The definition for (<*) and (*>)

Question

Can I assume that the below is true for all applicatives ?

f1 <* f2 = fmap const f1 <*> f2 

and

 f1 *> f2 = fmap (flip const ) f1  <*> f2  

Answer 1

Yes. From the documentation for Applicative:

The other methods have the following default definitions, which may be overridden with equivalent specialized implementations:

• u *> v = (id <$ u) <*> v
• u <* v = liftA2 const u v

The key word there is "equivalent". Since your definitions are equivalent to those ones*, they must also be equivalent to those of all lawful Applicatives.

*If you're not convinced that your definitions are equivalent to those ones, here's some hints:

• fmap f x = f <$> x
• liftA2 f x y = f <$> x <*> y
• flip const = const id
• x <$ m = const x <$> m