Scala Programming Projects

Laws

As with other Cats type classes, an Apply instance must obey certain laws.

Given a type F that has an Apply[F] instance, for all types A, given an instance fa: F[A], the following equalities must be verified:

1. Product associativity: For all fb: F[B] and fc: F[C], the following applies:

(fa product (fb product fc)) ==  ((fa product fb) product fc).map {      case ((a, b), c) => (a, (b,c))    }

We can change the parenthesis and hence the evaluation order without changing the result.

2.  ap function composition: For all types B and C, given the instances fab: F[A => B] and fbc: F[B => C], the following applies:

(fbc <*> (fab <*> fa)) == ((fbc.map(_.compose[A] _) <*> fab) <*> fa)

This is similar to the function composition law that we saw in the ...