Output/Input

A purely functional program implements a function; it has no side effect. [...] if the side effect can’t be in the functional program, it will have to be outside it.

Tackling the Awkward Squad: monadic input/output, concurrency, exceptions, and foreign-language calls in Haskell, Simon Peyton Jones (pages 3-4 of 60).

One technique has been used for similar tasks:

This is discussed by Burton, and is built on by Harrison. The effect of this proposal is to place the non-determinism entirely outside the software [...]

Functional Programming and Operating Systems, Simon B. Jones and A. F. Sinclair (page 10 of 13).

It can also be used to provide access to external resources:

The approach generalizes so that a program can make use of other run-time information such as the current time or current amount of available storage.

Nondeterminism with Referential Transparency in Functional Programming Languages, F. Warren Burton (front page).

Perhaps it can be used for I/O...

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Details, details

How does it work?

[...] supply each program with an extra argument consisting of an infinite (lazy) binary tree of values. (We choose a tree [...] since any number of subtrees may be extracted from an infinite tree). In practice, these values will be determined at run time (when used as arguments to a special function [...]), but once fixed will never change.

...“a special function”: only one? More will definitely be needed! To keep matters simple, each value shall only be used once (if at all) as an argument to any such function.

main' :: Tree Exterior -> ...

 -- section 2
data Tree a = Node { contents :: a,
                     left     :: Tree a,
                     right    :: Tree a }

data Exterior                      -- the abstract value type
getchar :: Exterior -> Char        -- the special functions
putchar :: Char -> Exterior -> ()  -- (add more as needed :-)

Avoiding gratuitous repetition:

type OI  =  Tree Exterior

getChar' :: OI -> Char
getChar' =  getchar . contents

putChar' :: Char -> OI -> ()
putChar' c = putchar c . contents

An alternative abstraction

About those trees: are they really necessary? If OI was an abstract data type, the use of trees could at least be confined to the implementation:

data OI
getChar' :: OI -> Char
putChar' :: Char -> OI -> ()

...provided that single-use property applies directly to OI values (thereby deeming “special” any function which uses an OI argument). That includes the initial OI value supplied to each program:

main' :: OI -> ...

But most Haskell programs will need more:

part    :: OI -> (OI, OI)
part t  =  (left t, right t)

...than two OI values:

parts   :: OI -> [OI]
parts t =  let (t1, t2) = part t in t1 : parts t2

So OI can be a tree-free abstract data type after all:

data OI
partOI  :: OI -> (OI, OI)
getChar :: OI -> Char
putChar :: Char -> OI -> ()

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Other interfaces

• monad

type M a   =  OI -> a

unit       :: a -> M a
unit x     =  \ u -> let !_ = partOI u in x 

bind       :: M a -> (a -> M b) -> M b
bind m k   =  \ u -> let !(u1, u2) = partOI u in
                     let !x = m u1 in
                     let !y = k x u2 in
                     y

getcharM   :: M Char
getcharM   =  getChar

putcharM   :: Char -> M () 
putcharM   =  putChar

• comonad:

type C a         =  (OI, a)

extract          :: C a -> a
extract (u, x)   =  let !_ = partOI u in x

duplicate        :: C a -> C (C a)
duplicate (u, x) =  let !(u1, u2) = partOI u in
                    (u2, (u1, x))

extend           :: (C a -> b) -> C a -> C b
extend h (u, x)  =  let !(u1, u2) = partOI u in
                    let !y        = h (u1, x) in
                    (u2, y)

getcharC         :: C () -> Char
getcharC (u, ()) =  getChar u

putcharC         :: C Char -> ()
putcharC (u, c)  =  putChar c u

• arrow:

type A b c   =  (OI -> b) -> (OI -> c)

arr          :: (b -> c) -> A b c
arr f        =  \ c' u -> let !x = c' u in f x

both         :: A b c -> A b' c' -> A (b, b') (c, c')
f' `both` g' =  \ c' u -> let !(u1:u2:u3:_) = partsOI u in
                          let !(x, x')      = c' u1 in
                          let !y            = f' (unit x) u2 in
                          let !y'           = g' (unit x') u3 in
                          (y, y')
                where
                  unit x u = let !_ = partOI u in x

getcharA     :: A () Char
getcharA     =  \ c' u -> let !(u1, u2) = partOI u in
                          let !_        = c' u1 in
                          let !ch       = getChar u2 in
                          ch     

putcharA     :: A Char ()
putcharA     =  \ c' u -> let !(u1, u2) = partOI u in
                          let !ch       = c' u1 in
                          let !z        = putChar ch u2 in
                          z

The OI interface can also be used to implement I/O models used in earlier versions of Haskell:

• dialogues:

runD :: ([Response] -> [Request]) -> OI -> ()
runD d u = foldr (\ (!_) -> id) () $ yet $ \ l -> zipWith respond (d l) (partsOI u)

yet :: (a -> a) -> a
yet f = f (yet f)

respond :: Request -> OI -> Response
respond Getq     u = let !c = getChar u in Getp c
respond (Putq c) u = let !_ = putChar c u in Putp

data Request  = Getq | Putq Char
data Response = Getp Char | Putp

• continuations:

type Answer = OI -> ()

runK :: Answer -> OI -> ()
runK a u = a u

doneK :: Answer
doneK = \ u -> let !_ = partOI u in ()

getcharK :: (Char -> Answer) -> Answer
getcharK k   = \ u -> let !(u1, u2) = partOI u in
                      let !c        = getChar u1 in
                      let !a        = k c in
                      a u2

putcharK :: Char -> Answer -> Answer
putcharK c a = \ u -> let !(u1, u2) = partOI u in
                      let !_        = putChar c u1 in
                      a u2

...and even that world state-passing style used in GHC, which is also used by Clean, Single-Assignment C and as part of the I/O model used for the verification of interactive programs in CakeML, remembering that OI values can only be used once:

newtype World = W OI

getcharL :: World -> (Char, World)
getcharL (W u) = let !(u1, u2) = partOI u in
                 let !c = getChar u1 in
                 (c, W u2)

putcharL :: Char -> World -> World
putcharL c (W u) = let !(u1, u2) = partOI u in
                   let !_ = putChar c u1 in
                   W u2

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See also

• Plainly partible
• Disposing of dismissives
• IO then abstraction