CommutativeMonadLaws

implicit abstract def F: CommutativeMonad[F]

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

def apProductConsistent[A, B](fa: F[A], f: F[(A) ⇒ B]): IsEq[F[B]]

def applicativeComposition[A, B, C](fa: F[A], fab: F[(A) ⇒ B], fbc: F[(B) ⇒ C]): IsEq[F[C]]

This law is applyComposition stated in terms of pure.

def applicativeHomomorphism[A, B](a: A, f: (A) ⇒ B): IsEq[F[B]]

def applicativeIdentity[A](fa: F[A]): IsEq[F[A]]

def applicativeInterchange[A, B](a: A, ff: F[(A) ⇒ B]): IsEq[F[B]]

def applicativeMap[A, B](fa: F[A], f: (A) ⇒ B): IsEq[F[B]]

def applicativeUnit[A](a: A): IsEq[F[A]]

def applyCommutative[A, B, C](fa: F[A], fb: F[B], f: (A, B) ⇒ C): IsEq[F[C]]

def applyComposition[A, B, C](fa: F[A], fab: F[(A) ⇒ B], fbc: F[(B) ⇒ C]): IsEq[F[C]]

final def asInstanceOf[T0]: T0

def clone(): AnyRef

def covariantComposition[A, B, C](fa: F[A], f: (A) ⇒ B, g: (B) ⇒ C): IsEq[F[C]]

def covariantIdentity[A](fa: F[A]): IsEq[F[A]]

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

def flatMapAssociativity[A, B, C](fa: F[A], f: (A) ⇒ F[B], g: (B) ⇒ F[C]): IsEq[F[C]]

def flatMapConsistentApply[A, B](fa: F[A], fab: F[(A) ⇒ B]): IsEq[F[B]]

def flatMapFromTailRecMConsistency[A, B](fa: F[A], fn: (A) ⇒ F[B]): IsEq[F[B]]

It is possible to implement flatMap from tailRecM and map and it should agree with the flatMap implementation.

def flatmapCommutative[A, B, C](fa: F[A], fb: F[B], g: (A, B) ⇒ F[C]): IsEq[F[C]]

final def getClass(): Class[_]

def hashCode(): Int

def invariantComposition[A, B, C](fa: F[A], f1: (A) ⇒ B, f2: (B) ⇒ A, g1: (B) ⇒ C, g2: (C) ⇒ B): IsEq[F[C]]

def invariantIdentity[A](fa: F[A]): IsEq[F[A]]

final def isInstanceOf[T0]: Boolean

def kleisliAssociativity[A, B, C, D](f: (A) ⇒ F[B], g: (B) ⇒ F[C], h: (C) ⇒ F[D], a: A): IsEq[F[D]]

The composition of cats.data.Kleisli arrows is associative.

def kleisliLeftIdentity[A, B](a: A, f: (A) ⇒ F[B]): IsEq[F[B]]

pure is the left identity element under left-to-right composition of cats.data.Kleisli arrows.

def kleisliRightIdentity[A, B](a: A, f: (A) ⇒ F[B]): IsEq[F[B]]

pure is the right identity element under left-to-right composition of cats.data.Kleisli arrows.

def map2EvalConsistency[A, B, C](fa: F[A], fb: F[B], f: (A, B) ⇒ C): IsEq[F[C]]

def map2ProductConsistency[A, B, C](fa: F[A], fb: F[B], f: (A, B) ⇒ C): IsEq[F[C]]

def mapFlatMapCoherence[A, B](fa: F[A], f: (A) ⇒ B): IsEq[F[B]]

Make sure that map and flatMap are consistent.

def monadLeftIdentity[A, B](a: A, f: (A) ⇒ F[B]): IsEq[F[B]]

def monadRightIdentity[A](fa: F[A]): IsEq[F[A]]

def monoidalLeftIdentity[A](fa: F[A]): (F[(Unit, A)], F[A])

def monoidalRightIdentity[A](fa: F[A]): (F[(A, Unit)], F[A])

def mproductConsistency[A, B](fa: F[A], fb: (A) ⇒ F[B]): IsEq[F[(A, B)]]

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

def productLConsistency[A, B](fa: F[A], fb: F[B]): IsEq[F[A]]

def productRConsistency[A, B](fa: F[A], fb: F[B]): IsEq[F[B]]

def semigroupalAssociativity[A, B, C](fa: F[A], fb: F[B], fc: F[C]): (F[(A, (B, C))], F[((A, B), C)])

final def synchronized[T0](arg0: ⇒ T0): T0

def tailRecMConsistentFlatMap[A](a: A, f: (A) ⇒ F[A]): IsEq[F[A]]

lazy val tailRecMStackSafety: IsEq[F[Int]]

def toString(): String

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit