# Difference between revisions of "Output/Input"

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+ | === <u>Clearing away the smoke and mirrors</u> === | ||

− | + | <div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote"> | |

− | + | The implementation in GHC uses the following one: | |

− | < | + | |

− | + | <haskell> | |

+ | type IO a = World -> (a, World) | ||

+ | </haskell> | ||

+ | |||

+ | An <code>IO</code>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! | ||

+ | |||

+ | <tt>[https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.168.4008&rep=rep1&type=pdf A History of Haskell: Being Lazy With Class], Paul Hudak, John Hughes, Simon Peyton Jones and Philip Wadler.</tt> | ||

+ | </div> | ||

+ | |||

+ | ...so what starts out as an I/O action of type: | ||

+ | |||

+ | <haskell> | ||

+ | World -> (a, World) | ||

+ | </haskell> | ||

+ | |||

+ | is changed by GHC to approximately: | ||

+ | |||

+ | <haskell> | ||

+ | () -> (a, ()) | ||

+ | </haskell> | ||

+ | |||

+ | As the returned unit-value <code>()</code> contains no useful information, that type can be simplified further: | ||

+ | |||

+ | <haskell> | ||

+ | () -> a | ||

+ | </haskell> | ||

+ | |||

+ | Why "approximately"? Because "logically" a function in Haskell has no observable effects. | ||

+ | |||

+ | ---- | ||

+ | === <u>Previously seen</u> === | ||

+ | |||

+ | Variations of the type <code>() -> a</code> have appeared elsewhere: | ||

+ | |||

+ | * 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: | ||

+ | :{| | ||

+ | |<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote"> | ||

+ | |||

+ | The use of <code>λ</code>, and in particular (to avoid an irrelevant bound variable) of <code>λ()</code> , 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. | ||

+ | </div> | ||

+ | <sup> </sup> | ||

+ | <haskell> | ||

+ | (\ () -> …) :: () -> a | ||

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | * page 3 of [https://www.cs.bham.ac.uk/~udr/papers/assign.pdf Assignments for Applicative Languages] by Vipin Swarup, Uday S. Reddy and Evan Ireland: | ||

+ | :{| | ||

+ | |<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote"> | ||

+ | A value of type <code>Obs 𝜏</code> is called an ''observer''. Such a value observes (i.e. views or inspects) a state and returns a value of type <code>𝜏</code>. [...] An observer type <code>Obs 𝜏</code> may be viewed as an implicit function space from the set of states to the type <code>𝜏</code>. | ||

+ | </div> | ||

+ | <sup> </sup> | ||

+ | <haskell> | ||

+ | type Obs tau = State -> tau | ||

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | * [https://image.slidesharecdn.com/lazyio-120422092926-phpapp01/95/lazy-io-15-728.jpg page 15] of ''Non-Imperative Functional Programming] by Nobuo Yamashita: | ||

+ | |||

+ | :{| | ||

+ | <haskell> | ||

+ | type a :-> b = OI a -> b | ||

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | * [http://h2.jaguarpaw.co.uk/posts/mtl-style-for-free MTL style for free] by Tom Ellis: | ||

+ | |||

+ | :{| | ||

+ | <haskell> | ||

+ | data Time_ a = GetCurrentTime (UTCTime -> a) | ||

+ | |||

+ | data Lock_ a = AcquireLock (Maybe Lock -> a) NominalDiffTime Key | ||

+ | | RenewLock (Maybe Lock -> a) NominalDiffTime Lock | ||

+ | | ReleaseLock (() -> a) Lock | ||

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | * page 2 of [https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.128.9269&rep=rep1&type=pdf Unique Identifiers in Pure Functional Languages] by Péter Diviánszky. | ||

+ | :{| | ||

+ | |<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote"> | ||

+ | [...] The type <code>Id</code> can be hidden by the synonym data type | ||

+ | <pre> | ||

+ | :: Create a :== Id -> a | ||

+ | </pre> | ||

+ | </div> | ||

+ | <sup> </sup> | ||

+ | <haskell> | ||

+ | type Create a = Id -> a | ||

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | * page 26 of [https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.91.3579&rep=rep1&type=pdf How to Declare an Imperative] by Philip Wadler: | ||

+ | :{| | ||

+ | |<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>. | ||

+ | <pre> | ||

+ | type 'a io = unit -> a | ||

+ | </pre> | ||

+ | </div> | ||

+ | <sup> </sup> | ||

+ | <haskell> | ||

+ | type Io a = () -> a | ||

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | * [https://stackoverflow.com/questions/6647852/haskell-actual-io-monad-implementation-in-different-language/6706442#6706442 ysdx's answer] to [https://stackoverflow.com/questions/6647852/haskell-actual-io-monad-implementation-in-different-language this SO question]: | ||

+ | :{| | ||

+ | |<div style="border-left:1px solid lightgray; padding: 1em" alt="blockquote"> | ||

+ | Let's say you want to implement <code>IO</code> in SML : | ||

+ | <pre> | ||

+ | structure Io : MONAD = | ||

+ | struct | ||

+ | type 'a t = unit -> 'a | ||

+ | ⋮ | ||

+ | end | ||

+ | </pre> | ||

+ | </div> | ||

+ | <sup> </sup> | ||

+ | <haskell> | ||

+ | type T a = () -> a | ||

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | * [https://stackoverflow.com/questions/45136398/is-the-monadic-io-construct-in-haskell-just-a-convention/45141523#45141523 luqui's answer] to [https://stackoverflow.com/questions/45136398/is-the-monadic-io-construct-in-haskell-just-a-convention this SO question]: | ||

+ | :{| | ||

+ | |<haskell> | ||

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

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | * [https://stackoverflow.com/questions/15418075/the-reader-monad/15419592#15419592 luqui's answer] to [https://stackoverflow.com/questions/15418075/the-reader-monad this SO question]: | ||

+ | :{| | ||

+ | |<haskell> | ||

+ | newtype Supply r a = Supply { runSupply :: r -> a } | ||

+ | </haskell> | ||

+ | |} | ||

+ | |||

+ | Of these, it is the implementation of <code>OI a</code> in Yamashita's [https://hackage.haskell.org/package/oi 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 <code>decision</code> type described by F. Warren Burton in [https://academic.oup.com/comjnl/article-pdf/31/3/243/1157325/310243.pdf Nondeterminism with Referential Transparency in Functional Programming Languages]. | ||

+ | |||

+ | ---- | ||

+ | === <code>IO</code><u>, redefined</u> === | ||

+ | |||

+ | Based on these and other observations, a reasonable generalisation of these examples would be <code>OI -> a</code>, which then implies: | ||

+ | |||

+ | <haskell> | ||

+ | type IO a = OI -> a | ||

+ | </haskell> | ||

+ | |||

+ | Using Burton's ''pseudodata'' approach: | ||

+ | |||

+ | <haskell> | ||

+ | -- 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 | ||

+ | </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: | ||

+ | |||

+ | <haskell> | ||

+ | data OI | ||

+ | part :: OI -> (OI, OI) | ||

+ | getChar' :: OI -> Char | ||

+ | putChar' :: Char -> OI -> () | ||

+ | </haskell> | ||

+ | <sup> </sup> | ||

+ | |||

+ | ---- | ||

+ | |||

+ | See also: | ||

+ | |||

+ | * [[IO, partible-style]] | ||

+ | * [[IO then abstraction]] | ||

+ | * [[Open research problems]] |

## Revision as of 13:52, 2 November 2021

__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__

Variations of the type `() -> a`

have appeared elsewhere:

- 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) 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

- 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 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

- MTL style for free by Tom Ellis:

data Time_ a = GetCurrentTime (UTCTime -> a) data Lock_ a = AcquireLock (Maybe Lock -> a) NominalDiffTime Key | RenewLock (Maybe Lock -> a) NominalDiffTime Lock | ReleaseLock (() -> a) Lock

- 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 26 of How to Declare an Imperative by Philip Wadler:

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

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 }

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 generalisation 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 allows for 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: