data Op = Add | Sub | Mul | Div

data Expr = Val Int | App Op Expr Expr

valid :: Op -> Int -> Int -> Bool
valid Add _ _ = True
valid Sub x y = x > y
valid Mul _ _ = True
valid Div x y = x `mod` y == 0

apply :: Op -> Int -> Int -> Int
apply Add x y = x + y
apply Sub x y = x - y
apply Mul x y = x * y
apply Div x y = x `div` y

eval :: Expr -> [Int]
eval (Val n) = [n | n > 0]
eval (App o l r) = [apply o x y | x <- eval l,
                                  y <- eval r,
                                  valid o x y ]


-- so for example if i run:
eval (App Add (Val 1) (Val 9))
-- i will get 10
-- (the validity check is OK. i just add them together.)

-- what i dont understand is why this return the empty list?

eval (App Add (Val 1) (App Sub (Val 2) (Val 3)))


-- so at first in the list comprehension 'x' gets (Val 1) (which evaluate to 1) and the 'y' is translated to
eval (App Sub (Val 2) (Val 3))
{-
and then in the list comprehension there 'x' will be
(Val 2) (which translate to 2) and 'y' will be (Val 3) (which translate to 3).
the validity here get 'False' because 2 - 3 is negative number and we not allow it.
so as i understand i get back the empty list.
so now back to the first list comprehension, 'x' is still 2 but now 'y' is [].
and this is what i don't understand:
why i eventually get back the empty list?
is it because the function 'eval' that takes 'Expr' which only gets:
-}
Val Int | App Op Expr Expr
{-
(and here i get the empty list in the second 'Expr' which can't be because the empty list), is not an 'Expr'?
i understand that i can't Add together 'Expr' and [] (it's not in the type signature).
but why i don't recieve an error if it's not in the type signature?
why i get the empty list without error?
-}