Scala example source code file (ScalazProperties.scala)
The ScalazProperties.scala Scala example source codepackage scalaz
package scalacheck
import org.scalacheck.{Arbitrary, Gen, Prop, Properties}
import Prop.forAll
import Scalaz._
/**
* Scalacheck properties that should hold for instances of type classes defined in Scalaz Core.
*/
object ScalazProperties {
private def newProperties(name: String)(f: Properties => Unit): Properties = {
val p = new Properties(name)
f(p)
p
}
object equal {
def commutativity[A](implicit A: Equal[A], arb: Arbitrary[A]) = forAll(A.equalLaw.commutative _)
def reflexive[A](implicit A: Equal[A], arb: Arbitrary[A]) = forAll(A.equalLaw.reflexive _)
def transitive[A](implicit A: Equal[A], arb: Arbitrary[A]) = forAll(A.equalLaw.transitive _)
def naturality[A](implicit A: Equal[A], arb: Arbitrary[A]) = forAll(A.equalLaw.naturality _)
def laws[A](implicit A: Equal[A], arb: Arbitrary[A]): Properties =
newProperties("equal") { p =>
p.property("commutativity") = commutativity[A]
p.property("reflexive") = reflexive[A]
p.property("transitive") = transitive[A]
p.property("naturality") = naturality[A]
}
}
object order {
def antisymmetric[A](implicit A: Order[A], arb: Arbitrary[A]) =
forAll(A.orderLaw.antisymmetric _)
def transitiveOrder[A](implicit A: Order[A], arb: Arbitrary[A]) = forAll(A.orderLaw.transitiveOrder _)
def orderAndEqualConsistent[A](implicit A: Order[A], arb: Arbitrary[A]) = forAll(A.orderLaw.orderAndEqualConsistent _)
import scala.math.{Ordering => SOrdering}
def scalaOrdering[A: Order: SOrdering: Arbitrary] = forAll((a1: A, a2: A) => Order[A].order(a1, a2) == Ordering.fromInt(SOrdering[A].compare(a1, a2)))
def laws[A](implicit A: Order[A], arb: Arbitrary[A]): Properties =
newProperties("order") { p =>
p.include(equal.laws[A])
p.property("antisymmetric") = antisymmetric[A]
p.property("transitive order") = transitiveOrder[A]
p.property("order and equal consistent") = orderAndEqualConsistent[A]
}
}
object enum {
def succpred[A](implicit A: Enum[A], arb: Arbitrary[A]) = forAll(A.enumLaw.succpred _)
def predsucc[A](implicit A: Enum[A], arb: Arbitrary[A]) = forAll(A.enumLaw.predsucc _)
def minmaxpred[A](implicit A: Enum[A]): Prop = A.enumLaw.minmaxpred
def minmaxsucc[A](implicit A: Enum[A]): Prop = A.enumLaw.minmaxsucc
private[this] val smallInt = Gen.choose(-100, 100)
def succn[A](implicit A: Enum[A], arb: Arbitrary[A]) = forAll((x: A) => forAll(smallInt)(A.enumLaw.succn(x, _)))
def predn[A](implicit A: Enum[A], arb: Arbitrary[A]) = forAll((x: A) => forAll(smallInt)(A.enumLaw.predn(x, _)))
def succorder[A](implicit A: Enum[A], arb: Arbitrary[A]) = forAll(A.enumLaw.succorder _)
def predorder[A](implicit A: Enum[A], arb: Arbitrary[A]) = forAll(A.enumLaw.predorder _)
def laws[A](implicit A: Enum[A], arb: Arbitrary[A]): Properties =
newProperties("enum") { p =>
p.include(order.laws[A])
p.property("predecessor then successor is identity") = succpred[A]
p.property("successor then predecessor is identity") = predsucc[A]
p.property("predecessor of the min is the max") = minmaxpred[A]
p.property("successor of the max is the min") = minmaxsucc[A]
p.property("n-successor is n-times successor") = succn[A]
p.property("n-predecessor is n-times predecessor") = predn[A]
p.property("successor is greater or equal") = succorder[A]
p.property("predecessor is less or equal") = predorder[A]
}
}
object semigroup {
def associative[A](implicit A: Semigroup[A], eqa: Equal[A], arb: Arbitrary[A]) = forAll(A.semigroupLaw.associative _)
def laws[A](implicit A: Semigroup[A], eqa: Equal[A], arb: Arbitrary[A]): Properties =
newProperties("semigroup") { p =>
p.property("associative") = associative[A]
}
}
object monoid {
def leftIdentity[A](implicit A: Monoid[A], eqa: Equal[A], arb: Arbitrary[A]) = forAll(A.monoidLaw.leftIdentity _)
def rightIdentity[A](implicit A: Monoid[A], eqa: Equal[A], arb: Arbitrary[A]) = forAll(A.monoidLaw.rightIdentity _)
def laws[A](implicit A: Monoid[A], eqa: Equal[A], arb: Arbitrary[A]): Properties =
newProperties("monoid") { p =>
p.include(semigroup.laws[A])
p.property("left identity") = leftIdentity[A]
p.property("right identity") = rightIdentity[A]
}
}
object invariantFunctor {
def identity[F[_], X](implicit F: InvariantFunctor[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(F.invariantFunctorLaw.invariantIdentity[X] _)
def composite[F[_], X, Y, Z](implicit F: InvariantFunctor[F], af: Arbitrary[F[X]], axy: Arbitrary[(X => Y)],
ayz: Arbitrary[(Y => Z)], ayx: Arbitrary[(Y => X)], azy: Arbitrary[(Z => Y)], ef: Equal[F[Z]]) =
forAll(F.invariantFunctorLaw.invariantComposite[X, Y, Z] _)
def laws[F[_]](implicit F: InvariantFunctor[F], af: Arbitrary[F[Int]], axy: Arbitrary[(Int => Int)],
ef: Equal[F[Int]]): Properties =
newProperties("invariantFunctor") { p =>
p.property("identity") = identity[F, Int]
p.property("composite") = composite[F, Int, Int, Int]
}
}
object functor {
def identity[F[_], X](implicit F: Functor[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(F.functorLaw.identity[X] _)
def composite[F[_], X, Y, Z](implicit F: Functor[F], af: Arbitrary[F[X]], axy: Arbitrary[(X => Y)],
ayz: Arbitrary[(Y => Z)], ef: Equal[F[Z]]) =
forAll(F.functorLaw.composite[X, Y, Z] _)
def laws[F[_]](implicit F: Functor[F], af: Arbitrary[F[Int]], axy: Arbitrary[(Int => Int)],
ef: Equal[F[Int]]): Properties =
newProperties("functor") { p =>
p.include(invariantFunctor.laws[F])
p.property("identity") = identity[F, Int]
p.property("composite") = composite[F, Int, Int, Int]
}
}
object profunctor {
def identity[M[_,_], A, B](implicit M: Profunctor[M], mba: Arbitrary[M[A, B]], ef: Equal[M[A,B]]) =
forAll(M.profunctorLaw.identity[A, B] _)
def compose[M[_,_], A, B, C, D, E, F](implicit M: Profunctor[M], mab: Arbitrary[M[A, D]], fba: Arbitrary[(B => A)], fcb: Arbitrary[(C => B)], fde: Arbitrary[(D => E)], fef: Arbitrary[(E => F)], e: Equal[M[C, F]]) =
forAll(M.profunctorLaw.composite[A, B, C, D, E, F] _ )
def laws[M[_,_]](implicit F: Profunctor[M], af: Arbitrary[M[Int, Int]], itf: Arbitrary[(Int => Int)], e: Equal[M[Int, Int]]): Properties =
newProperties("profunctor") { p =>
p.property("identity") = identity[M, Int, Int]
p.property("composite") = compose[M, Int, Int, Int, Int, Int, Int]
}
}
object align {
def collapse[F[_], A](implicit F: Align[F], E: Equal[F[A \&/ A]], A: Arbitrary[F[A]]): Prop =
forAll(F.alignLaw.collapse[A] _)
def laws[F[_]](implicit F: Align[F], af: Arbitrary[F[Int]],
e: Equal[F[Int]], ef: Equal[F[Int \&/ Int]]): Properties =
newProperties("align") { p =>
p.include(functor.laws[F])
p.property("collapse") = collapse[F, Int]
}
}
object apply {self =>
def composition[F[_], X, Y, Z](implicit ap: Apply[F], afx: Arbitrary[F[X]], au: Arbitrary[F[Y => Z]],
av: Arbitrary[F[X => Y]], e: Equal[F[Z]]) = forAll(ap.applyLaw.composition[X, Y, Z] _)
def laws[F[_]](implicit F: Apply[F], af: Arbitrary[F[Int]],
aff: Arbitrary[F[Int => Int]], e: Equal[F[Int]]): Properties =
newProperties("apply") { p =>
p.include(functor.laws[F])
p.property("composition") = self.composition[F, Int, Int, Int]
}
}
object applicative {
def identity[F[_], X](implicit f: Applicative[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(f.applicativeLaw.identityAp[X] _)
def homomorphism[F[_], X, Y](implicit ap: Applicative[F], ax: Arbitrary[X], af: Arbitrary[X => Y], e: Equal[F[Y]]) =
forAll(ap.applicativeLaw.homomorphism[X, Y] _)
def interchange[F[_], X, Y](implicit ap: Applicative[F], ax: Arbitrary[X], afx: Arbitrary[F[X => Y]], e: Equal[F[Y]]) =
forAll(ap.applicativeLaw.interchange[X, Y] _)
def mapApConsistency[F[_], X, Y](implicit ap: Applicative[F], ax: Arbitrary[F[X]], afx: Arbitrary[X => Y], e: Equal[F[Y]]) =
forAll(ap.applicativeLaw.mapLikeDerived[X, Y] _)
def laws[F[_]](implicit F: Applicative[F], af: Arbitrary[F[Int]],
aff: Arbitrary[F[Int => Int]], e: Equal[F[Int]]): Properties =
newProperties("applicative") { p =>
p.include(ScalazProperties.apply.laws[F])
p.property("identity") = applicative.identity[F, Int]
p.property("homomorphism") = applicative.homomorphism[F, Int, Int]
p.property("interchange") = applicative.interchange[F, Int, Int]
p.property("map consistent with ap") = applicative.mapApConsistency[F, Int, Int]
}
}
object bind {
def associativity[M[_], X, Y, Z](implicit M: Bind[M], amx: Arbitrary[M[X]], af: Arbitrary[(X => M[Y])],
ag: Arbitrary[(Y => M[Z])], emz: Equal[M[Z]]) =
forAll(M.bindLaw.associativeBind[X, Y, Z] _)
def bindApConsistency[M[_], X, Y](implicit M: Bind[M], amx: Arbitrary[M[X]],
af: Arbitrary[M[X => Y]], emy: Equal[M[Y]]) =
forAll(M.bindLaw.apLikeDerived[X, Y] _)
def laws[M[_]](implicit a: Bind[M], am: Arbitrary[M[Int]],
af: Arbitrary[Int => M[Int]], ag: Arbitrary[M[Int => Int]], e: Equal[M[Int]]): Properties =
newProperties("bind") { p =>
p.include(ScalazProperties.apply.laws[M])
p.property("associativity") = bind.associativity[M, Int, Int, Int]
p.property("ap consistent with bind") = bind.bindApConsistency[M, Int, Int]
}
}
object bindRec {
def tailrecBindConsistency[M[_], X](implicit M: BindRec[M], ax: Arbitrary[X], af: Arbitrary[X => M[X]],
emx: Equal[M[X]]) =
forAll(M.bindRecLaw.tailrecBindConsistency[X] _)
def laws[M[_]](implicit a: BindRec[M], am: Arbitrary[M[Int]],
af: Arbitrary[Int => M[Int]], ag: Arbitrary[M[Int => Int]], e: Equal[M[Int]]): Properties =
newProperties("bindRec") { p =>
p.property("tailrecM is consistent with bind") = bindRec.tailrecBindConsistency[M, Int]
}
}
object monad {
def rightIdentity[M[_], X](implicit M: Monad[M], e: Equal[M[X]], a: Arbitrary[M[X]]) =
forAll(M.monadLaw.rightIdentity[X] _)
def leftIdentity[M[_], X, Y](implicit am: Monad[M], emy: Equal[M[Y]], ax: Arbitrary[X], af: Arbitrary[(X => M[Y])]) =
forAll(am.monadLaw.leftIdentity[X, Y] _)
def laws[M[_]](implicit a: Monad[M], am: Arbitrary[M[Int]],
af: Arbitrary[Int => M[Int]], ag: Arbitrary[M[Int => Int]], e: Equal[M[Int]]): Properties =
newProperties("monad") { p =>
p.include(applicative.laws[M])
p.include(bind.laws[M])
p.property("right identity") = monad.rightIdentity[M, Int]
p.property("left identity") = monad.leftIdentity[M, Int, Int]
}
}
object cobind {
def cobindAssociative[F[_], A, B, C, D](implicit F: Cobind[F], D: Equal[D], fa: Arbitrary[F[A]],
f: Arbitrary[F[A] => B], g: Arbitrary[F[B] => C], h: Arbitrary[F[C] => D]) =
forAll(F.cobindLaw.cobindAssociative[A, B, C, D] _)
def laws[F[_]](implicit a: Cobind[F], am: Arbitrary[F[Int]], e: Equal[F[Int]]): Properties =
newProperties("cobind") { p =>
p.include(functor.laws[F])
p.property("cobind associative") = cobindAssociative[F, Int, Int, Int, Int]
}
}
object comonad {
def cobindLeftIdentity[F[_], A](implicit F: Comonad[F], F0: Equal[F[A]], fa: Arbitrary[F[A]]) =
forAll(F.comonadLaw.cobindLeftIdentity[A] _)
def cobindRightIdentity[F[_], A, B](implicit F: Comonad[F], F0: Equal[B], fa: Arbitrary[F[A]], f: Arbitrary[F[A] => B]) =
forAll(F.comonadLaw.cobindRightIdentity[A, B] _)
def laws[F[_]](implicit a: Comonad[F], am: Arbitrary[F[Int]],
af: Arbitrary[F[Int] => Int], e: Equal[F[Int]]): Properties =
newProperties("comonad") { p =>
p.include(cobind.laws[F])
p.property("cobind left identity") = cobindLeftIdentity[F, Int]
p.property("cobind right identity") = cobindRightIdentity[F, Int, Int]
}
}
private def resizeProp(p: Prop, max: Int): Prop =
Prop(params => p(params.withSize(params.size % (max + 1))))
object traverse {
def identityTraverse[F[_], X, Y](implicit f: Traverse[F], afx: Arbitrary[F[X]], axy: Arbitrary[X => Y], ef: Equal[F[Y]]) =
forAll(f.traverseLaw.identityTraverse[X, Y] _)
def purity[F[_], G[_], X](implicit f: Traverse[F], afx: Arbitrary[F[X]], G: Applicative[G], ef: Equal[G[F[X]]]) =
forAll(f.traverseLaw.purity[G, X] _)
def sequentialFusion[F[_], N[_], M[_], A, B, C](implicit fa: Arbitrary[F[A]], amb: Arbitrary[A => M[B]], bnc: Arbitrary[B => N[C]],
F: Traverse[F], N: Applicative[N], M: Applicative[M], MN: Equal[M[N[F[C]]]]): Prop =
forAll(F.traverseLaw.sequentialFusion[N, M, A, B, C] _)
def naturality[F[_], N[_], M[_], A](nat: (M ~> N))
(implicit fma: Arbitrary[F[M[A]]], F: Traverse[F], N: Applicative[N], M: Applicative[M], NFA: Equal[N[F[A]]]): Prop =
forAll(F.traverseLaw.naturality[N, M, A](nat) _)
def parallelFusion[F[_], N[_], M[_], A, B](implicit fa: Arbitrary[F[A]], amb: Arbitrary[A => M[B]], anb: Arbitrary[A => N[B]],
F: Traverse[F], N: Applicative[N], M: Applicative[M], MN: Equal[(M[F[B]], N[F[B]])]): Prop =
forAll(F.traverseLaw.parallelFusion[N, M, A, B] _)
def laws[F[_]](implicit fa: Arbitrary[F[Int]], F: Traverse[F], EF: Equal[F[Int]]): Properties =
newProperties("traverse") { p =>
p.include(functor.laws[F])
p.include(foldable.laws[F])
p.property("identity traverse") = identityTraverse[F, Int, Int]
import std.list._, std.option._, std.stream._
p.property("purity.option") = purity[F, Option, Int]
p.property("purity.stream") = purity[F, Stream, Int]
p.property("sequential fusion") = resizeProp(sequentialFusion[F, Option, List, Int, Int, Int], 3)
// TODO naturality, parallelFusion
}
}
object bifoldable {
def leftFMConsistent[F[_, _], A, B](implicit F: Bifoldable[F], afa: Arbitrary[F[A, B]], ea: Equal[A], eb: Equal[B]) =
forAll(F.bifoldableLaw.leftFMConsistent[A, B] _)
def rightFMConsistent[F[_, _], A, B](implicit F: Bifoldable[F], afa: Arbitrary[F[A, B]], ea: Equal[A], eb: Equal[B]) =
forAll(F.bifoldableLaw.rightFMConsistent[A, B] _)
def laws[F[_, _]](implicit fa: Arbitrary[F[Int, Int]], F: Bifoldable[F]): Properties =
newProperties("bifoldable") { p =>
p.property("consistent left bifold") = leftFMConsistent[F, Int, Int]
p.property("consistent right bifold") = rightFMConsistent[F, Int, Int]
implicit val left = F.leftFoldable[Int]
implicit val right = F.rightFoldable[Int]
p.include(foldable.laws[F[?, Int]])
p.include(foldable.laws[F[Int, ?]])
}
}
object bitraverse {
def laws[F[_, _]](implicit fa: Arbitrary[F[Int,Int]], F: Bitraverse[F], EF: Equal[F[Int, Int]]): Properties =
newProperties("bitraverse") { p =>
p.include(bifoldable.laws[F])
implicit val left = F.leftTraverse[Int]
implicit val right = F.rightTraverse[Int]
p.include(traverse.laws[F[?, Int]])
p.include(traverse.laws[F[Int, ?]])
}
}
object plus {
def associative[F[_], X](implicit f: Plus[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(f.plusLaw.associative[X] _)
def laws[F[_]](implicit F: Plus[F], afx: Arbitrary[F[Int]], ef: Equal[F[Int]]): Properties =
newProperties("plus") { p =>
p.include(semigroup.laws[F[Int]](F.semigroup[Int], implicitly, implicitly))
p.property("associative") = associative[F, Int]
}
}
object plusEmpty {
def leftPlusIdentity[F[_], X](implicit f: PlusEmpty[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(f.plusEmptyLaw.leftPlusIdentity[X] _)
def rightPlusIdentity[F[_], X](implicit f: PlusEmpty[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(f.plusEmptyLaw.rightPlusIdentity[X] _)
def laws[F[_]](implicit F: PlusEmpty[F], afx: Arbitrary[F[Int]], af: Arbitrary[Int => Int], ef: Equal[F[Int]]): Properties =
newProperties("plusEmpty") { p =>
p.include(plus.laws[F])
p.include(monoid.laws[F[Int]](F.monoid[Int], implicitly, implicitly))
p.property("left plus identity") = leftPlusIdentity[F, Int]
p.property("right plus identity") = rightPlusIdentity[F, Int]
}
}
object isEmpty {
def emptyIsEmpty[F[_], X](implicit f: IsEmpty[F]):Prop =
f.isEmptyLaw.emptyIsEmpty[X]
def emptyPlusIdentity[F[_], X](implicit f: IsEmpty[F], afx: Arbitrary[F[X]]) =
forAll(f.isEmptyLaw.emptyPlusIdentity[X] _)
def laws[F[_]](implicit F: IsEmpty[F], afx: Arbitrary[F[Int]], ef: Equal[F[Int]]): Properties =
newProperties("isEmpty") { p =>
p.include(plusEmpty.laws[F])
p.property("empty is empty") = emptyIsEmpty[F, Int]
p.property("empty plus identity") = emptyPlusIdentity[F, Int]
}
}
object monadPlus {
def emptyMap[F[_], X](implicit f: MonadPlus[F], afx: Arbitrary[X => X], ef: Equal[F[X]]) =
forAll(f.monadPlusLaw.emptyMap[X] _)
def leftZero[F[_], X](implicit F: MonadPlus[F], afx: Arbitrary[X => F[X]], ef: Equal[F[X]]) =
forAll(F.monadPlusLaw.leftZero[X] _)
def rightZero[F[_], X](implicit F: MonadPlus[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(F.strongMonadPlusLaw.rightZero[X] _)
def laws[F[_]](implicit F: MonadPlus[F], afx: Arbitrary[F[Int]], afy: Arbitrary[F[Int => Int]], ef: Equal[F[Int]]): Properties =
newProperties("monad plus") { p =>
p.include(monad.laws[F])
p.include(plusEmpty.laws[F])
p.property("empty map") = emptyMap[F, Int]
p.property("left zero") = leftZero[F, Int]
}
def strongLaws[F[_]](implicit F: MonadPlus[F], afx: Arbitrary[F[Int]], afy: Arbitrary[F[Int => Int]], ef: Equal[F[Int]]) =
newProperties("monad plus") { p =>
p.include(laws[F])
p.property("right zero") = rightZero[F, Int]
}
}
object foldable {
def leftFMConsistent[F[_], A](implicit F: Foldable[F], afa: Arbitrary[F[A]], ea: Equal[A]) =
forAll(F.foldableLaw.leftFMConsistent[A] _)
def rightFMConsistent[F[_], A](implicit F: Foldable[F], afa: Arbitrary[F[A]], ea: Equal[A]) =
forAll(F.foldableLaw.rightFMConsistent[A] _)
def laws[F[_]](implicit fa: Arbitrary[F[Int]], F: Foldable[F], EA: Equal[Int]): Properties =
newProperties("foldable") { p =>
p.property("consistent left fold") = leftFMConsistent[F, Int]
p.property("consistent right fold") = rightFMConsistent[F, Int]
}
}
object foldable1 {
type Pair[A] = (A, A)
def leftFM1Consistent[F[_], A](implicit F: Foldable1[F], fa: Arbitrary[F[A]], ea: Equal[A]) =
forAll(F.foldable1Law.leftFM1Consistent[A] _)
def rightFM1Consistent[F[_], A](implicit F: Foldable1[F], fa: Arbitrary[F[A]], ea: Equal[A]) =
forAll(F.foldable1Law.rightFM1Consistent[A] _)
def laws[F[_]](implicit fa: Arbitrary[F[Int]],
F: Foldable1[F], EA: Equal[Int]): Properties =
newProperties("foldable1") { p =>
p.include(foldable.laws[F])
p.property("consistent left fold1") = leftFM1Consistent[F, Int]
p.property("consistent right fold1") = rightFM1Consistent[F, Int]
}
}
object traverse1 {
def identityTraverse1[F[_], X, Y](implicit f: Traverse1[F], afx: Arbitrary[F[X]], axy: Arbitrary[X => Y], ef: Equal[F[Y]]) =
forAll(f.traverse1Law.identityTraverse1[X, Y] _)
def sequentialFusion1[F[_], N[_], M[_], A, B, C](implicit fa: Arbitrary[F[A]], amb: Arbitrary[A => M[B]], bnc: Arbitrary[B => N[C]],
F: Traverse1[F], N: Apply[N], M: Apply[M], MN: Equal[M[N[F[C]]]]): Prop =
forAll(F.traverse1Law.sequentialFusion1[N, M, A, B, C] _)
def naturality1[F[_], N[_], M[_], A](nat: (M ~> N))
(implicit fma: Arbitrary[F[M[A]]], F: Traverse1[F], N: Apply[N], M: Apply[M], NFA: Equal[N[F[A]]]): Prop =
forAll(F.traverse1Law.naturality1[N, M, A](nat) _)
def parallelFusion1[F[_], N[_], M[_], A, B](implicit fa: Arbitrary[F[A]], amb: Arbitrary[A => M[B]], anb: Arbitrary[A => N[B]],
F: Traverse1[F], N: Apply[N], M: Apply[M], MN: Equal[(M[F[B]], N[F[B]])]): Prop =
forAll(F.traverse1Law.parallelFusion1[N, M, A, B] _)
def laws[F[_]](implicit fa: Arbitrary[F[Int]], F: Traverse1[F], EF: Equal[F[Int]]): Properties =
newProperties("traverse1") { p =>
p.include(traverse.laws[F])
p.include(foldable1.laws[F])
p.property("identity traverse1") = identityTraverse1[F, Int, Int]
import std.list._, std.option._
p.property("sequential fusion (1)") = resizeProp(sequentialFusion1[F, Option, List, Int, Int, Int], 3)
// TODO naturality1, parallelFusion1
}
}
object zip {
def zipPreservation[F[_], X](implicit F: Zip[F], FF: Functor[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(F.zipLaw.zipPreservation[X] _)
def zipSymmetric[F[_], X, Y](implicit F: Zip[F], FF: Functor[F], afx: Arbitrary[F[X]], afy: Arbitrary[F[Y]], ef: Equal[F[X]]) =
forAll(F.zipLaw.zipSymmetric[X, Y] _)
def laws[F[_]](implicit fa: Arbitrary[F[Int]], F: Zip[F], FF: Functor[F], EF: Equal[F[Int]]): Properties =
newProperties("zip") { p =>
p.property("preserves structure") = zipPreservation[F, Int]
p.property("symmetry") = zipSymmetric[F, Int, Int]
}
}
object contravariant {
def identity[F[_], X](implicit F: Contravariant[F], afx: Arbitrary[F[X]], ef: Equal[F[X]]) =
forAll(F.contravariantLaw.identity[X] _)
def composite[F[_], X, Y, Z](implicit F: Contravariant[F], af: Arbitrary[F[Z]], axy: Arbitrary[(X => Y)],
ayz: Arbitrary[(Y => Z)], ef: Equal[F[X]]) =
forAll(F.contravariantLaw.composite[Z, Y, X] _)
def laws[F[_]](implicit F: Contravariant[F], af: Arbitrary[F[Int]], axy: Arbitrary[(Int => Int)],
ef: Equal[F[Int]]): Properties =
newProperties("contravariant") { p =>
p.include(invariantFunctor.laws[F])
p.property("identity") = identity[F, Int]
p.property("composite") = composite[F, Int, Int, Int]
}
}
object divide {
def composition[F[_], A](implicit F: Divide[F], A: Arbitrary[F[A]], E: Equal[F[A]]) =
forAll(F.divideLaw.composition[A] _)
def laws[F[_]](implicit F: Divide[F], af: Arbitrary[F[Int]], axy: Arbitrary[Int => Int],
ef: Equal[F[Int]]): Properties =
newProperties("divide") { p =>
p.include(contravariant.laws[F])
p.property("composition") = composition[F, Int]
}
}
object divisible {
def rightIdentity[F[_], A](implicit F: Divisible[F], A: Arbitrary[F[A]], E: Equal[F[A]]) =
forAll(F.divisibleLaw.rightIdentity[A] _)
def leftIdentity[F[_], A](implicit F: Divisible[F], A: Arbitrary[F[A]], E: Equal[F[A]]) =
forAll(F.divisibleLaw.leftIdentity[A] _)
def laws[F[_]](implicit F: Divisible[F], af: Arbitrary[F[Int]], axy: Arbitrary[Int => Int],
ef: Equal[F[Int]]): Properties =
newProperties("divisible") { p =>
p.include(divide.laws[F])
p.property("right identity") = rightIdentity[F, Int]
p.property("left identity") = leftIdentity[F, Int]
}
}
object compose {
def associative[=>:[_, _], A, B, C, D](implicit ab: Arbitrary[A =>: B], bc: Arbitrary[B =>: C],
cd: Arbitrary[C =>: D], C: Compose[=>:], E: Equal[A =>: D]) =
forAll(C.composeLaw.associative[A, B, C, D] _)
def laws[=>:[_, _]](implicit C: Compose[=>:], AB: Arbitrary[Int =>: Int], E: Equal[Int =>: Int]): Properties =
newProperties("compose") { p =>
p.property("associative") = associative[=>:, Int, Int, Int, Int]
p.include(semigroup.laws[Int =>: Int](C.semigroup[Int], implicitly, implicitly))
}
}
object category {
def leftIdentity[=>:[_, _], A, B](implicit ab: Arbitrary[A =>: B], C: Category[=>:], E: Equal[A =>: B]) =
forAll(C.categoryLaw.leftIdentity[A, B] _)
def rightIdentity[=>:[_, _], A, B](implicit ab: Arbitrary[A =>: B], C: Category[=>:], E: Equal[A =>: B]) =
forAll(C.categoryLaw.rightIdentity[A, B] _)
def laws[=>:[_, _]](implicit C: Category[=>:], AB: Arbitrary[Int =>: Int], E: Equal[Int =>: Int]): Properties =
newProperties("category") { p =>
p.include(compose.laws[=>:])
p.property("left identity") = leftIdentity[=>:, Int, Int]
p.property("right identity") = rightIdentity[=>:, Int, Int]
p.include(monoid.laws[Int =>: Int](C.monoid[Int], implicitly, implicitly))
}
}
object associative {
def leftRight[=>:[_, _], X, Y, Z](implicit F: Associative[=>:], af: Arbitrary[X =>: (Y =>: Z)], ef: Equal[X =>: (Y =>: Z)]) =
forAll(F.associativeLaw.leftRight[X, Y, Z] _)
def rightLeft[=>:[_, _], X, Y, Z](implicit F: Associative[=>:], af: Arbitrary[(X =>: Y) =>: Z], ef: Equal[(X =>: Y) =>: Z]) =
forAll(F.associativeLaw.rightLeft[X, Y, Z] _)
def laws[=>:[_, _]](implicit F: Associative[=>:],
al: Arbitrary[(Int =>: Int) =>: Int], ar: Arbitrary[Int =>: (Int =>: Int)],
el: Equal[(Int =>: Int) =>: Int], er: Equal[Int =>: (Int =>: Int)]): Properties =
newProperties("associative") { p =>
p.property("left and then right reassociation is identity") = leftRight[=>:, Int, Int, Int]
p.property("right and then left reassociation is identity") = rightLeft[=>:, Int, Int, Int]
}
}
object bifunctor {
def laws[F[_, _]](implicit F: Bifunctor[F], E: Equal[F[Int, Int]], af: Arbitrary[F[Int, Int]],
axy: Arbitrary[(Int => Int)]): Properties =
newProperties("bifunctor") { p =>
p.include(functor.laws[F[?, Int]](F.leftFunctor[Int], implicitly, implicitly, implicitly))
p.include(functor.laws[F[Int, ?]](F.rightFunctor[Int], implicitly, implicitly, implicitly))
}
}
object lens {
def identity[A, B](l: Lens[A, B])(implicit A: Arbitrary[A], EA: Equal[A]) = forAll(l.lensLaw.identity _)
def retention[A, B](l: Lens[A, B])(implicit A: Arbitrary[A], B: Arbitrary[B], EB: Equal[B]) = forAll(l.lensLaw.retention _)
def doubleSet[A, B](l: Lens[A, B])(implicit A: Arbitrary[A], B: Arbitrary[B], EB: Equal[A]) = forAll(l.lensLaw.doubleSet _)
def laws[A, B](l: Lens[A, B])(implicit A: Arbitrary[A], B: Arbitrary[B], EA: Equal[A], EB: Equal[B]): Properties =
newProperties("lens") { p =>
p.property("identity") = identity[A, B](l)
p.property("retention") = retention[A, B](l)
p.property("doubleSet") = doubleSet[A, B](l)
}
}
object monadError {
def raisedErrorsHandled[F[_], E, A](implicit me: MonadError[F, E], eq: Equal[F[A]], ae: Arbitrary[E], afea: Arbitrary[E => F[A]]) =
forAll(me.monadErrorLaw.raisedErrorsHandled[A] _)
def errorsRaised[F[_], E, A](implicit me: MonadError[F, E], eq: Equal[F[A]], ae: Arbitrary[E], aa: Arbitrary[A]) =
forAll(me.monadErrorLaw.errorsRaised[A] _)
def errorsStopComputation[F[_], E, A](implicit me: MonadError[F, E], eq: Equal[F[A]], ae: Arbitrary[E], aa: Arbitrary[A]) =
forAll(me.monadErrorLaw.errorsStopComputation[A] _)
def laws[F[_], E](implicit me: MonadError[F, E], am: Arbitrary[F[Int]], afap: Arbitrary[F[Int => Int]], aeq: Equal[F[Int]], ae: Arbitrary[E]): Properties =
newProperties("monad error"){ p =>
p.include(monad.laws[F])
p.property("raisedErrorsHandled") = raisedErrorsHandled[F, E, Int]
p.property("errorsRaised") = errorsRaised[F, E, Int]
p.property("errorsStopComputation") = errorsStopComputation[F, E, Int]
}
}
}
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