Difference between revisions of "Output/Input"

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</haskell>
 
</haskell>
  
As the returned unit-value <code>()</code> contains no useful information, that type can be simplified further:
+
The result (of type <code>a</code>) can then be returned directly:
  
 
<haskell>
 
<haskell>
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</haskell>
 
</haskell>
  
<sub>Why "approximately"? Because "logically" a function in Haskell has no observable effects.</sub>
+
<sub>Why <i>"approximately"</i>? Because <i>"logically"</i> a function in Haskell has no observable effects.</sub>
  
 
----
 
----
 
=== <u>Previously seen</u> ===
 
=== <u>Previously seen</u> ===
  
Variations of the type <code>() -> a</code> have appeared elsewhere:
+
The type <code>() -> a</code> (or variations of it) have appeared elsewhere - examples include:
  
 
* page 2 of 13 in [https://fi.ort.edu.uy/innovaportal/file/20124/1/22-landin_correspondence-between-algol-60-and-churchs-lambda-notation.pdf A Correspondence Between ALGOL 60 and Church's Lambda-Notation: Part I] by Peter Landin:
 
* page 2 of 13 in [https://fi.ort.edu.uy/innovaportal/file/20124/1/22-landin_correspondence-between-algol-60-and-churchs-lambda-notation.pdf A Correspondence Between ALGOL 60 and Church's Lambda-Notation: Part I] by Peter Landin:
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<haskell>
 
<haskell>
 
(\ () -> …) :: () -> a
 
(\ () -> …) :: () -> a
 +
</haskell>
 +
|}
 +
 +
* page 148 of 168 in [https://web.archive.org/web/20021107080915/https://www.cl.cam.ac.uk/techreports/UCAM-CL-TR-285.pdf Functional programming and Input/Output] by Andrew Gordon:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
<pre>
 +
abstype 'a Job = JOB of unit -> 'a
 +
</pre>
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
data Job a = JOB (() -> a)
 
</haskell>
 
</haskell>
 
|}
 
|}
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<haskell>
 
<haskell>
 
data Time_ a = GetCurrentTime (UTCTime -> a)
 
data Time_ a = GetCurrentTime (UTCTime -> a)
 +
</haskell>
 +
|}
 +
 +
* [http://h2.jaguarpaw.co.uk/posts/impure-lazy-language An impure lazy programming language], also by Tom Ellis:
  
data Lock_ a = AcquireLock (Maybe Lock -> a) NominalDiffTime Key
+
:{|
            | RenewLock (Maybe Lock -> a) NominalDiffTime Lock
+
<haskell>
            | ReleaseLock (() -> a) Lock
+
data IO a = IO (() -> a)
 
</haskell>
 
</haskell>
 
|}
 
|}
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|}
 
|}
  
* page 7 of [https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.701.930&rep=rep1&type=pdf Functional Reactive Animation] by Paul Hudak and Conal Elliott:
+
* page 7 of [https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.701.930&rep=rep1&type=pdf Functional Reactive Animation] by Conal Elliott and Paul Hudak:
 
:{|
 
:{|
 
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 
An early implementation of Fran represented behaviors as implied in the formal semantics:
 
An early implementation of Fran represented behaviors as implied in the formal semantics:
 
<haskell>
 
<haskell>
data Behavior a = Time -> a
+
data Behavior a = Behavior (Time -> a)
 
</haskell>
 
</haskell>
 
</div>
 
</div>
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:{|
 
:{|
 
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
The type <code>'a io</code> is represented by a function expecting a dummy argument of type unit and returning a value of type <code>'a</code>.
+
The type <code>'a io</code> is represented by a function expecting a dummy argument of type <code>unit</code> and returning a value of type <code>'a</code>.
 
<pre>
 
<pre>
 
type 'a io = unit -> a
 
type 'a io = unit -> a
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<haskell>
 
<haskell>
 
type Io a = () -> a
 
type Io a = () -> a
 +
</haskell>
 +
|}
 +
 +
* The [https://www.vex.net/~trebla/haskell/IO.xhtml Haskell I/O Tutorial] by Albert Lai:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
But I can already tell you why we cannot follow other languages and use simply <code>X</code> or <code>() -> X</code>.
 +
</div>
 +
|}
 +
 +
* [http://comonad.com/reader/2011/free-monads-for-less-3 Free Monads for Less (Part 3 of 3): Yielding IO] by Edward Kmett:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
<haskell>
 +
newtype OI a = forall o i. OI (FFI o i) o (i -> a) deriving Functor
 +
</haskell>
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
type Oi a = forall i . i -> a
 +
</haskell>
 +
|}
 +
 +
* page 27 of [https://blog.higher-order.com/assets/scalaio.pdf Purely Functional I/O in Scala] by Rúnar Bjarnason:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
<pre>
 +
class IO[A](run: () => A)
 +
</pre>
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
class Io a where run :: () -> a
 +
</haskell>
 +
|}
 +
 +
* [http://www.fssnip.net/6i/title/Tiny-IO-Monad igeta's snippet]:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
<pre>
 +
type IO<'T> = private | Action of (unit -> 'T)
 +
</pre>
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
data IO t = Action (() -> t)
 
</haskell>
 
</haskell>
 
|}
 
|}
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newtype Supply r a = Supply { runSupply :: r -> a }
 
newtype Supply r a = Supply { runSupply :: r -> a }
 
</haskell>
 
</haskell>
 +
|}
 +
 +
* [https://stackoverflow.com/questions/51770808/how-exactly-does-ios-work-under-the-hood/51772273#51772273 chi's answer] to [https://stackoverflow.com/questions/51770808/how-exactly-does-ios-work-under-the-hood this SO question]:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
As long as we have its special case <code>IO c = () ~> c</code>, we can represent (up to isomorphism) […] <code>a ~> c</code> […]
 +
</div>
 +
|}
 +
 +
* [https://luxlang.blogspot.com/2016/01/monads-io-and-concurrency-in-lux.html Monads, I/O and Concurrency in Lux] by Eduardo Julián:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
<pre>
 +
(deftype #export (IO a)
 +
  (-> Void a))
 +
</pre>
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
type IO a = (->) Void a
 +
</haskell>
 +
|}
 +
 +
* [https://mperry.github.io/2014/01/03/referentially-transparent-io.html Referentially Transparent Input/Output in Groovy] by Mark Perry:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
<pre>
 +
abstract class SimpleIO<A> {
 +
    abstract A run()
 +
}
 +
</pre>
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
class SimpleIO a where
 +
    run :: () -> a
 +
</haskell>
 +
|}
 +
 +
* [https://github.com/php-fp/php-fp-io#readme The <code>IO</code> Monad for PHP] by Tom Harding:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
<pre>
 +
__construct :: (-> a) -> IO a
 +
</pre>
 +
[...]  The parameter to the constructor must be a zero-parameter [none-adic] function that returns a value.
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
data IO a = IO (() -> a)
 +
__construct :: (() -> a) -> IO a
 +
__construct = IO
 +
</haskell>
 +
|}
 +
 +
* [https://medium.com/@luijar/the-observable-disguised-as-an-io-monad-c89042aa8f31 The Observable disguised as an IO Monad] by Luis Atencio:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
<code>IO</code> is a very simple monad that implements a slightly modified version of our abstract interface with the difference that instead of wrapping a value <code>a</code>, it wraps a side effect function <code>() -> a</code>.
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
data IO a = Wrap (() -> a)
 +
</haskell>
 +
|}
 +
 +
* [https://weblogs.asp.net/dixin/category-theory-via-c-sharp-18-more-monad-io-monad More Monad: <code>IO<></code> Monad], from [https://weblogs.asp.net/dixin/Tags/Category%20Theory dixin's Category Theory via C#] series:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
The definition of <code>IO<></code> is simple:
 +
<pre>
 +
public delegate T IO<out T>();
 +
</pre>
 +
[...]
 +
* <code>IO<T></code> is used to represent a impure function. When a <code>IO<T></code> function is applied, it returns a <code>T</code> value, with side effects.
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
type IO t = () -> t
 +
</haskell>
 +
|}
 +
 +
* [https://discuss.ocaml.org/t/io-monad-for-ocaml/4618/11 ivg's post] in [https://discuss.ocaml.org/t/io-monad-for-ocaml/4618 <code>IO</code> Monad for OCaml]
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
So let’s implement the <code>IO</code> Monad right now and here. Given that OCaml is strict and that the order of function applications imposes the order of evaluation, the <code>IO</code> Monad is just a thunk, e.g.,
 +
<pre>
 +
type 'a io = unit -> 'a
 +
</pre>
 +
</div>
 +
<sup> </sup>
 +
<haskell>
 +
type Io a = () -> a
 +
</haskell>
 +
|}
 +
 +
* [https://arrow-kt.io/docs/effects/io Why <code>suspend</code> over <code>IO</code>] in [https://arrow-kt.io/docs/fx Arrow Fx]:
 +
:{|
 +
|<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote">
 +
[...] So <code>suspend () -> A</code> offers us the exact same guarantees as <code>IO<A></code>.
 +
</div>
 
|}
 
|}
  
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</haskell>
 
</haskell>
  
Of course, in an actual implementation <code>OI</code> would be abstract like <code>World</code>, and for similar reasons. This allows for a simpler implementation for <code>OI</code> and its values, instead of being based on (theoretically) infinite structured values like binary trees. That simplicity has benefits for the <code>OI</code> interface, in this case:
+
Of course, in an actual implementation <code>OI</code> would be abstract like <code>World</code>, and for similar reasons. This permits a simpler implementation for <code>OI</code> and its values, instead of being based on (theoretically) infinite structured values like binary trees. That simplicity has benefits for the <code>OI</code> interface, in this case:
  
 
<haskell>
 
<haskell>
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</haskell>
 
</haskell>
 
<sup> </sup>
 
<sup> </sup>
 
----
 
 
=== <u>Various questions</u> ===
 
 
* Is the C language "purely functional"?
 
 
::No:
 
::* C isn't "pure" - it allows unrestricted access to observable effects, including those of I/O.
 
::* C isn't "functional" - it was never intended to be [[Referential transparency|referentially transparent]], which severely restricts the ability to use [[Equational reasoning examples|equational reasoning]].
 
 
* Can functional programming be liberated from the von Neumann paradigm?
 
 
::That remains an [[Open research problems|open research problem]].
 
 
* Can a language be "purely functional" or "denotative"?
 
 
::Conditionally, yes - the condition being the language is restricted in what domains it can be used in:
 
 
::* If a language is free of observable effects, including those of I/O, then the only other place where those effects can reside is within its implementation.
 
::* There is no bound on the ways in which observable effects can be usefully combined, leading to a similarly-unlimited variety of imperative computations.
 
::* A finite implementation cannot possibly accommodate all of those computations, so a subset of them must be chosen. This restricts the implementation and language to those domains supported by the chosen computations.
 
 
* Why do our programs need to read input and write output?
 
 
::Because programs are usually written for [https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.628.7053&rep=rep1&type=pdf practical] purposes, such as implementing domain-specific [https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.7.2089&rep=rep1&type=pdf little languages].
 
  
 
----
 
----
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=== <u>See also</u> ===
 
=== <u>See also</u> ===
  
 +
* [https://pqnelson.github.io/2021/07/29/monadic-io-in-ml.html Monadic IO in Standard ML]
 
* [[Disposing of dismissives]]
 
* [[Disposing of dismissives]]
* [[IO, partible-style]]
 
 
* [[IO then abstraction]]
 
* [[IO then abstraction]]
 
* [https://okmij.org/ftp/Computation/IO-monad-history.html The IO monad in 1965]
 
* [https://okmij.org/ftp/Computation/IO-monad-history.html The IO monad in 1965]

Latest revision as of 04:27, 9 June 2022


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, ())

The result (of type a) can then be returned directly:

() -> 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:

The use of λ, and in particular (to avoid an irrelevant bound variable) of λ() , 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
abstype 'a Job = JOB of unit -> 'a

data Job a = JOB (() -> a)

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 type 𝜏. [...] An observer type Obs 𝜏 may be viewed as an implicit function space from the set of states to the type 𝜏.

type Obs tau = State -> tau
  • page 15 of Non-Imperative Functional Programming by Nobuo Yamashita:
type a :-> b = OI a -> b
data Time_ a = GetCurrentTime (UTCTime -> a)
data IO a = IO (() -> a)

[...] The type Id can be hidden by the synonym data type

:: Create a  :==  Id -> a

type Create a = Id -> a

An early implementation of Fran represented behaviors as implied in the formal semantics:

data Behavior a = Behavior (Time -> a)

The type 'a io is represented by a function expecting a dummy argument of type unit and returning a value of type 'a.

type 'a io = unit -> a

type Io a = () -> a

But I can already tell you why we cannot follow other languages and use simply X or () -> X.

newtype OI a = forall o i. OI (FFI o i) o (i -> a) deriving Functor

type Oi a = forall i . i -> a
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 […]

(deftype #export (IO a)
  (-> Void a))

type IO a = (->) Void a
abstract class SimpleIO<A> {
    abstract A run()
}

class SimpleIO a where
    run :: () -> a
__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

IO is a very simple monad that implements a slightly modified version of our abstract interface with the difference that instead of wrapping a value a, it wraps a side effect function () -> a.

data IO a = Wrap (() -> a)

The definition of IO<> is simple:

public delegate T IO<out T>();

[...]

  • IO<T> is used to represent a impure function. When a IO<T> function is applied, it returns a T 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, the IO 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 as IO<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 -> ()


See also