simplify function

Simplify.hs

simplify :: (Num a, Eq a, Floating a) => Expr a -> Expr a
simplify (Const a :+: Const b) = Const (a + b)
simplify (a       :+: Const 0) = simplify a
simplify (Const 0 :+: a      ) = simplify a

simplify (Const a :*: Const b) = Const (a*b)
simplify (a :*: Const 1)         = simplify a
simplify (Const 1 :*: a)         = simplify a
simplify (a :*: Const 0)         = Const 0
simplify (Const 0 :*: a)         = Const 0

simplify (Const a :^: Const b)       = Const (a**b)
simplify (a :^: Const 1)             = simplify a
simplify (a :^: Const 0)             = Const 1
simplify ((c :^: Const b) :^: Const a) = c :^: (Const (a*b))

simplify (Const a :*: (Const b :*: expr)) = (Const $ a*b) :*: (simplify expr)
simplify (Const a :*: expr :*: Const b) = (Const $ a*b) :*: (simplify expr)
simplify (expr :*: Const a :*: Const b) = (Const $ a*b) :*: (simplify expr)
simplify (Const a :*: (b :+: c))        = (Const a :*: (simplify b)) :+: (Const a :*: (simplify c))

simplify (Const 0 :/: a        ) = Const 0
simplify (Const a :/: Const 0)   = error "Division by zero!"
simplify (Const a :/: Const b)   | a == b = Const 1 -- only when a == b
simplify (a       :/: Const 1)   = simplify a

simplify (a :/: b)  = (simplify a) :/: (simplify b)
simplify (a :^: b)  = (simplify a) :^: (simplify b)
simplify (a :*: b)  = (simplify a) :*: (simplify b)
simplify (a :+: b)  = (simplify a) :+: (simplify b)
simplify x          = id x

fullSimplify expr = fullSimplify' expr (Const 0) -- placeholder
  where fullSimplify' cur last | cur == last = cur
                               | otherwise = let cur' = simplify cur
                                             in fullSimplify' cur' cur