trait ApplicativeLaw extends ApplyLaw
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- def composite[A, B, C](fa: F[A], f1: (A) => B, f2: (B) => C)(implicit FC: Equal[F[C]]): Boolean
A series of maps may be freely rewritten as a single map on a composed function.
A series of maps may be freely rewritten as a single map on a composed function.
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- FunctorLaw
- def composition[A, B, C](fbc: F[(B) => C], fab: F[(A) => B], fa: F[A])(implicit FC: Equal[F[C]]): Boolean
Lifted functions can be fused.
Lifted functions can be fused.
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- ApplyLaw
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- def homomorphism[A, B](ab: (A) => B, a: A)(implicit FB: Equal[F[B]]): Boolean
point
distributes over function applications. - def identity[A](fa: F[A])(implicit FA: Equal[F[A]]): Boolean
The identity function, lifted, is a no-op.
The identity function, lifted, is a no-op.
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- FunctorLaw
- def identityAp[A](fa: F[A])(implicit FA: Equal[F[A]]): Boolean
point(identity)
is a no-op. - def interchange[A, B](f: F[(A) => B], a: A)(implicit FB: Equal[F[B]]): Boolean
point
is a left and right identity, F-wise. - def invariantComposite[A, B, C](fa: F[A], f1: (A) => B, g1: (B) => A, f2: (B) => C, g2: (C) => B)(implicit FC: Equal[F[C]]): Boolean
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- InvariantFunctorLaw
- def invariantIdentity[A](fa: F[A])(implicit FA: Equal[F[A]]): Boolean
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map
is like the one derived frompoint
andap
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