First example of Harrison's "Handbook of Practical Logic and Automated Reasoning" in Haskell

harr1.hs

data Expr =
    Var String
  | Const Int
  | Add Expr Expr
  | Mult Expr Expr

simplify1 :: Expr -> Expr
simplify1 e = case e of
  Add (Const 0) x           -> x
  Add x (Const 0)           -> x
  Add (Const a) (Const b)   -> Const $ a + b
  Mult x (Const 0)          -> Const 0
  Mult (Const 0) x          -> Const 0
  Mult x (Const 1)          -> x
  Mult (Const 1) x          -> x
  Mult (Const a) (Const b)  -> Const $ a * b
  _                         -> e

simplify :: Expr -> Expr
simplify e = case e of
  Add x y   -> simplify1 $ Add (simplify x) (simplify y)
  Mult x y  -> simplify1 $ Mult (simplify x) (simplify y)
  _         -> simplify1 e

expr1 = Add (Mult (Add (Const 1) (Mult (Const 0) (Var "x"))) (Const 3)) (Const 12)