Output/Input
Clearing away the smoke and mirrors
The implementation in GHC uses the following one:
type IO a = World -> (a, World)
An IO
computation is a function that (logically) takes the state of the world, and returns a modified world as well as the return value. Of course, GHC does not actually pass the world around; instead, it passes a dummy “token,” to ensure proper sequencing of actions in the presence of lazy evaluation, and performs input and output as actual side effects!
A History of Haskell: Being Lazy With Class, Paul Hudak, John Hughes, Simon Peyton Jones and Philip Wadler.
...so what starts out as an I/O action of type:
World -> (a, World)
is changed by GHC to approximately:
() -> (a, ())
As the returned unit-value ()
contains no useful information, that type can be simplified further:
() -> a
Why "approximately"? Because "logically" a function in Haskell has no observable effects.
Previously seen
The type () -> a
(or variations of it) have appeared elsewhere - examples include:
- page 2 of 13 in A Correspondence Between ALGOL 60 and Church's Lambda-Notation: Part I by Peter Landin:
The use of
λ
, and in particular (to avoid an irrelevant bound variable) ofλ()
, to delay and possibly avoid evaluation is exploited repeatedly in our model of ALGOL 60. A function that requires an argument-list of length zero is called a none-adic function.(\ () -> …) :: () -> a
- page 148 of 168 in Functional programming and Input/Output by Andrew Gordon:
abstype 'a Job = JOB of unit -> 'a
data Job a = JOB (() -> a)
- page 3 of Assignments for Applicative Languages by Vipin Swarup, Uday S. Reddy and Evan Ireland:
A value of type
Obs 𝜏
is called an observer. Such a value observes (i.e. views or inspects) a state and returns a value of type𝜏
. [...] An observer typeObs 𝜏
may be viewed as an implicit function space from the set of states to the type𝜏
.type Obs tau = State -> tau
- page 15 of Non-Imperative Functional Programming by Nobuo Yamashita:
type a :-> b = OI a -> b
- MTL style for free by Tom Ellis:
data Time_ a = GetCurrentTime (UTCTime -> a)
- An impure lazy programming language, also by Tom Ellis:
data IO a = IO (() -> a)
- page 2 of Unique Identifiers in Pure Functional Languages by Péter Diviánszky:
[...] The type
Id
can be hidden by the synonym data type:: Create a :== Id -> a
type Create a = Id -> a
- page 7 of Functional Reactive Animation by Conal Elliott and Paul Hudak:
An early implementation of Fran represented behaviors as implied in the formal semantics:
data Behavior a = Behavior (Time -> a)
- page 26 of How to Declare an Imperative by Philip Wadler:
The type
'a io
is represented by a function expecting a dummy argument of typeunit
and returning a value of type'a
.type 'a io = unit -> a
type Io a = () -> a
- The Haskell I/O Tutorial by Albert Lai:
But I can already tell you why we cannot follow other languages and use simply
X
or() -> X
.
- Free Monads for Less (Part 3 of 3): Yielding IO by Edward Kmett:
newtype OI a = forall o i. OI (FFI o i) o (i -> a) deriving Functor
type Oi a = forall i . i -> a
- page 27 of Purely Functional I/O in Scala by Rúnar Bjarnason:
class IO[A](run: () => A)
class Io a where run :: () -> a
type IO<'T> = private | Action of (unit -> 'T)
data IO t = Action (() -> t)
Let's say you want to implement
IO
in SML :structure Io : MONAD = struct type 'a t = unit -> 'a ⋮ end
type T a = () -> a
newtype IO a = IO { runIO :: () -> a }
newtype Supply r a = Supply { runSupply :: r -> a }
As long as we have its special case
IO c = () ~> c
, we can represent (up to isomorphism) […]a ~> c
[…]
- Monads, I/O and Concurrency in Lux by Eduardo Julián:
(deftype #export (IO a) (-> Void a))
type IO a = (->) Void a
- Referentially Transparent Input/Output in Groovy by Mark Perry:
abstract class SimpleIO<A> { abstract A run() }
class SimpleIO a where run :: () -> a
- The
IO
Monad for PHP by Tom Harding:
__construct :: (-> a) -> IO a
[...] The parameter to the constructor must be a zero-parameter [none-adic] function that returns a value.
data IO a = IO (() -> a) __construct :: (() -> a) -> IO a __construct = IO
- The Observable disguised as an IO Monad by Luis Atencio:
IO
is a very simple monad that implements a slightly modified version of our abstract interface with the difference that instead of wrapping a valuea
, it wraps a side effect function() -> a
.data IO a = Wrap (() -> a)
- More Monad:
IO<>
Monad, from dixin's Category Theory via C# series:
The definition of
IO<>
is simple:public delegate T IO<out T>();
[...]
IO<T>
is used to represent a impure function. When aIO<T>
function is applied, it returns aT
value, with side effects.
type IO t = () -> t
So let’s implement the
IO
Monad right now and here. Given that OCaml is strict and that the order of function applications imposes the order of evaluation, theIO
Monad is just a thunk, e.g.,type 'a io = unit -> 'a
type Io a = () -> a
[...] So
suspend () -> A
offers us the exact same guarantees asIO<A>
.
Of these, it is the implementation of OI a
in Yamashita's oi package which is most interesting as its values are monousal - once used, their contents remain constant. This single-use property also appears in the implementation of the abstract decision
type described by F. Warren Burton in Nondeterminism with Referential Transparency in Functional Programming Languages.
IO
, redefined
Based on these and other observations, a reasonable distillment of these examples would be OI -> a
, which then implies:
type IO a = OI -> a
Using Burton's pseudodata approach:
-- abstract; single-use I/O-access mediator
data Exterior
getchar :: Exterior -> Char
putchar :: Char -> Exterior -> ()
-- from section 2 of Burton's paper
data Tree a = Node { contents :: a,
left :: Tree a,
right :: Tree a }
-- utility definitions
type OI = Tree Exterior
getChar' :: OI -> Char
getChar' = getchar . contents
putChar' :: Char -> OI -> ()
putChar' c = putchar c . contents
part :: OI -> (OI, OI)
parts :: OI -> [OI]
part t = (left t, right t)
parts t = let !(t1, t2) = part t in
t1 : parts t2
Of course, in an actual implementation OI
would be abstract like World
, and for similar reasons. This permits a simpler implementation for OI
and its values, instead of being based on (theoretically) infinite structured values like binary trees. That simplicity has benefits for the OI
interface, in this case:
data OI
part :: OI -> (OI, OI)
getChar' :: OI -> Char
putChar' :: Char -> OI -> ()