IO, partible-style

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IO is the monad you cannot avoid.

Why Haskell is so HARD? (And how to deal with it); Saurabh Nanda.

...but you kept looking anyway, and here you are!

[...] the input/output story for purely-functional languages was weak and unconvincing, let alone error recovery, concurrency, etc. Over the last few years, a surprising solution has emerged: the monad. I say "surprising" because anything with as exotic a name as "monad" - derived from category theory, one of the most abstract branches of mathematics - is unlikely to be very useful to red-blooded programmers. But one of the joys of functional programming is the way in which apparently-exotic theory can have a direct and practical application, and the monadic story is a good example.

Tackling the Awkward Squad: monadic input/output, concurrency, exceptions, and foreign-language calls in Haskell, Simon Peyton Jones.

...with that (ahem) "joy" leading to more than a few helpful guides about the topic - that monadic interface: it's abstract alright!

This is hard stuff. Two years ago I spent several hours to write 3 lines invoking IO computations.

Trying to understand the IO (); "belka", Haskell Discourse.

Is that you?

[...] And I still don't believe in monads. :-)

Retrospective Thoughts on BitC; Jonathan S. Shapiro, bitc-dev mailing list.

You are not alone.


IO, using OI

Our definition of IO is a type synonym:

type IO a = OI -> a

with OI being an abstract partible type:

data OI a
primitive primPartOI :: OI -> (OI, OI)

instance Partible OI where
    part = primPartOI

Like primPartOI, most other primitives for the OI type also accept an OI-value as their last (or only) argument e.g:

primitive primGetChar :: OI -> Char
primitive primPutChar :: Char -> OI -> ()
        

Borrowing the running example from Philip Wadler's How to Declare an Imperative:

echo   :: OI -> ()
echo u =  let !(u1:u2:u3:_) = parts u
              !c            = primGetChar u1 in
          if c == '\n' then
            ()
          else
            let !_ = primPutChar c u2
            in  echo u3

Wadler also provides an SML version:

val echoML    : unit -> unit
fun echoML () = let val c = getcML () in
                if c = #"\n" then
                  ()
                else
                  (putcML c; echoML ())
                end

in which we replace SML's sequencing operator ;:

val echoML    : unit -> unit
fun echoML () = let val c = getcML () in
                if c = #"\n" then
                  ()
                else
                  let val _ = putcML c in
                  echoML ()
                  end
                end

If we compare it to our Haskell version:

echo   :: OI -> ()
echo u =  let !(u1:u2:u3:_) = parts u
              !c            = primGetChar u1 in
          if c == '\n' then
            ()
          else
            let !_ = primPutChar c u2
            in  echo u3

--
val echoML    : unit -> unit
fun echoML () =
                let val c = getcML () in
                if c = #"\n" then
                  ()
                else
                  let val _ = putcML c in
                  echoML ()
                  end
                end

...we can now see just how similar the two versions of echo really are: apart from the obvious changes of syntax, the Haskell version replaces all use of unit-values with OI-values, and adds an extra call to parts to provide them.

So there you have it: for the price of some extra calls and bindings, we can have SML-style I/O in Haskell. Furthermore, as the prevailing definition for SML has been available since 1997, there should be plenty of I/O tutorials to choose from...

At this point, you may be tempted to try something like:

type IO a = () -> a

primitive might_get_Char :: () -> Char
primitive might_put_Char :: Char -> ()
        ⋮

While this might work in some situations, it's unreliable in general. Why?

But - if after all that - you're still not convinced, then perhaps you'll be happier programming in SML...

...you're still here: nice!  Now for a small example - here's a basic version of interact, using those OI-based definitions:

interact      :: (String -> String) -> OI -> ()
interact d u  =  let !(u1, u2) = part u in
                 putStr (d $ getContents u1) u2

putStr        :: String -> OI -> ()
putStr s u    =  foldr (\(!_) -> id) () $ zipWith primPutChar s $ parts u

getContents   :: OI -> String
getContents u =  case map getChar (parts u) of
                   l@(!c:_) -> l
                   l        -> l


Some annoyances

  • Extra parameters and arguments - As noted by Sigbjørn Finne and Simon Peyton Jones in Programming Reactive Systems in Haskell, passing around all those OI-values correctly can be tedious for large definitions.
  • Polymorphic references - It's been known for a very long time in the SML community that naive declarations for operations using mutable references breaks type safety:
primitive newPolyRef :: a -> OI -> PolyRef a
primitive readPolyRef :: PolyRef a -> OI -> a
primitive writePolyRef :: PolyRef a -> a -> OI -> ()

kah_BOOM u = let …
                 !vehicle = newPolyRef undefined u1
                 !_       = writePolyRef ("0" :: [Char]) u2
                 !crash   = readPolyRef vehicle u3
                 burn     = 1 :: Int
             in
                 crash + burn
SML's solution is to make all mutable references monomorphic through the use of dedicated syntax:
let val r = ref (…)
         ⋮
One alternative for Haskell would be to extend type signatures to support monomorphic type-variables:
primitive newIORef   :: monomo a . a -> OI -> IORef a
primitive readIORef  :: monomo a . IORef a -> OI -> a
primitive writeIORef :: monomo a . IORef a -> a -> OI -> ()

{- would be rejected by the extended type system: 
kah_BOOM u = let !(u1:u2:u3:_) = parts u
                 !vehicle      = newIORef undefined u1          -- vehicle :: monomo a . IORef a
                 !_            = writeIORef ("0" :: [Char]) u2  -- vehicle :: IORef [Char]
                 !crash        = readIORef vehicle u3           -- vehicle :: IORef [Char] ≠ IORef Int
                 burn          = 1 :: Int
             in
                 crash + burn
-}
In standard Haskell, one of the few places this already occurs (albeit implicitly) is the parameters of a function:
{- will be rejected by the standard Haskell type system

ker_plunk f = (f True, f 'b')

-}

One solution

  • Extra parameters and arguments - What is needed is a succinct interface to "hide the plumbing" used to pass around OI-values:
instance Monad ((->) OI) where
     return x = \u -> case part u of !_ -> x
     m >>= k  = \u -> case part u of
                        (u1, u2) -> case m u1 of
                                      !x -> k x u2
  • Polymorphic references - we now make IO into an abstract data type:
module Abstract.IO
(
    Monad (..),
    getChar, putChar, 
    newIORef, readIORef, writeIORef,
                 
)
where

instance Monad ((->) OI) where
     return x = \u -> case part u of !_ -> x
     m >>= k  = \u -> case part u of
                        (u1, u2) -> case m u1 of
                                      !x -> k x u2

getChar    :: IO Char
getChar    =  primGetChar

putChar    :: Char -> IO ()
putChar    =  primPutChar

newIORef   :: a -> IO (IORef a)
newIORef   =  primNewIORef

readIORef  :: IORef a -> IO a
readIORef  =  primReadIORef

writeIORef :: IORef a -> a -> IO ()
writeIORef =  primWriteIORef


 -- these are now local, private entities --
type IO a = OI -> a

data OI a
primitive primPartOI  :: OI -> (OI, OI)

primitive primGetChar :: OI -> Char
primitive primPutChar :: Char -> OI -> ()
        

data IORef
primitive primNewIORef    :: a -> OI -> IORef a
primitive primReadIORef   :: IORef a -> OI -> a
primitive primWriteIORef  :: IORef a -> a -> OI -> ()
        
With the IO type now made abstract, the only way to use IO-values is by using:
  • the visible IO operations: getChar, putChar, etc.
  • the monadic interface - Monad(return, (>>=), …) (or via Haskell's do-notation).
The key here is the type of (>>=), for IO-values:
(>>=) :: IO a -> (a -> IO b) -> IO b
in particular, the type of the second argument:
(a -> IO b)
...it's a function, so the value it receives will be rendered monomorphic in the function's result (of type IO b).
As (>>=) is now the only IO operation which can retrieve a result from an IO-value, mutable references (IORef …) simply cannot be used polymorphically.

GHC's solution

newtype IO a = IO (State# RealWorld -> (# State# RealWorld, a #))

...you may have noticed that we've already made liberal use of one Haskell extension - bang-patterns - and it would be useful to stay as close as possible to standard Haskell, so we'll simplify matters:

newtype IO a = IO (IOState -> (IOState, a))  -- unboxed-tuple replaced by standard one 

type IOState = State# RealWorld

Now to make the changes:

  • to the type - IOState uses an OI-value:
newtype IOState = IOS OI
  • to the I/O-specific operations - each one will use the OI-value in the initial state to provide two new OI-values: one to make up the final state; the other being used by the OI-primitive:
getChar   :: IO Char
getChar   =  IO $ \(IOS u) -> let !(u1, u2) = part u
                                  !c        = primGetChar u1
                              in  (IOS u2, c)

putChar   :: Char -> IO ()
putChar c =  IO $ \(IOS u) -> let !(u1, u2) = part u
                                  !t        = primPutChar c u1
                              in  (IOS u2, t)

 -- etc.
  • to the overloaded operations - you've probably seen it all before:
instance Monad IO where
    return x   = IO $ \(!s) -> (s, x)
    IO m >>= k = IO $ \(!s) -> let !(s', x) = m s
                                   !(IO w)  = k x
                               in  w s'
(...if you haven't: it's ye ol' pass-the-planet state-passing technique.)

One aspect which doesn't change is IO and its operations being abstract. In fact, the need is even more pressing: in addition to preventing the misuse of certain OI-operations, being an abstract data type prevents IOState-values from being erroneously reused.


Conclusions

  • Why is Haskell I/O monadic - to avoid having to use extra arguments and parameters everywhere.
  • Why is Haskell I/O abstract - to ensure I/O works as intended, by preventing the misuse of internal data.
  • Why is Haskell I/O unusual - because of Haskell's nonstrict evaluation and thus its focus on referential transparency, contrary to most other programming languages.

Further reading

If you've managed to get all the way to here, State in Haskell by John Launchbury and Simon Peyton Jones is also worth reading, if you're interested in how GHC eventually arrived at its current definition of IO.