3rd Interpreter: Adding a Register

The code for this section is Register.hs.

module Register where

import Control.Monad.State

data Exp = Const Int | Neg Exp | Add Exp Exp
         | X  -- new register X

instance Show Exp where
  show (Const i) = show i
  show (Neg e)   = "-" ++ show e
  show (Add e1 e2) = show e1 ++ " + " ++ show e2
  show X           = "X"

-- | Just a copy 
eval2 :: Exp -> Maybe Int
eval2 (Const i)   = return i
eval2 (Neg e)     = do
                      v <- eval2 e
                      return (- v)
eval2 (Add e1 e2) = do
                      v1 <- eval2 e1
                      v2 <- eval2 e2
                      return (v1 + v2)

eval2 X           = undefined -- How do we do handle this?

Here’s how we handle this:

• Create a new monad from Identity with an Int register: StateT Int Identity
• This new monad has two operations
  • get that reads the current value of the register
  • put that updates the value of the register
• StateT Int is known as a monad transformer

The code below does just that

readX :: StateT Int Identity Int
readX = get

eval3 :: Exp -> StateT Int Identity Int
eval3 (Const i)   = return i
eval3 (Neg e)     = do
                      v <- eval3 e
                      return (- v)
eval3 (Add e1 e2) = do
                      v1 <- eval3 e1
                      v2 <- eval3 e2
                      return (v1 + v2)

eval3 X           = readX