IO Semantics

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Semantics of IO: A Continuation Approach

The following is inspired by Luke Palmer's post. This only describes one possible semantics of IO a; your actually implementation may vary.

The idea is to define IO as

newtype IO a = IO {runIO :: (a -> IOTree) -> IOTree}

This is equivalent to defining IO as Cont IOTree from the monad template library. The monad functions for IO are derived from the monad functions for Cont.

return x = IO (\k -> k x)
x >>= f = IO (\k -> runIO x (\a -> runIO (f a) k))

IOTree is the ultimate result of a program. For simplicity we will give an example of IOTree that gives semantics for teletype IO.

data IOTree = Done
            | PutChar Char IOTree
            | GetChar (Char -> IOTree)

(This is a tree because the GetChar node has one subtree for every character)

IOTree contains all the information needed to execute teletype interactions. One interprets (or executes) an IOTree by tracing a route from root of the tree to a leaf.

If a PutChar node is encountered, the character data contained at that node is output to the terminal and then its subtree is executed. It is only at this point that Haskell code is ever necessarily evaluated in order to determine what character should be displayed before continuing. If a GetChar node is encountered, a character is read from the terminal (blocking if necessary) and the subtree corresponding to the character received is executed. If Done is encountered the program ends. The primitive IO commands are defined using these constructors.

putChar :: Char -> IO ()
putChar x = IO (\k -> PutChar x (k ()))

getChar :: IO Char
getChar = IO (\k -> GetChar (\x -> k x))

If the PutChar constructor was defined (isomorphically) as

	| PutChar Char (() -> IOTree)

Then the primitive IO commands could be defined directly in terms of these constructors:

putChar :: Char -> IO ()
putChar = IO . PutChar

getChar :: IO Char
getChar = IO GetChar

Other teletype commands can be defined in terms of these primitives

putStr :: String -> IO ()
putStr = mapM_ putChar

More generally speaking, IOTree will represent the desired interaction with the operating system. For every system call there will be a corresponding constructor in IOTree of the form

	| SysCallName p1 p2 ... pn (r -> IOTree)

where p1 ... pn are the parameters for the system call, and r is the result of the system call. (Thus PutChar and GetChar will not occur as constructors of IOTree if they don't correspond to system calls)

We said that the ultimate result of a program is an IOTree, however the main function has type IO (). This is isomorphic to (() -> IOTree) -> IOTree, or equivalently IOTree -> IOTree which is not right.

The simple solution to this is that the runtime system produces an IOTree from main by evaluating runIO main (\() -> Done) :: IOTree. Here \() -> Done represents the "rest of the program", which in this case is nothing.

The sophisticated solution to this problem is that main is passed to the operating system which will bind the next program (perhaps a shell) to main. Thus the semantics of our Haskell program becomes embedded into the semantics of the entire operating system run.

The type for IO a that we have given contains invalid programs such as

IO (\k -> filterTree (not . isPutChar) (k ())) :: IO ()

which would remove the output of any future putChar commands. However, none of these illegal programs can be generated from the monadic interface and the primitive operations provided.