# Difference between revisions of "Continuation"

EndreyMark (talk | contribs) (→Citing haskellized Scheme examples from Wikipedia: fixing a mistyped link (I mixed up Wikipedia's two articles on CPS) and more exact description about the modifications in the quoted text) |
EndreyMark (talk | contribs) m (Typographic corrections: (1) spell-check with ispell; (2) using <hask> instead of <code> at all _Haskell_ examples, even if no visual difference can be seen. Scheme examples remain between <code>'s) |
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=== Citing haskellized Scheme examples from Wikipedia === |
=== Citing haskellized Scheme examples from Wikipedia === |
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− | Quoting the Scheme examples (with their explanatory texts) from Wikipedia's [http://en.wikipedia.org/wiki/Continuation-passing_style#Examples Continuation-passing style] article, but Scheme examples are translated to Haskell, and some straightforward modifications are made to the explanations (e.g. replacing word ''Scheme'' with ''Haskell'', or using |
+ | Quoting the Scheme examples (with their explanatory texts) from Wikipedia's [http://en.wikipedia.org/wiki/Continuation-passing_style#Examples Continuation-passing style] article, but Scheme examples are translated to Haskell, and some straightforward modifications are made to the explanations (e.g. replacing word ''Scheme'' with ''Haskell'', or using abbreviated name <hask>fac</hask> instead of <code>factorial</code>). |

In the Haskell programming language, the simplest of direct-style functions is the identity function: |
In the Haskell programming language, the simplest of direct-style functions is the identity function: |
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idCPS a ret = ret a |
idCPS a ret = ret a |
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</haskell> |
</haskell> |
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− | where < |
+ | where <hask>ret</hask> is the continuation argument (often also called <hask>k</hask>). A further comparison of direct and CPS style is below. |

{| |
{| |
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!<center>Direct style</center>!!<center>Continuation passing style</center> |
!<center>Direct style</center>!!<center>Continuation passing style</center> |
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|} |
|} |
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− | The translations shown above show that CPS is a global transformation; the direct-style factorial, < |
+ | The translations shown above show that CPS is a global transformation; the direct-style factorial, <hask>fac</hask> takes, as might be expected, a single argument. The CPS factorial, <hask>facCPS</hask> takes two: the argument and a continuation. Any function calling a CPS-ed function must either provide a new continuation or pass its own; any calls from a CPS-ed function to a non-CPS function will use implicit continuations. Thus, to ensure the total absence of a function stack, the entire program must be in CPS. |

− | As an exception, < |
+ | As an exception, <hask>mysqrt</hask> calls <hask>sqrt</hask> without a continuation — here <hask>sqrt</hask> is considered a primitive [http://en.wikipedia.org/wiki/Operator_%28programming%29 operator]; that is, it is assumed that <hask>sqrt</hask> will compute its result in finite time and without abusing the stack. Operations considered primitive for CPS tend to be arithmetic, constructors, accessors, or mutators; any [http://en.wikipedia.org/wiki/Big_O_notation O(1) operation] will be considered primitive. |

The quotation ends here. |
The quotation ends here. |
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Maybe it is confusing, that |
Maybe it is confusing, that |
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− | * the type of the (non-continuation) argument of the discussed functions (< |
+ | * the type of the (non-continuation) argument of the discussed functions (<hask>idCPS</hask>, <hask>mysqrtCPS</hask>, <hask>facCPS</hask>) |

* and the type of the argument of the continuations |
* and the type of the argument of the continuations |
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coincide in the above examples. It is not a necessity (it does not belong to the essence of the continuation concept), so I try to figure out an example which avoids this confusing coincidence: |
coincide in the above examples. It is not a necessity (it does not belong to the essence of the continuation concept), so I try to figure out an example which avoids this confusing coincidence: |
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newSentenceCPS c k = k (elem c ".?!") |
newSentenceCPS c k = k (elem c ".?!") |
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</haskell> |
</haskell> |
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− | but this is a rather |
+ | but this is a rather uninteresting example. Let us see another one that uses at least recursion: |

<haskell> |
<haskell> |
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mylength :: [a] -> Integer |
mylength :: [a] -> Integer |
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</haskell> |
</haskell> |
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− | You can |
+ | You can download the Haskell source code (the original examples plus the new ones): [[Media:Continuation.hs|Continuation.hs]]. |

== Continuation monad == |
== Continuation monad == |

## Revision as of 01:31, 25 May 2006

## Contents

## General or introductory materials

### Powerful metaphors, images

Here is a collection of short descriptions, analogies or metaphors, that illustrate this difficult concept, or an aspect of it.

#### Imperative metaphors

- “In computing, a continuation is a representation of the execution state of a program (for example, the call stack) at a certain point in time” (Wikipedia's Continuation).
- “At its heart,
`call/cc`

is something like the`goto`

instruction (or rather, like a label for a`goto`

instruction); but a Grand High Exalted`goto`

instruction... The point about`call/cc`

is that it is not a*static*(lexical)`goto`

instruction but a*dynamic*one“ (David Madore's A page about`call/cc`

)

#### Functional metaphors

- “Continuations represent the future of a computation, as a function from an intermediate result to the final result“ (Continuation monad section in Jeff Newbern's All About Monads)
- “The idea behind CPS is to pass around as a function argument what to do next“ (Yet Another Haskell Tutorial written by Hal Daume III, 4.6 Continuation Passing Style, pp 53-56))

### Links

- Wikipedia's Continuation is a surprisingly good introductory material on this topic. See also Continuation-passing style.
- Yet Another Haskell Tutorial written by Hal Daume III contains a section on continuation passing style (4.6 Continuation Passing Style, pp 53-56)
- HaWiki has a page on ContinuationPassingStyle, and some related pages linked from there, too.
- David Madore's A page about
`call/cc`

describes the concept, and his The Unlambda Programming Language page shows how he implemented this construct in an esoteric functional programming language.

## Examples

### Citing haskellized Scheme examples from Wikipedia

Quoting the Scheme examples (with their explanatory texts) from Wikipedia's Continuation-passing style article, but Scheme examples are translated to Haskell, and some straightforward modifications are made to the explanations (e.g. replacing word *Scheme* with *Haskell*, or using abbreviated name `fac`

instead of `factorial`

).

In the Haskell programming language, the simplest of direct-style functions is the identity function:

```
id :: a -> a
id a = a
```

which in CPS becomes:

```
idCPS :: a -> (a -> r) -> r
idCPS a ret = ret a
```

where `ret`

is the continuation argument (often also called `k`

). A further comparison of direct and CPS style is below.

```
mysqrt :: Floating a => a -> a
mysqrt a = sqrt a
print (mysqrt 4) :: IO ()
``` |
```
mysqrtCPS :: a -> (a -> r) -> r
mysqrtCPS a k = k (sqrt a)
mysqrtCPS 4 print :: IO ()
``` |

```
mysqrt 4 + 2 :: Floating a => a
``` |
```
mysqrtCPS 4 (+ 2) :: Floating a => a
``` |

```
fac :: Integral a => a -> a
fac 0 = 1
fac n'@(n + 1) = n' * fac n
fac 4 + 2 :: Integral a => a
``` |
```
facCPS :: a -> (a -> r) -> r
facCPS 0 k = k 1
facCPS n'@(n + 1) k = facCPS n $ \ret -> k (n' * ret)
facCPS 4 (+ 2) :: Integral a => a
``` |

The translations shown above show that CPS is a global transformation; the direct-style factorial, `fac`

takes, as might be expected, a single argument. The CPS factorial, `facCPS`

takes two: the argument and a continuation. Any function calling a CPS-ed function must either provide a new continuation or pass its own; any calls from a CPS-ed function to a non-CPS function will use implicit continuations. Thus, to ensure the total absence of a function stack, the entire program must be in CPS.

As an exception, `mysqrt`

calls `sqrt`

without a continuation — here `sqrt`

is considered a primitive operator; that is, it is assumed that `sqrt`

will compute its result in finite time and without abusing the stack. Operations considered primitive for CPS tend to be arithmetic, constructors, accessors, or mutators; any O(1) operation will be considered primitive.

The quotation ends here.

### More general examples

Maybe it is confusing, that

- the type of the (non-continuation) argument of the discussed functions (
`idCPS`

,`mysqrtCPS`

,`facCPS`

) - and the type of the argument of the continuations

coincide in the above examples. It is not a necessity (it does not belong to the essence of the continuation concept), so I try to figure out an example which avoids this confusing coincidence:

```
newSentence :: Char -> Bool
newSentence = flip elem ".?!"
newSentenceCPS :: Char -> (Bool -> r) -> r
newSentenceCPS c k = k (elem c ".?!")
```

but this is a rather uninteresting example. Let us see another one that uses at least recursion:

```
mylength :: [a] -> Integer
mylength [] = 0
mylength (_ : as) = succ (mylength as)
mylengthCPS :: [a] -> (Integer -> r) -> r
mylengthCPS [] k = k 0
mylengthCPS (_ : as) k = mylengthCPS as (k . succ)
test8 :: Integer
test8 = mylengthCPS [1..2006] id
test9 :: IO ()
test9 = mylengthCPS [1..2006] print
```

You can download the Haskell source code (the original examples plus the new ones): Continuation.hs.

## Continuation monad

- Jeff Newbern's All About Monads contains a section on it.
- Control.Monad.Cont is contained by Haskell Hierarchical Libraries.