Haskell 多态型

Question

I am working on an excercise but i don't know how to create the division function

-- defines data type with two constructors
data Expr = Val Int | Div Expr Expr

-- defines a function that turns an expression into an integer
-- eval :: Expr -> Int


-- eval (Div x y) = Div x * Div y
-- write an evaluation function for both Expr types
-- TODO eval (Val n) =
eval (Val n) = n


-- TODO eval (Div x y) =



-- now calculate 6 / 3 with the created function
-- TODO testeval =
testeval = eval (Div (Val 6) (Val 3))

Answer 1

Let's look at the first case:

eval (Val n) = n

By the definition of Val , n is an Int , so we simply return n . Then, for example, eval (Val 3) == 3 , eval (Val 10) == 10 , etc.

Now let's look at the second case.

eval (Div x y) = ???

By the definition of Div both x and y have type Expr , so we can't simply return one or the other, and we don't know how to do math on Expr values. But we do now how to do math on Int values:

> 6 `div` 3
2

and we know we can use eval to get an Int from an Expr :

> eval (Val 6)
6

So the first thing you need to do is use eval to evaluate both x and y to get their Int values. Once you have them, you can use div to produce the desired value.

> eval (Div (Val 6) (Val 3))
2