/**
* Generic test to verify if a type obey the applicative laws.
*
* @param callable $assertEqual Asserting function (Applicative $a1, Applicative $a2, $message)
* @param callable $pure Applicative "constructor"
* @param Applicative $u Applicative f => f (a -> b)
* @param Applicative $v Applicative f => f (a -> b)
* @param Applicative $w Applicative f => f (a -> b)
* @param callable $f (a -> b)
* @param mixed $x Value to put into a applicative
*/
public static function test(callable $assertEqual, callable $pure, Applicative $u, Applicative $v, Applicative $w, callable $f, $x)
{
// identity: pure id <*> v = v
$assertEqual($pure(f\identity)->ap($v), $v, 'identity');
// homomorphism: pure f <*> pure x = pure (f x)
$assertEqual($pure($f)->ap($pure($x)), $pure($f($x)), 'homomorphism');
// interchange: u <*> pure x = pure ($ x) <*> u
$assertEqual($u->ap($pure($x)), $pure(f\applicator($x))->ap($u), 'interchange');
// composition: pure (.) <*> u <*> v <*> w = u <*> (v <*> w)
$compose = f\curryN(2, f\compose);
$assertEqual($pure($compose)->ap($u)->ap($v)->ap($w), $u->ap($v->ap($w)), 'composition');
}
