On 2017-11-30 14:18, Ray wrote:

what does JOIN (*) do?

(*) :: Num a => a -> a -> a

join (*) :: Num a => a -> a

when we feed a number to join (*),for instance;

λ> : join (*) 3

9

it seems thata JOIN (*) become a square function.

what does JOIN do to (*) to make that happen?

You can figure it out by using equational reasoning and evaluating the expression manually: join (*) 3 Function application is left-associative, so this is equivalent to (join (*)) 3 The 'join' function is defined as (http://hackage.haskell.org/package/base-4.10.0.0/docs/src/GHC.Base.html#join) join x = x >>= id So we can replace 'join (*)' in our above expression with ((*) >>= id) 3 (>>=) for functions is defined as f >>= k = \ r -> k (f r) r So with that at hand, we get (\r -> id ((*) r) r) 3 'id x' is just 'x', so we get (\r -> (*) r r) 3 With infix syntax, this can be written as (\r -> r * r) 3 If you now apply that function, you get 3 * 3 Which gives your result '9'. -- Frerich Raabe - raabe@froglogic.com www.froglogic.com - Multi-Platform GUI Testing