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The law as it is currently written is meaningless, because nowhere have we defined the implementation of 'ap'. The reader of the Control.Monad documentation is provided with only a type signature, > ap :: Monad m => m (a -> b) -> m a -> m b an informal description, > In many situations, the liftM operations can be replaced by uses of > ap, which promotes function application. and a relationship between 'ap' and the 'liftM' functions > return f `ap` x1 `ap` ... `ap` xn > is equivalent to > liftMn f x1 x2 ... xn Without knowing how 'ap' is defined, a law involving 'ap' cannot provide any guidance for how to write a lawful Monad instance, nor can we conclude anything from the law. I suspect that a reader equipped with the understanding that 'ap' was defined prior to the invention of the Applicative class could deduce that 'ap' must be defined in terms of (>>=), but nowhere as far as I can tell have we written this down explicitly for readers without the benefit of historical context. If the law is meant to express a relationship among (<*>), (>>=), and 'return', it seems that it is better off making this statement directly, sidestepping 'ap' altogether.
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