Get the sum and product of integres defined in a tree

I have a little problem understanding how to to the following in Haskell:

Lets say I have a statement similar to this ones:

• a * (b + c)
• a + (b * c)
• a + (b * ( c + d))
• a * (b + ( c * d))
• etc. etc.

I want to express these statements in a tree and evaluate the result of each, for starters I defined the following data structure:

data statement = Number Int 
          开发者_如何学Python     | Product statement statement 
               | Sum statement statement
               deriving (Eq, Show)

For an example Tree to work with, I used the following function:

a :: statement
a = Product (Number 2) (Sum (Number 5) (Number 1))

Now I want to build a function treeResult which gives me the result of my statement defined, but I don't know how to approach this problem. The integer returned for the above statement should be 12.

My first guess was to write a function that takes "statement" as a parameter and returns an int, for starters only with simple statements.

treeResult :: statement -> Int
treeResult (Number a) = a
treeResult (Product (Number a) (Number b)) = a*b
treeResult (Sum (Number a) (Number b)) = a+b

Now I know that I need something that works recursive but I don't know how to write it in haskell, can someone help me out here, please?

First off: statement needs to be capitalized since it's not a type variable. But that's the least important thing.

treeResult :: Statement -> Int
treeResult (Number x) = x

Obviously correct so far. We're matching the Number constructor, extract the Int and return that - well-typed and does what it should.

treeResult (Product (Number a) (Number b)) = a*b
treeResult (Sum (Number a) (Number b)) = a+b

This is well-typed, but it is not general enough. In this pattern, you are restricting the fields of Product and Sum to Numbers, but in fact they can be any Statement. So you instead need to define the Product/Sum:

treeResult (Product a b) = ...
treeResult (Sum a b) = ...

But we can't just add/multiply the two Statements. (+) and (*) are not defined for them (we're kind of doing that right now). When one operand is a Product, how do we get its value as an Int? By evaluating it. Statement is recursive, so we need recursion to evaluate it. Thus, the function becomes

treeResult (Product a b) = (treeResult a) * (treeResult b)
treeResult (Sum a b) = (treeResult a) + (treeResult b)

treeResult (Sum statement1 statement2) = treeResult statement1 + treeResult statement2

Similar for Product. This is simply recognizing

• result of (a + b) == result of a + result of b

(BTW, the data type should be called Statement with an uppercase S.

data Statement = Number Int | Product Statement Statement | Sum Statement Statement
                 deriving (Eq, Show)

)