Re: [Haskell-cafe] iterative algorithms: how to do it in Haskell?
On Thu, Aug 17, 2006 at 01:23:19AM -0400, [EMAIL PROTECTED] wrote: G'day all. Quoting Chris Kuklewicz [EMAIL PROTECTED]: The compiler may not deforest that list, so creating the list may be a small overhead of this method. And in return, you get: - Code that is smaller than the imperative version, AND - a reusable function, making the next incarnation of an algorithm like this even shorter. For most interesting cases, the cost of f and goOn will surely dominate anyway. Note that f x should be f a above. Yes, you're right. I abstracted out f after testing and before posting. Chris, Christian, Andrew, Antti-Juhani and Ivan, Thanks for your answers, they were very enlightening (though it will take some time to understand everything). Haskell looks even more elegant than Scheme... Best, Tamas ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] iterative algorithms: how to do it in Haskell?
Hi,
I am a newbie learning Haskell. I have used languages with functional
features before (R, Scheme) but not purely functional ones without
side-effects.
Most of the programming I do is numerical (I am an economist). I
would like to know how to implement the iterative algorithm below in
Haskell.
f is an a-a function, and there is a stopping rule
goOn(a,anext) :: a a - Bool which determines when to stop. The
algorithm looks like this (in imperative pseudocode):
a = ainit
while (true) {
anext - f(a)
if (goOn(a,anext))
a - anext
else
stop and return anext
}
For example, f can be a contraction mapping and goOn a test based on
the metric. I don't know how to do this in a purely functional
language, especially if the object a is large and I would like it to
be garbage collected if the iteration goes on.
Thank you,
Tamas
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Re: [Haskell-cafe] iterative algorithms: how to do it in Haskell?
Tamas K Papp wrote:
Hi,
I am a newbie learning Haskell. I have used languages with functional
features before (R, Scheme) but not purely functional ones without
side-effects.
Most of the programming I do is numerical (I am an economist). I
would like to know how to implement the iterative algorithm below in
Haskell.
f is an a-a function, and there is a stopping rule
goOn(a,anext) :: a a - Bool which determines when to stop. The
algorithm looks like this (in imperative pseudocode):
a = ainit
while (true) {
anext - f(a)
if (goOn(a,anext))
a - anext
else
stop and return anext
}
For example, f can be a contraction mapping and goOn a test based on
the metric. I don't know how to do this in a purely functional
language, especially if the object a is large and I would like it to
be garbage collected if the iteration goes on.
Thank you,
Tamas
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iterUntil :: (a - a - Bool) - (a - a) - a - a
iterUntil goOn f aInit =
let loop a =
let a' = f a
in if goOn a a'
then loop a'-- tail recursive (so a will be collected)
else a'
in loop aInit
--
Chris
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Re: [Haskell-cafe] iterative algorithms: how to do it in Haskell?
Tamas K Papp wrote:
f is an a-a function, and there is a stopping rule
goOn(a,anext) :: a a - Bool which determines when to stop. The
algorithm looks like this (in imperative pseudocode):
a = ainit
while (true) {
anext - f(a)
if (goOn(a,anext))
a - anext
else
stop and return anext
}
For example, f can be a contraction mapping and goOn a test based on
the metric. I don't know how to do this in a purely functional
language, especially if the object a is large and I would like it to
be garbage collected if the iteration goes on.
The idea is to make the iteration variables arguments to a
tail-recursive function:
let foo a | goOn a anext = foo anext
| otherwise= anext
where anext = f a
in foo ainit
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Re: [Haskell-cafe] iterative algorithms: how to do it in Haskell?
Chris Kuklewicz wrote:
Tamas K Papp wrote:
Hi,
I am a newbie learning Haskell. I have used languages with functional
features before (R, Scheme) but not purely functional ones without
side-effects.
Most of the programming I do is numerical (I am an economist). I
would like to know how to implement the iterative algorithm below in
Haskell.
f is an a-a function, and there is a stopping rule goOn(a,anext) ::
a a - Bool which determines when to stop. The
algorithm looks like this (in imperative pseudocode):
a = ainit
while (true) {
anext - f(a)
if (goOn(a,anext))
a - anext
else
stop and return anext
}
For example, f can be a contraction mapping and goOn a test based on
the metric. I don't know how to do this in a purely functional
language, especially if the object a is large and I would like it to
be garbage collected if the iteration goes on.
Thank you,
Tamas
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iterUntil :: (a - a - Bool) - (a - a) - a - a
iterUntil goOn f aInit =
let loop a =
let a' = f a
in if goOn a a'
then loop a'-- tail recursive (so a will be collected)
else a'
in loop aInit
In Haskell you can do this
iterUntil :: (a - a - Bool) - (a - a) - a - a
iterUntil goOn f a | goOn a anext = iterUntil goOn f anext
| otherwise= anext
where anext = f a
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Re: [Haskell-cafe] iterative algorithms: how to do it in Haskell?
[EMAIL PROTECTED] wrote:
G'day Tamas.
Quoting Tamas K Papp [EMAIL PROTECTED]:
f is an a-a function, and there is a stopping rule
goOn(a,anext) :: a a - Bool which determines when to stop. The
algorithm looks like this (in imperative pseudocode):
a = ainit
while (true) {
anext - f(a)
if (goOn(a,anext))
a - anext
else
stop and return anext
}
Here are a couple more suggestions.
First, this function scans an infinite list and stops when p x1 x2
is true for two adjacent elements x1 and x2:
findFixpoint p (x1:xs@(x2:_))
| p x1 x2 = x2
| otherwise = findFixpoint p xs
Then you just need to pass it [ainit, f ainit, f (f ainit), ...]:
findFixpoint dontGoOn (iterate f ainit)
Note that the function to pass to findFixpoint here is the condition
to use to _stop_.
The compiler may not deforest that list, so creating the list may be a small
overhead of this method.
If you're comfortable with monads, it's possible to directly simulate
complex imperative control flow. It's not recommended to do this
unless the flow is very complex, but here we are for the record:
import Control.Monad.Cont
-- I used a Newton-Raphson square root evaluation for testing,
-- but it has the same structure as your algorithm.
mysqrt :: Double - Double
mysqrt x
= runCont (callCC loop) id
where
ainit = x * 0.5
f x = 0.5 * (a + x/a)
goOn a1 a2 = abs (a1 - a2) 1e-5
loop break
= loop' ainit
where
loop' a
= do
let anext = f a
if goOn a anext
then loop' anext
else break anext
callCC defines a point outside the loop that you can break to.
You simply call that function (called a continuation) and the
loop is broken.
Cheers,
Andrew Bromage
Note that f x should be f a above. But I like it. My version of the above
looks like
import Control.Monad.Cont
mysqrt :: Double - Double
mysqrt x = doWhile goOn f aInit
where
aInit = x * 0.5
f a = 0.5 * (a + x/a)
goOn a1 a2 = abs (a1 - a2) 1e-5
doWhile :: (a - a - Bool) - (a - a) - a - a
doWhile goOn f x0 = runCont (callCC withBreak) id
where withBreak break =
let loop x = do let x' = f x
when (not (goOn x x')) (break x')
loop x'
in loop x0
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Re: [Haskell-cafe] iterative algorithms: how to do it in Haskell?
G'day all. Quoting Chris Kuklewicz [EMAIL PROTECTED]: The compiler may not deforest that list, so creating the list may be a small overhead of this method. And in return, you get: - Code that is smaller than the imperative version, AND - a reusable function, making the next incarnation of an algorithm like this even shorter. For most interesting cases, the cost of f and goOn will surely dominate anyway. Note that f x should be f a above. Yes, you're right. I abstracted out f after testing and before posting. Cheers, Andrew Bromage ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
