-- Example Monad from Lecture 5A 2013, a stack.
-- This is a special case of the State monad.
----------------
type Stack = [Int]

newtype StackOp a = StackOp (Stack -> (a,Stack))

run :: StackOp a -> Stack -> (a,Stack) 
run (StackOp f) s = f s

pop :: StackOp Int
pop = StackOp $ \(x:xs) -> (x,xs) -- can fail

push :: Int -> StackOp ()
push i = StackOp $ \s -> ((),i:s)

add :: StackOp ()
add = StackOp $ \(x:y:xs) -> ((),x+y:xs) -- can fail

emptyStack = []

-- (>>=) :: StackOp a -> (a -> StackOp b) -> StackOp b
instance Monad StackOp
  where return n = StackOp $ \s -> (n,s)
        sop >>= f  = StackOp $ \s -> 
                           let (i,s') = run sop s
                           in run (f i) s'
swap' :: StackOp ()
swap' = StackOp $ \s -> 
          let (a,s') = run pop s
              (b,s'') = run pop s'
              (_,s''') = run (push a) s''
          in  run (push b) s'''
swap = do 
     a <- pop
     b <- pop
     push a
     push b