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import {binary, liftArbitraries, option, unary, unaryToKind} from '#arbitrary'
import type {LawSet, LiftEquivalence} from '#law'
import {liftEquivalences} from '#law'
import {Monoid as MO} from '@effect/typeclass'
import {Equivalence as EQ, Option as OP, pipe, Predicate as PR} from 'effect'
import type {Kind, TypeLambda} from 'effect/HKT'
import fc from 'fast-check'
/**
* Options for testing
* [parameterized-type](https://github.com/Effect-TS/effect/blob/main/packages/typeclass/README.md#parameterized-types)
* typeclasses. All the typeclass laws here expect their arguments to be of
* this type.
* @typeParam Typeclass - The type lambda of the typeclass under tests. For
* example when testing an instance of `Covariant<Array<string>>`, `Typeclass`
* would be the type lambda of the higher-kinded type `Covariant`.
* @typeParam F - The type lambda of the datatype under test. For example when
* testing an instance of `Covariant<Array<string>>`, `F` would be the
* type lambda of the higher-kinded type `Array`.
* @category harness
*/
export interface ParameterizedGiven<
Typeclass extends TypeLambda,
F1 extends TypeLambda,
A,
B = A,
C = A,
R = never,
O = unknown,
E = unknown,
> extends GivenConcerns<F1, A, B, C, R, O, E> {
/**
* The higher-kinded type `Typeclass<F>` is the typeclass instance under test.
* For example when testing the `Monad` laws on an `Either<number, string>`,
* this would be `Monad<Either>`.
*/
F: Kind<Typeclass, R, O, E, F1>
}
/**
* Unfolded requirements for testing parameterized typeclass laws.
* These are set as the union of all arguments required by the law predicates
* for parameterized typeclass laws.
*
* For example, the field `aob` is required by the
* {@link filterableLaws} _composition_ typeclass law, and `bab` by * the the
* _reduce_ law of {@link foldableLaws}.
*
* The nomenclature is based on the types of expressions, and is designed to
* make it easy, or at least easy as possible, for the author of law tests
* to find the correct arguments required by the predicates they are checking:
*
* 1. `A`, `B`, and `C` are the underlying types. There are no predicates in any
* parameterized typeclass law that require _more_ than three type parameters.
* 2. Arbitraries
* 1. Lower case `a`, `b`, and `c` are the names of arbitraries for the three
* underlying types.
* 2. The arbitraries for the data type under test are called `fa`, `fb`,
* and `fc`, standing for arbitraries of `F<A>`, `F<B>`, and `F<C>`
* respectively.
* 3. For simple unary arbitrary functions between two different underlying
* types, for example `A ⇒ B`, we use the lower case type names of argument
* followed by return value. For example an arbitrary for a function of type
* `C ⇒ B` we use the field name `cb`.
* 4. Binary functions use the same pattern, so an arbitrary for a function
* of type `(b: B, a: A) => B` will be called `bab`.
* 5. Unary function from a type to itself are named `endo[TYPE]`, for
* example `endoA` is the name of an arbitrary a function `A ⇒ A`.
* 6. Arbitraries for functions that lift an underlying type into the data
* type under test, also use the same naming pattern, except the return type
* is prefixed with a lowercase `f`. For example, `afb` is an arbitrary for
* a function of the type `A ⇒ F<B>`, where `F` is the higher-kinded
* datatype under test.
* 7. Arbitraries that lift an underlying type into the `Option` data type
* are also named in this way, except the `f` is replaced by an `o`. `aob`,
* for example, is the field where you will find an arbitrary function of
* type `A ⇒ Option<B>`.
* 8. `Applicative` laws, for example, require a function of the type:
* `(of: <T>(a: T) => F<T>>) => Arbitrary<F<(a: A) => B>>>`. I.e.:
* a function tht takes a _lifting_ function, and returns an arbitrary
* for the unary function `(a: A) => B`. These are called just like
* the lifted function argument would have been called (`afb`), but with
* an `Of` suffix, and the `f` is moved to the head position. The function
* above, for example, would be found in a field called `fabOf`.
* 3. Equivalences
* 1. The equivalences for the underlying types are called `equalsA`,
* `equalsB`, and `equalsC`.
* 2. The equivalences for the data type under test are called `equalsFa`,
* `equalsFb`, and `equalsFc`.
* 4. For laws that require predicates, we have fields `predicateA`,
* `predicateB`, and `predicateC`, for functions that take a value of the
* underlying type and returns a boolean.
*
* Having _all_ given arguments for all predicates in a central place is less
* [open-closed](https://en.wikipedia.org/wiki/Open%E2%80%93closed_principle).
* We still do it though, as it massively simplifies the code unfolding
* law predicate arguments.
* @typeParam Typeclass - The type lambda of the typeclass under tests. For
* example when testing an instance of `Covariant<Array<string>>`, `Typeclass`
* would be the type lambda of the higher-kinded type `Covariant`.
* @typeParam F - The type lambda of the datatype under test. For example when
* testing an instance of `Covariant<Array<string>>`, `F` would be the
* type lambda of the higher-kinded type `Array`.
* @typeParam A - First underlying type for the typeclass tests.
* @typeParam B - second underlying type for the typeclass tests.
* @typeParam C - Third underlying type for the typeclass tests. _Three_ is the
* maximum number of type parameters required by any predicate of the parameterized
* typeclass laws.
*/
export interface UnfoldedGiven<
Typeclass extends TypeLambda,
F1 extends TypeLambda,
A,
B = A,
C = A,
R = never,
O = unknown,
E = unknown,
> extends ParameterizedGiven<Typeclass, F1, A, B, C, R, O, E> {
equalsFa: EQ.Equivalence<Kind<F1, R, O, E, A>>
equalsFb: EQ.Equivalence<Kind<F1, R, O, E, B>>
equalsFc: EQ.Equivalence<Kind<F1, R, O, E, C>>
fa: fc.Arbitrary<Kind<F1, R, O, E, A>>
fb: fc.Arbitrary<Kind<F1, R, O, E, B>>
fc: fc.Arbitrary<Kind<F1, R, O, E, C>>
endoA: fc.Arbitrary<(a: A) => A>
ab: fc.Arbitrary<(a: A) => B>
bc: fc.Arbitrary<(a: B) => C>
ba: fc.Arbitrary<(a: B) => A>
cb: fc.Arbitrary<(a: C) => B>
bab: fc.Arbitrary<(b: B, a: A) => B>
afb: fc.Arbitrary<(a: A) => Kind<F1, R, O, E, B>>
bfc: fc.Arbitrary<(b: B) => Kind<F1, R, O, E, C>>
aob: fc.Arbitrary<(a: A) => OP.Option<B>>
boc: fc.Arbitrary<(a: B) => OP.Option<C>>
fabOf: (
of: <T>(a: T) => Kind<F1, R, O, E, T>,
) => fc.Arbitrary<Kind<F1, R, O, E, (a: A) => B>>
fbcOf: (
of: <T>(a: T) => Kind<F1, R, O, E, T>,
) => fc.Arbitrary<Kind<F1, R, O, E, (a: B) => C>>
}
/**
* Unfold a {@link ParameterizedGiven} into all arguments required by predicates
* of parameterized typeclass laws.
* @param given - The options to unfold.
* @category harness
*/
export const unfoldGiven = <
Typeclass extends TypeLambda,
F extends TypeLambda,
A,
B = A,
C = A,
R = never,
O = unknown,
E = unknown,
>(
given: ParameterizedGiven<Typeclass, F, A, B, C, R, O, E>,
): UnfoldedGiven<Typeclass, F, A, B, C, R, O, E> => {
const {a, b, c, equalsA, equalsB, equalsC, getArbitrary, getEquivalence} =
given,
[equalsFa, equalsFb, equalsFc] = liftEquivalences(getEquivalence)(
equalsA,
equalsB,
equalsC,
),
[fa, fb, fc] = liftArbitraries(getArbitrary)(a, b, c),
endoA = unary<A>()(a),
ab = unary<A>()(b),
bc = unary<B>()(c),
ba = unary<B>()(a),
cb = unary<C>()(b)
return {
...given,
equalsFa,
equalsFb,
equalsFc,
fa,
fb,
fc,
endoA,
ab,
bc,
ba,
cb,
bab: binary<B, A>()(b),
afb: pipe(b, unaryToKind<A>()(getArbitrary)),
bfc: pipe(c, unaryToKind<B>()(getArbitrary)),
aob: pipe(b, option, unary<A>()),
boc: pipe(c, option, unary<B>()),
fabOf: (of: <T>(a: T) => Kind<F, R, O, E, T>) => ab.map(of),
fbcOf: (of: <T>(a: T) => Kind<F, R, O, E, T>) => bc.map(of),
}
}
/**
* Use [module augmentation](https://www.typescriptlang.org/docs/handbook/declaration-merging.html)
* to add entries here for a new typeclasses. Used to map from typeclass
* name to the typeclass type lambda.
* @internal
* @category model
*/
export interface ParameterizedLambdas {}
/**
* The _equivalence_ and _arbitrary_ concerns of typeclass test options,
* together with an optional `Monoid` for the underlying type `A`
*
* Everything required to build laws for a typeclass except the instances under
* test.
* @category model
*/
export interface GivenConcerns<
F extends TypeLambda,
A,
B = A,
C = A,
R = never,
O = unknown,
E = unknown,
> extends GivenArbitraries<F, A, B, C, R, O, E>,
GivenEquivalence<F, A, B, C, R, O, E>,
GivenPredicates<A, B, C> {
/**
* Required `Monoid` for the underlying type `A`, useful for typeclasses
* like `Applicative` that can build their own `Monoid` instance from it.
*/
Monoid: MO.Monoid<A>
}
// The _equivalence_ concern of typeclass test options.
// @category model
interface GivenEquivalence<F extends TypeLambda, A, B, C, R, O, E> {
/** An equivalence for the underlying type `A`. */
equalsA: EQ.Equivalence<A>
/** An equivalence for the underlying type `B`. */
equalsB: EQ.Equivalence<B>
/** An equivalence for the underlying type `C`. */
equalsC: EQ.Equivalence<C>
/**
* A function that will get an equivalence for the type under test from an
* equivalence for the underlying type.
*/
getEquivalence: LiftEquivalence<F, R, O, E>
}
// The _arbitrary_ concern of typeclass test options.
// @category model
export interface GivenArbitraries<F extends TypeLambda, A, B, C, R, O, E> {
/** An arbitrary for the underlying type `A`. */
a: fc.Arbitrary<A>
/** An arbitrary for the underlying type `B`. */
b: fc.Arbitrary<B>
/** An arbitrary for the underlying type `C`. */
c: fc.Arbitrary<C>
/**
* A function that will get an arbitrary for the type under test from an
* arbitrary for the underlying type.
*/
getArbitrary: LiftArbitrary<F, R, O, E>
}
// The _predicate_ concern of typeclass test options. For each of the three
// underlying types, an arbitrary for its predicate.
interface GivenPredicates<A, B, C> {
/** Predicate for values of type `A`. */
predicateA: fc.Arbitrary<PR.Predicate<A>>
/** Predicate for values of type `B`. */
predicateB: fc.Arbitrary<PR.Predicate<B>>
/** Predicate for values of type `C`. */
predicateC: fc.Arbitrary<PR.Predicate<C>>
}
/**
* Interface for functions that build typeclass laws.
* @category harness
*/
export interface BuildParameterized<Typeclass extends TypeLambda> {
<F extends TypeLambda, A, B = A, C = A, R = never, O = unknown, E = unknown>(
given: ParameterizedGiven<Typeclass, F, A, B, C, R, O, E>,
suffix?: string,
): LawSet
}
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