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Applicative as AP,
Monad as MD,
SemiApplicative as SA,
} from '@effect/typeclass'
import {Applicative as optionApplicative} from '@effect/typeclass/data/Option'
import {identity, pipe} from 'effect'
import {apply, compose} from 'effect/Function'
import type {TypeLambda} from 'effect/HKT'
import {addLawSets, Law, lawTests} from '../../../law.js'
import {monoidLaws} from '../concrete/Monoid.js'
import {withOuterOption} from './compose.js'
import {covariantLaws} from './Covariant.js'
import type {BuildParameterized, ParameterizedGiven as Given} from './given.js'
import {unfoldGiven} from './given.js'
import {BuildInternal} from './internal.js'
/**
* Typeclass laws for `Applicative`.
* @category typeclass laws
*/
export const applicativeLaws: BuildParameterized<ApplicativeTypeLambda> = <
F1 extends TypeLambda,
A,
B = A,
C = A,
R = never,
O = unknown,
E = unknown,
>(
given: Given<ApplicativeTypeLambda, F1, A, B, C, R, O, E>,
suffix?: string,
) => {
const {Monoid: monoid, F, fa, equalsA, getEquivalence} = unfoldGiven(given)
return pipe(
buildLaws(`Alternative${suffix ?? ''}`, given),
pipe(given, covariantLaws, addLawSets),
addLawSets(
buildLaws(...withOuterOption('Applicative', given, optionApplicative)),
),
pipe(
{
suffix: 'Applicative.getMonoid()',
a: fa,
F: pipe(monoid, AP.getMonoid(F)<A, R, O, E>),
equalsA: getEquivalence(equalsA),
},
monoidLaws,
addLawSets,
),
)
}
const buildLaws: BuildInternal<ApplicativeTypeLambda> = <
F extends TypeLambda,
A,
B = A,
C = A,
R = never,
O = unknown,
E = unknown,
>(
name: string,
given: Given<ApplicativeTypeLambda, F, A, B, C, R, O, E>,
) => {
const {F, a, fa, equalsFa, equalsFb, equalsFc, ab, fabOf, fbcOf} =
unfoldGiven(given)
const [fab, fbc] = [fabOf(F.of), fbcOf(F.of)],
[ap, of, map] = [SA.ap(F), F.of, F.map]
return lawTests(
name,
Law(
'identity',
'id ▹ of ▹ ap(a) = a',
fa,
)(a => equalsFa(pipe(identity<A>, of, ap(a)), a)),
Law(
'homomorphism',
'ab ▹ of ▹ (a ▹ of ▹ ap) = a ▹ ab ▹ of',
a,
ab,
)((a, ab) => equalsFb(pipe(ab, of, ap(of(a))), pipe(a, ab, of))),
Law(
'associative composition',
'fbc ▹ map(compose) ▹ ap(fab) ▹ ap(fa) = fbc ▹ ap(fab ▹ ap(fa))',
fa,
fab,
fbc,
)((fa, fab, fbc) => {
const left = pipe(
fbc,
map(bc => compose(bc)<A>),
ap(fab),
ap(fa),
)
const right = pipe(fbc, ap(pipe(fab, ap(fa))))
return equalsFc(left, right)
}),
Law(
'interchange',
'fab ▹ ap(of(a)) = a ▹ apply ▹ of ▹ ap(Fab)',
a,
fab,
)((a, fab) => {
type AB = (ab: (a: A) => B) => B
return equalsFb(pipe(fab, ap(of(a))), pipe(a, apply, of<AB>, ap(fab)))
}),
Law(
'map consistency',
'fa ▹ map(ab) = ab ▹ of ▹ ap(fa)',
fa,
ab,
)((fa, ab) => equalsFb(pipe(fa, map(ab)), pipe(ab, F.of, ap(fa)))),
Law(
'product consistency',
'fab ▹ ap(fa) = product(fab, fa) ▹ map(([ab, a]) ⇒ ab(a))',
fa,
fab,
)((fa, fab) =>
equalsFb(
pipe(fab, ap(fa)),
pipe(
F.product(fab, fa),
map(([f, a]) => f(a)),
),
),
),
// Some applicatives do not have monads. For example: when the applicative is
// composed we have no monad for this law.
...('flatMap' in F
? [
Law(
'flatMap consistency',
'fab ▹ ap(fa) = fab ▹ flatMap(ab ⇒ map(fa, ab))',
fa,
fab,
)((fa, fab) => {
const flatMap = F.flatMap as MD.Monad<F>['flatMap']
return equalsFb(
ap(fab, fa),
pipe(
fab,
flatMap(ab => map(fa, ab)),
),
)
}),
]
: []),
)
}
/**
* Type lambda for the `Applicative` typeclass.
* @category type lambda
*/
export interface ApplicativeTypeLambda extends TypeLambda {
readonly type: AP.Applicative<this['Target'] & TypeLambda>
}
declare module './given.js' {
interface ParameterizedLambdas {
Applicative: ApplicativeTypeLambda
}
}
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