IO monad haskell 中的阶乘函数

Question

I am doing the factorial function in the IO monad haskell. I followed the example mod3 in order to do the factorial function with IO monad. I cant understand why my code is wrong. I want to see if n>=1, and then do the factorial to n. Lastly adding to the (n,r2) and return. Can anyone help understand that?

while :: IO Bool -> IO () -> IO ()
while test body =
  do b <- test
     if b
       then do {body ; while test body}  -- same-line syntax for do
       else return ()

-- remainder when integer-dividing n by 3
mod3 :: Integer -> IO Integer
mod3 n = do r <- newIORef n
            while
              (do {v <- readIORef r; return (v >= 3)})
              (do {v <- readIORef r; writeIORef r (v-3)})
            readIORef r          

-- ghci> fact 4
-- (4,24)
fact :: Integer -> IO (Integer, Integer)
fact n = do r2 <- newIORef n
            while 
            (do {v2 <- readIORef r2; return (v2 >= 1)})
            (do {v2 <- readIORef r2; writeIORef r2 (v2*fact(v2-1))})
            readIORef (n,r2) 

Answer 1

In this part of your code:

readIORef (n,r2) 

(n,r2) is not a IORef. r2 is an IORef, so you this is legal:

readIORef r2

So how about trying this:

1. read the IORef r2 getting a value
2. return the pair (n, ...) where ... is the value you got in step 1

Answer 2

First, indent the arguments of while , otherwise they are new statements.

fact :: Integer -> IO (Integer, Integer)
fact n = do r2 <- newIORef n
            while 
              (do {v2 <- readIORef r2; return (v2 >= 1)})
              (do {v2 <- readIORef r2; writeIORef r2 (v2*fact(v2-1))})
            readIORef (n,r2) 

Second, the while look roughly corresponds to the imperative code:

while r2 >= 1 :
  r2 = r2 * fact(r2-1)

This makes no sense: why the recursive call? Surely you know how to write the factorial in imperative style in a conventional imperative language; start from that and convert it to Haskell.

Answer 3

I see two problems that are preventing compilation. The first is that fact (v2-1) has type IO (Integer, Integer) , yet you are trying to multiply it by v2 :: Integer . You need to sequence fact (v2-1) like you sequence readIORef r2 , the multiply by the second component of the pair.

Second, you are misusing readIORef . You can see it's signature here . It takes an IORef a , not a pair.