[Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
Hi All,
I got up this morning {after not much sleep} to find these very
helpful suggestions/comments:
from Scott Turner:
{... See: http://www.haskell.org/hawiki/ExistentialTypes ...}
From Bulat Ziganshin:
{...
you can read recent discussion on this in this topic, or look at
http://haskell.org/haskellwiki/OOP_vs_type_classes
}
From Lennart Augustsson,
A wonderfully instructive code fragment:
{...
data Value = D Double | S String | B Bool
type Stack = [Value]
-- Add top stack elements
plus :: Stack -> Stack
plus (D x : D y : vs) = D (x+y) : vs
plus ( _ : _ : _) = error "Bad operands to plus"
plus_ = error "Not enough operands on stack"
...} see his post for the continuation...
With these suggestions I have plenty to study now.. and probably a whole
redesign of some of the things that I have already implemented.. with
most likely a great boost in speed of execution, and much cleaner
code. I must admit that some of these concepts have not come as
easily to me as to some that have had formal education in these
matters... This list and the materials from Haskell.org, papers on
various websites, and documentation with GHC and it's libraries are my
entire exposure.. so when stuck, kind folks from the net community are
my, I guess mentors would be the word I am looking for... and for that
I am very greatful!
I am not in a real race... but I have to thank everyone that
participated in this spawned off of the main topic discussion... for
all their patience with my questions..
Thanks again to All for the clarification and links to more reading,
gene
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Re: [Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
I don't know exactly what types you have as base types in your implementation, but here's a small code fragment that of what I had in mind. data Value = D Double | S String | B Bool type Stack = [Value] -- Add top stack elements plus :: Stack -> Stack plus (D x : D y : vs) = D (x+y) : vs plus ( _ : _ : _) = error "Bad operands to plus" plus_ = error "Not enough operands on stack" equal :: Stack -> Stack equal (D x : D y : vs) = B (x == y) : vs equal (S x : S y : vs) = B (x == y) : vs equal (B x : B y : vs) = B (x == y) : vs equal ( _ : _ : _) = error "Bad operands to equal" equal_ = error "Not enough operands on stack" -- Lennart On Aug 21, 2006, at 04:42 , Gene A wrote: Lennart and all, On 8/19/06, Lennart Augustsson <[EMAIL PROTECTED]> wrote: There are much better ways than storing strings on the stack. Like using a data type with constructors for the different types that you can store. -- Lennart Off topic, but this is important info for me! Okay then, by doing that you can define a new type that "encodes" the other types.. such that you can actually end up storing the different types such as Int, Integer,Real, String, etc into a list . using this new type to so that even though you are in effect storing differing types to a list.. they are actually of the same type and thus legal... without doing an explicit bunch of "read"/"show" combinations.. to actually convert.. like Num for example... and being able to use +,* on any of the numeric types... but can you have a list of type [Num] ?? I thought that it had to be the base types of Int, Integer, Float, Double etc.. No? thanks, gene ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
Hello Gene, Monday, August 21, 2006, 12:42:17 PM, you wrote: > being able to use +,* on any of the numeric types... but can you have > a list of type [Num] ?? I thought that it had to be the base types of > Int, Integer, Float, Double etc.. No? you can, using existentials: data Number = forall a. (Num a, Show a) => Num a main = print [Num (1::Int), Num (1.1::Double), Num (1::Integer)] but that is not really very important. in my own practice, homogeneous lists are suffice in almost all cases you can read recent discussion on this in this topic, or look at http://haskell.org/haskellwiki/OOP_vs_type_classes, where John Meacham and me describes how existentials can partially emulate OOP classes -- Best regards, Bulatmailto:[EMAIL PROTECTED] ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
On 2006 August 21 Monday 04:42, Gene A wrote: > but can you have > a list of type [Num] ?? I thought that it had to be the base types of > Int, Integer, Float, Double etc.. No? See http://www.haskell.org/hawiki/ExistentialTypes ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
Lennart and all, On 8/19/06, Lennart Augustsson <[EMAIL PROTECTED]> wrote: There are much better ways than storing strings on the stack. Like using a data type with constructors for the different types that you can store. -- Lennart Off topic, but this is important info for me! Okay then, by doing that you can define a new type that "encodes" the other types.. such that you can actually end up storing the different types such as Int, Integer,Real, String, etc into a list . using this new type to so that even though you are in effect storing differing types to a list.. they are actually of the same type and thus legal... without doing an explicit bunch of "read"/"show" combinations.. to actually convert.. like Num for example... and being able to use +,* on any of the numeric types... but can you have a list of type [Num] ?? I thought that it had to be the base types of Int, Integer, Float, Double etc.. No? thanks, gene ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
There are much better ways than storing strings on the stack. Like using a data type with constructors for the different types that you can store. -- Lennart On Aug 19, 2006, at 11:51 , Gene A wrote: Hi Lennart, This morning when I posted..it was about 2:30am and had been up a long time... bad habits.. I sent a message to Henk-Jan to that effect, but didn't send to the entire list.. anyway thanks to both for the followups... I still tend to sometimes do things the hard way in Haskell. Started trying to learn it starting in I think Nov-Dec. of 2005, so not too awfully long, but with a lot of other things soaking up time, not as far along as I wished to be in even this amount of time... Most interesting language I have used yet. but yes not sure why not the precision.. but I think when I tried that with the way I had the thing in the original, I used (**) 1/3 and got an error message which I was too tired to even read,..and just changed it to 0. or whatever however many 3's , and just got it posted.. I don't think that those functions are of much use, the thing was that when I wrote them, not at 2AM in the morning, I remember thinking just how easy it was to do pretty much anything you want with this language.. Off topic, but one of my tests of a language, old habit this, is as soon as I know enough to be dangerous, I try writing a forth interpreter in it. I have started such a thing, a module I call Hforth, and it is operational, but do to the nature of lists not holding homogeneos values in Haskell everything has to be stored with String values. This has the result of having to apply show function to store numerics to the stack and then to use the read function to convert back when popping the stack.. .. hmm still tired... Anyway the upshot is that a very rudimentary interpreter is up and running to do simple things with just builtins so far, but was built in a matter of some fairly small number of hours. Doesn't support line editing yet, so really not too good, but does support pushing strings and concatenation and some other things that are more tedious to write as primatives in other languages.. The only other language that was as easy to get to this stage with was scheme. Sorry for the ramble, gene On 8/19/06, Lennart Augustsson <[EMAIL PROTECTED]> wrote: On Aug 19, 2006, at 05:14 , Henk-Jan van Tuyl wrote: > > [...] >> *Iteration> fromtoby 12 42 3 (flip (**) 0.33) > > fromtoby 12 42 3 (**0.33) > And why approximate so much? fromtoby 12 42 3 (** (1/3)) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
Hi Lennart, This morning when I posted..it was about 2:30am and had been up a long time... bad habits.. I sent a message to Henk-Jan to that effect, but didn't send to the entire list.. anyway thanks to both for the followups... I still tend to sometimes do things the hard way in Haskell. Started trying to learn it starting in I think Nov-Dec. of 2005, so not too awfully long, but with a lot of other things soaking up time, not as far along as I wished to be in even this amount of time... Most interesting language I have used yet. but yes not sure why not the precision.. but I think when I tried that with the way I had the thing in the original, I used (**) 1/3 and got an error message which I was too tired to even read,..and just changed it to 0. or whatever however many 3's , and just got it posted.. I don't think that those functions are of much use, the thing was that when I wrote them, not at 2AM in the morning, I remember thinking just how easy it was to do pretty much anything you want with this language.. Off topic, but one of my tests of a language, old habit this, is as soon as I know enough to be dangerous, I try writing a forth interpreter in it. I have started such a thing, a module I call Hforth, and it is operational, but do to the nature of lists not holding homogeneos values in Haskell everything has to be stored with String values. This has the result of having to apply show function to store numerics to the stack and then to use the read function to convert back when popping the stack.. .. hmm still tired... Anyway the upshot is that a very rudimentary interpreter is up and running to do simple things with just builtins so far, but was built in a matter of some fairly small number of hours. Doesn't support line editing yet, so really not too good, but does support pushing strings and concatenation and some other things that are more tedious to write as primatives in other languages.. The only other language that was as easy to get to this stage with was scheme. Sorry for the ramble, gene On 8/19/06, Lennart Augustsson <[EMAIL PROTECTED]> wrote: On Aug 19, 2006, at 05:14 , Henk-Jan van Tuyl wrote: > > [...] >> *Iteration> fromtoby 12 42 3 (flip (**) 0.33) > > fromtoby 12 42 3 (**0.33) > And why approximate so much? fromtoby 12 42 3 (** (1/3)) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
On Aug 19, 2006, at 05:14 , Henk-Jan van Tuyl wrote: [...] *Iteration> fromtoby 12 42 3 (flip (**) 0.33) fromtoby 12 42 3 (**0.33) And why approximate so much? fromtoby 12 42 3 (** (1/3)) ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
On Sat, 19 Aug 2006 10:28:33 +0200, Gene A <[EMAIL PROTECTED]> wrote: *Iteration> fromtoby 1 12 2 (flip (^) 3) -- cubing of the base list above.. An easier way to write this: fromtoby 1 12 2 (^3) [...] *Iteration> fromtoby 12 42 3 (flip (**) 0.33) fromtoby 12 42 3 (**0.33) Greetings from the Yuma Desert, gene ___ Greetings from Holland, Henk-Jan van Tuyl -- http://Van.Tuyl.eu/ -- Using Opera's revolutionary e-mail client: https://secure.bmtmicro.com/opera/buy-opera.html?AID=789433 ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
Hi, Here is a little thing I came up with to simulate the construct "for x:= n1 to n2" and "for x:=n1 to n2 by n3" from purely imperative world to use in Haskell, I call the functions fromto and fromtoby.. they also take a function which consumes the x component and uses it in the computation. Just syntactic sugar.. best to wean off of this way of doing things.. but that is one of the nice things about Haskell, you CAN do this sort of thing easily. The definitions: fromto :: forall b a. Enum a => a -> a -> (a -> b) -> [b] fromto a b f = map f [a..b] -- -- fromtoby :: forall a b. (Num a, Enum a) => a -> a -> a -> (a -> b) -> [b] fromtoby a b c f = map f [a,a+c..b] -- -- Some applications using ghci with enhancements turned on... *Iteration> fromto 10 25 id [10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25] --raw list using id *Iteration> fromto 10 25 (2*) [20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50] -- list times 2 *Iteration> fromtoby 1 12 2 id -- using id to show what the base list is [1,3,5,7,9,11] *Iteration> fromtoby 1 12 2 (flip (^) 3) -- cubing of the base list above.. [1,27,125,343,729,1331] *Iteration> fromtoby 12 42 3 id [12,15,18,21,24,27,30,33,36,39,42] -- raw list gen'd by id *Iteration> fromtoby 12 42 3 (flip (**) 0.33) [2.2894284849170297, 2.4662120741078493, -- approx. cube roots 2.6207413939563993,2.7589241761011336, 2.884499140309247,2.9670416, 3.1072325056015817,3.2075343296219874, 3.3019272485002094,3.391211442600036, 3.4760266444533747] Greetings from the Yuma Desert, gene ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: iterative algorithms: how to do it in Haskell?
You might use the Prelude function until:
until :: (a -> Bool) -> (a -> a) -> a -> a
until (> 3) (+ 2) 0 = 4
or for your purpose:
until (\ a -> not (goOn(a, f(a))) f ainit
http://www.haskell.org/ghc/docs/latest/html/libraries/base/Prelude.html#v%3Auntil
http://www.haskell.org/onlinereport/prelude-index.html
http://www.haskell.org/onlinereport/standard-prelude.html#$vuntil
HTH Christian
Tamas K Papp schrieb:
> 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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