5 + (2*1) => 5 + 2

Here is my implementation.

\$5 + (2*1) => 5 + 2\$

Here is my implementation:

I'm learning Haskell, and one exercise was to implement squashing of identity-multiplications.

I'm learning Haskell, and one exercise was to implement squashing of identity-multiplications, e.g.:

5 + (2*1) => 5 + 2

The following code/definitions were given:

{-# OPTIONS_GHC -Wall #-}
module SQMULID where

import Data.Char
import Data.List
import Data.Maybe
import Test.HUnit
import Test.QuickCheck
import Test.QuickCheck.Gen


class Ring a where
  addId  :: a            -- additive identity
  addInv :: a -> a       -- additive inverse
  mulId  :: a            -- multiplicative identity

  add :: a -> a -> a     -- addition
  mul :: a -> a -> a     -- multiplication

-- | A datatype for storing and manipulating ring expressions.
data RingExpr a = Lit a
                | AddId
                | AddInv (RingExpr a)
                | MulId
                | Add (RingExpr a) (RingExpr a)
                | Mul (RingExpr a) (RingExpr a)
  deriving (Show, Eq)

instance Ring (RingExpr a) where
  addId  = AddId
  addInv = AddInv
  mulId  = MulId

  add = Add
  mul = Mul

-- The canonical instance for integers:
instance Ring Integer where
  addId  = 0
  addInv = negate
  mulId  = 1

  add = (+)
  mul = (*)

And here is my implementation.

Here is my implementation.

The following code/definitions were given:

{-# OPTIONS_GHC -Wall #-}
module SQMULID where

import Data.Char
import Data.List
import Data.Maybe
import Test.HUnit
import Test.QuickCheck
import Test.QuickCheck.Gen


class Ring a where
  addId  :: a            -- additive identity
  addInv :: a -> a       -- additive inverse
  mulId  :: a            -- multiplicative identity

  add :: a -> a -> a     -- addition
  mul :: a -> a -> a     -- multiplication

-- | A datatype for storing and manipulating ring expressions.
data RingExpr a = Lit a
                | AddId
                | AddInv (RingExpr a)
                | MulId
                | Add (RingExpr a) (RingExpr a)
                | Mul (RingExpr a) (RingExpr a)
  deriving (Show, Eq)

instance Ring (RingExpr a) where
  addId  = AddId
  addInv = AddInv
  mulId  = MulId

  add = Add
  mul = Mul

-- The canonical instance for integers:
instance Ring Integer where
  addId  = 0
  addInv = negate
  mulId  = 1

  add = (+)
  mul = (*)