convert an exression to a string representation?

Question

Consider the following Haskell code:

module Expr where

    -- Variables are named by strings, assumed to be identifiers:

    type Variable = String

    -- Representation of expressions:

    data Expr = Const Integer
          | Var Variable
          | Plus Expr Expr
          | Minus Expr Expr
          | Mult Expr Expr
          deriving (Eq, Show)


    simplify :: Expr->Expr

    simplify (Mult (Const 0)(Var"x"))
     = Const 0 
    simplify (Mult (Var "x") (Const 0))
     = Const 0
    simplify (Plus (Const 0) (Var "x")) 
    = Var "x"
    simplify (Plus (Var "x") (Const 0))
     = Var "x" 
    simplify (Mult (Const 1) (Var"x")) 
    = Var "x"
    simplify (Mult(Var"x") (Const 1))
     = Var "x" 
    simplify (Minus (Var"x") (Const 0))
     = Var "x"
    simplify (Plus (Const x) (Const y)) 
    = Const (x + y)
    simplify (Minus (Const x) (Const y))
    = Const (x - y)
    simplify (Mult (Const x) (Const y))
     = Const (x * y)
    simplify x = x

    toString :: Expr->String

How can I convert an expression to a string representation?

e.g.

toString (Var "x") = "x"  
toString (Plus (Var "x") (Const 1)) = "x + 1"  
toString (Mult (Plus (Var "x") (Const 1)) (Var "y"))  
       = "(x + 1) * y"

Answer 1

Here is everything you need to know for this: http://augustss.blogspot.com/2007/04/overloading-haskell-numbers-part-1.html

Answer 2

It looks like you almost have it.

Here's an example

toString (Plus e1 e2) = (toString e1) ++ " + " ++ (toString e2)
toString (Const i) = show i

Answer 3

Rather than call your function toString, it might be preferable to use the Show type class. Then your data type can be used anywhere that an instance of Show can be used. Show is the standard Haskell way of converting "things" into strings.

instance Show Expr where
    show (Var "x") = "x"
    -- etc.