A> => | ||
0 in arr ? Option.some(arr[0]) : Option.none(); | ||
const arrCoy = coyoneda((x: number) => x.toString())<Array.ArrayHkt>([ | ||
2, | ||
7, | ||
1, | ||
8, | ||
2, | ||
8, | ||
]); | ||
const optCoy = hoist<Array.ArrayHkt, Option.OptionHkt>(getFirst)(arrCoy); | ||
const actual = unCoyoneda<Option.OptionHkt, string, Option.Option<string>>( | ||
(map) => (image) => Option.map(map)(image), | ||
)(optCoy); | ||
assertEquals(actual, Option.some("2")); | ||
}); | ||
|
||
const getValue = unCoyoneda<Array.ArrayHkt, string, readonly string[]>( | ||
(map) => (image) => image.map(map), | ||
); | ||
|
||
Deno.test("functor laws", () => { | ||
const f = functor<Array.ArrayHkt>(); | ||
const arrCoy = coyoneda((x: number) => x.toString())<Array.ArrayHkt>([ | ||
1, | ||
4, | ||
2, | ||
3, | ||
5, | ||
2, | ||
3, | ||
]); | ||
|
||
// identity | ||
const mapped = f.map((x: string) => x)(arrCoy); | ||
assertEquals(getValue(mapped), getValue(arrCoy)); | ||
|
||
// composition | ||
const dup = (x: string) => x + x; | ||
const first = (x: string) => x.charAt(0); | ||
assertEquals( | ||
getValue(f.map((x: string) => dup(first(x)))(arrCoy)), | ||
getValue(f.map(dup)(f.map(first)(arrCoy))), | ||
); | ||
}); | ||
|
||
Deno.test("applicative functor laws", () => { | ||
const a = applicative(Array.applicative); | ||
const arrCoy = coyoneda((x: number) => x.toString())<Array.ArrayHkt>([ | ||
1, | ||
4, | ||
2, | ||
3, | ||
5, | ||
2, | ||
3, | ||
]); | ||
|
||
// identity | ||
assertEquals( | ||
getValue(a.apply(a.pure((x: string) => x))(arrCoy)), | ||
getValue(arrCoy), | ||
); | ||
|
||
// composition | ||
const exclamation = a.pure((x: string) => x + "!"); | ||
const question = a.pure((x: string) => x + "?"); | ||
assertEquals( | ||
getValue( | ||
a.apply( | ||
a.apply( | ||
a.apply(a.pure( | ||
(f: (x: string) => string) => | ||
(g: (x: string) => string) => | ||
(i: string) => f(g(i)), | ||
))(exclamation), | ||
)(question), | ||
)(arrCoy), | ||
), | ||
getValue(a.apply(exclamation)(a.apply(question)(arrCoy))), | ||
); | ||
|
||
// homomorphism | ||
const period = (x: string) => x + "."; | ||
assertEquals( | ||
getValue(a.apply(a.pure(period))(a.pure("Alice"))), | ||
getValue(a.pure(period("Alice"))), | ||
); | ||
|
||
// interchange | ||
assertEquals( | ||
getValue(a.apply(exclamation)(a.pure("Bob"))), | ||
getValue( | ||
a.apply(a.pure((op: (x: string) => string) => op("Bob")))( | ||
exclamation, | ||
), | ||
), | ||
); | ||
}); | ||
|
||
Deno.test("monad laws", () => { | ||
const m = monad(Array.monad); | ||
|
||
// left identity | ||
const upperCase = (x: string) => | ||
coyoneda((x: string) => x.toUpperCase())<Array.ArrayHkt>([x]); | ||
assertEquals( | ||
getValue(m.flatMap(upperCase)(m.pure("foo"))), | ||
getValue(upperCase("foo")), | ||
); | ||
|
||
// right identity | ||
const data = upperCase("bar"); | ||
assertEquals(getValue(m.flatMap(m.pure)(data)), getValue(data)); | ||
|
||
// associativity | ||
const shout = (x: string) => | ||
coyoneda((x: string) => x + " eh!")<Array.ArrayHkt>([x]); | ||
assertEquals( | ||
getValue(m.flatMap(shout)(m.flatMap(upperCase)(data))), | ||
getValue( | ||
m.flatMap((x: string) => m.flatMap(shout)(upperCase(x)))(data), | ||
), | ||
); | ||
}); | ||
|
||
Deno.test("comonad laws", () => { | ||
const w = comonad(Zipper.comonad); | ||
const lowerZipper = lower(Zipper.functor); | ||
const equality = Zipper.partialEquality(strict<number>()); | ||
const zipperCoy = coyoneda((x: number) => x + 1)<Zipper.ZipperHkt>( | ||
Zipper.singleton(42), | ||
); | ||
|
||
// duplicate then extract | ||
assertEquals( | ||
equality( | ||
lowerZipper(w.extract(w.duplicate(zipperCoy))), | ||
lowerZipper(zipperCoy), | ||
), | ||
true, | ||
); | ||
|
||
// extract as identity of map | ||
assertEquals( | ||
equality( | ||
lowerZipper(w.map(w.extract)(w.duplicate(zipperCoy))), | ||
lowerZipper(zipperCoy), | ||
), | ||
true, | ||
); | ||
|
||
// duplicate as identity of map | ||
const coyEquality = Zipper.partialEqUnary.liftEq( | ||
partialEqUnary(Zipper.partialEqUnary).liftEq( | ||
partialEqUnary(Zipper.partialEqUnary).liftEq(strict<number>().eq), | ||
), | ||
); | ||
assertEquals( | ||
coyEquality( | ||
lowerZipper(w.duplicate(w.duplicate(zipperCoy))), | ||
lowerZipper(w.map(w.duplicate)(w.duplicate(zipperCoy))), | ||
), | ||
true, | ||
); | ||
}); | ||
|
||
Deno.test("foldRT", () => { | ||
const arrCoy = coyoneda((x: number) => x + 1)<Array.ArrayHkt>( | ||
[42, 4, 3], | ||
); | ||
const actual = foldRT(Array.foldable)( | ||
(next: number) => (acc: readonly number[]) => [next, ...acc], | ||
)([])(arrCoy); | ||
assertEquals(actual, [43, 5, 4]); | ||
}); | ||
|
||
Deno.test("traversable functor laws", () => { | ||
const tra = traversable(Array.traversable); | ||
const arrCoy = coyoneda((x: string) => x + "!")<Array.ArrayHkt>(["42"]); | ||
|
||
// naturality | ||
const first = <T>( | ||
x: readonly T[], | ||
): Option.Option<T> => 0 in x ? Option.some(x[0]) : Option.none(); | ||
const dup = (x: string): readonly string[] => [x + "0", x + "1"]; | ||
const equality = partialEq({ | ||
lifter: Array.partialEqUnary, | ||
equality: (l: string, r: string) => l === r, | ||
}); | ||
const equalityOnOption = Option.partialEq(equality); | ||
assertEquals( | ||
equalityOnOption.eq( | ||
first(tra.traverse(Array.applicative)(dup)(arrCoy)), | ||
tra.traverse(Option.applicative)((item: string) => | ||
first(dup(item)) | ||
)(arrCoy), | ||
), | ||
true, | ||
); | ||
|
||
// identity | ||
assertEquals( | ||
equality.eq( | ||
tra.traverse(Identity.applicative)((a: string) => a)(arrCoy), | ||
arrCoy, | ||
), | ||
true, | ||
); | ||
|
||
// composition | ||
const firstCh = (x: string): Option.Option<string> => | ||
x.length > 0 ? Option.some(x.charAt(0)) : Option.none(); | ||
assertEquals( | ||
Array.partialEquality(equalityOnOption)( | ||
tra.traverse( | ||
Compose.applicative(Array.applicative)(Option.applicative), | ||
)((x: string) => Array.map(firstCh)(dup(x)))(arrCoy), | ||
Array.map(tra.traverse(Option.applicative)(firstCh))( | ||
tra.traverse(Array.applicative)(dup)(arrCoy), | ||
), | ||
), | ||
true, | ||
); | ||
}); | ||
|
||
Deno.test("distributive functor laws", () => { | ||
const g = distributive(Func.distributive<number>()); | ||
const fnEquality = ( | ||
l: (x: number) => readonly number[], | ||
r: (x: number) => readonly number[], | ||
) => { | ||
for (let i = -100; i < 100; ++i) { | ||
if (!Array.partialEq(strict<number>()).eq([...l(i)], [...r(i)])) { | ||
return false; | ||
} | ||
} | ||
return true; | ||
}; | ||
const lowerFn = lower(Func.functor<number>()); | ||
const data = [ | ||
coyoneda((x: number) => x + 1)<Apply2Only<Func.FnHkt, number>>((x) => | ||
x * 2 | ||
), | ||
coyoneda((x: number) => x + 2)<Apply2Only<Func.FnHkt, number>>((x) => | ||
x * 3 | ||
), | ||
]; | ||
|
||
// identity | ||
assertEquals( | ||
fnEquality( | ||
lowerFn(g.distribute(Array.functor)(data)), | ||
lowerFn( | ||
g.distribute(Array.functor)( | ||
Array.map(( | ||
x: Coyoneda<Apply2Only<Func.FnHkt, number>, number>, | ||
) => x)(data), | ||
), | ||
), | ||
), | ||
true, | ||
); | ||
|
||
// reversibility | ||
const funCoy: Coyoneda< | ||
Apply2Only<Func.FnHkt, number>, | ||
Func.Fn<number, number> | ||
> = coyoneda((x: number) => (y: number) => x + y)((x: number) => x - 1); | ||
const mapped: Func.Fn< | ||
number, | ||
Coyoneda<Apply2Only<Func.FnHkt, number>, number> | ||
> = Func.distributive<number>().distribute( | ||
functor<Apply2Only<Func.FnHkt, number>>(), | ||
)(funCoy); | ||
const reversed = g.distribute(Func.functor<number>())(mapped); | ||
|
||
for (let i = -100; i < 100; ++i) { | ||
for (let j = -100; j < 100; ++j) { | ||
assertEquals( | ||
lowerFn(reversed)(i)(j), | ||
lowerFn(funCoy)(i)(j), | ||
); | ||
} | ||
} | ||
}); |
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