I'm trying to write this function applying composition and partial application with Haskell:
function m n = (m^2) + n
I tried this with:
function m = (m^2).(+)
The problem with that approach is that (+)
is a binary operator. Since you put it at the right of the dot .
, it will not be applied to the left operand. So you have written:
function :: Num a => a -> a -> a
function m = (.) (m^2) (+) -- wrong
This is short for:
function m = \n -> ((m^2) ((+) n))
So that means that (+) n
will result in a function (n+)
and we will apply that function to the result of (m^2)
, which does not make much sense.
You can however simply use:
function :: Num a => a -> a -> a
function m = (+) (m^2)
Or:
function :: Num a => a -> a -> a
function m = ((m^2) +)
Given function m = (+) (m^2)
, if we apply n
on that function, we will obtain:
((+) (m^2)) n
-> (+) (m^2) n
-> (m^2) + n
You can further modify the function
and drop the m
argument as well, with:
function :: Num a => a -> a -> a
function = (+) . (^ 2)
Which is syntactical sugar for:
function :: Num a => a -> a -> a
function = (.) (+) (^2)
If we now apply m
on the function, it will evaluate to:
((.) (+) (^2)) m
-> (\x -> (+) ((^2) x)) m
-> (+) ((^2) m)
-> (+) (m^2)
So we obtain the state like in the previous command.
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