[Caml-list] Objects or modules ?

[Caml-list] Objects or modules ?

[Nicolas FRANCOIS]

I'd like to make a library managing mathematical data structures, for
example integers, polynoms, fractions, and more if anyone is interested. I
started on the module point of view, mainly to learn how to use modules
and functors. So this is the structure I have :

Ordered_Ring : module managing basic rings operations
Rationnals : Num rationnals adapted to Ordered_Ring
Polynoms : functor taking an ordered ring S in argument to make a module
managing S[x]
Q_polynoms : polynoms over rationnals.

But I see things differently now, mainly because I realized S[x] is an
euclidian ring just as S is, so they should inherit the same module, and
have common operations ((extended) Euclide, square_free factorization...).
in fact I realized this when I started writing my second gcd function.

So my point of view is now :

Euclidian_Ring : Functor taking a ring signature (data structure, basic
operation + and *, link with Z and Q...), and constructing an euclidian
ring with tools.
Rationnals : Euclidian_Ring(Sig_Num)
Sig_Pol : Functor constructing an abstract polynom module sig
Polynom : functor constructing a ring S[x] provided a ring S

Do you think this plan is correct ? Should I translate it to objects ? Is
there some drawbacks using modules or objects ?

Thanks for reading.

\bye

-- 

                   Nicolas FRANCOIS
            http://nicolas.francois.free.fr
 A TRUE Klingon programmer does NOT comment his code
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Re: [Caml-list] Objects or modules ?

[Chris Hecker]

>Do you think this plan is correct ? Should I translate it to objects ? Is
>there some drawbacks using modules or objects ?

This presentation by Xavier will get you started answering this question:

Objects and classes versus modules in Objective Caml
http://pauillac.inria.fr/~xleroy/talks/icfp99.ps.gz

Chris

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Re: [Caml-list] Objects or modules ?

[Blair Zajac]

Chris Hecker wrote:
> 
> >Do you think this plan is correct ? Should I translate it to objects ? Is
> >there some drawbacks using modules or objects ?
> 
> This presentation by Xavier will get you started answering this question:
> 
> Objects and classes versus modules in Objective Caml
> http://pauillac.inria.fr/~xleroy/talks/icfp99.ps.gz

What does the symbol [[ ]] mean in the paper?

It's used to describe closures

[[f(a)]] = [[f].code([[f], [[a]])

object method calls

[[o#m(a)]] = [[o]].methsuite(m)([[o]], [[a]])

Best,
Blair

-- 
Blair Zajac <blair@orcaware.com>
Web and OS performance plots - http://www.orcaware.com/orca/
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Re: [Caml-list] Objects or modules ?

[Markus Mottl]

On Sat, 29 Jun 2002, Nicolas FRANCOIS wrote:
> I'd like to make a library managing mathematical data structures, for
> example integers, polynoms, fractions, and more if anyone is interested. I
> started on the module point of view, mainly to learn how to use modules
> and functors. So this is the structure I have :

You might also want to take a look at Christophe Raffalli's library for
formal and numerical calculus to grab a few ideas:

  http://lama-d134.univ-savoie.fr/sitelama/Membres/pages_web/RAFFALLI/formel.html

Regards,
Markus Mottl

-- 
Markus Mottl                                             markus@oefai.at
Austrian Research Institute
for Artificial Intelligence                  http://www.oefai.at/~markus
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Re: [Caml-list] Objects or modules ?

[Nicolas FRANCOIS]

Le Sat, 29 Jun 2002 12:22:52 +0200 Markus Mottl <markus@oefai.at> a écrit
:

> You might also want to take a look at Christophe Raffalli's library for
> formal and numerical calculus to grab a few ideas:
> 
>   http://lama-d134.univ-savoie.fr/sitelama/Membres/pages_web/RAFFALLI/formel.html

OK, I got it. If I really understand this, this is a pre-project for FOC.
Am I right ?

Now that I adapted it to OCaml 3.04 (Streams not recognized by standard
OCaml now), I have a new problem : this is a definition for a quotient
ring (there's a similar one for a quotient field in case the ideal is
primitive) ;

(in algebra.mli)
module Quotient :
  functor(R : Euclidian_Ring) ->
    functor(Elt : One_element with type elem = R.elem) ->
      Ring with type elem = R.elem
  
(in algebra.ml)
module Quotient = 
  functor (R : Euclidian_Ring) -> 
  functor (Elt : One_element with type elem = R.elem) ->
  struct
    type elem = R.elem
    let zero = R.zero
    let one = R.one
    let t_of_int = R.t_of_int
    let (++) = R.(++)
    let (--) = R.(--)
    let ( ** ) = R.( ** )
    let (==) a b = R.(==) (R.(mod) (R.(--) a b) Elt.elt) R.zero
    let opp = R.opp
    let normalize x = R.(mod) (R.normalize x) Elt.elt
    let print x = R.print (normalize x)
    let write ch x = R.write ch (normalize x)
    let parse = R.parse
    let read = R.read
    let write_bin ch x = R.write_bin ch (normalize x)
    let read_bin = R.read_bin
    let conjugate = R.conjugate
  end

I'd like to use this functor to create a ring Z/pZ, providing a (possibliy
prime) integer p. My problem is : what is the correct way to use this ?

Thanks for reading.

\bye

-- 

                   Nicolas FRANCOIS
            http://nicolas.francois.free.fr
 A TRUE Klingon programmer does NOT comment his code
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Re: [Caml-list] Objects or modules ?

[Nicolas FRANCOIS]

Le Thu, 4 Jul 2002 01:16:11 +0200 Nicolas FRANCOIS (AKA El Bofo)
<nicolas.francois@free.fr> a écrit :

> Le Sat, 29 Jun 2002 12:22:52 +0200 Markus Mottl <markus@oefai.at> a
> écrit:
> 
> > You might also want to take a look at Christophe Raffalli's library
> > for formal and numerical calculus to grab a few ideas:
> > 
> >   http://lama-d134.univ-savoie.fr/sitelama/Membres/pages_web/RAFFALLI/formel.html
> 
> OK, I got it. If I really understand this, this is a pre-project for
> FOC. Am I right ?
> 
> Now that I adapted it to OCaml 3.04 (Streams not recognized by standard
> OCaml now), I have a new problem : this is a definition for a quotient
> ring (there's a similar one for a quotient field in case the ideal is
> primitive) ;
> 
> (in algebra.mli)
> module Quotient :
>   functor(R : Euclidian_Ring) ->
>     functor(Elt : One_element with type elem = R.elem) ->
>       Ring with type elem = R.elem
>   
> (in algebra.ml)
> module Quotient = 
>   functor (R : Euclidian_Ring) -> 
>   functor (Elt : One_element with type elem = R.elem) ->
>   struct
>     type elem = R.elem
>     let zero = R.zero
>     let one = R.one
>     let t_of_int = R.t_of_int
>     let (++) = R.(++)
>     let (--) = R.(--)
>     let ( ** ) = R.( ** )
>     let (==) a b = R.(==) (R.(mod) (R.(--) a b) Elt.elt) R.zero
>     let opp = R.opp
>     let normalize x = R.(mod) (R.normalize x) Elt.elt
>     let print x = R.print (normalize x)
>     let write ch x = R.write ch (normalize x)
>     let parse = R.parse
>     let read = R.read
>     let write_bin ch x = R.write_bin ch (normalize x)
>     let read_bin = R.read_bin
>     let conjugate = R.conjugate
>   end
> 
> I'd like to use this functor to create a ring Z/pZ, providing a
> (possibliy prime) integer p. My problem is : what is the correct way to
> use this ?

OK, I found a way : 

(file essai.ml)
open Algebra

module Five : (One_element with type elem = Ring_MZ.elem) =
  struct
    type elem = Ring_MZ.elem
    let elt = Ring_MZ.t_of_int 5
  end
open Five

module Z5Z = Quotient_prime (Ring_MZ) (Five)

open Polynomial

module P = Make(Z5Z)

open P

let p1 = monome (Z5Z.t_of_int 8) 0
	 ++ monome (Z5Z.t_of_int 4) 1
	 ++ monome (Z5Z.t_of_int 1) 2;;
	   
let p2 = monome (Z5Z.t_of_int 3) 1
	 ++ monome (Z5Z.t_of_int 1) 12
	 ++ monome (Z5Z.t_of_int 2) 14;;

print (p1 ** (p2 // p1) ++ (p2 mod p1) -- p2)


(The end for the ones how know the package Formel)

Is there a way to do things simpler ?

\bye


-- 

                   Nicolas FRANCOIS
            http://nicolas.francois.free.fr
 A TRUE Klingon programmer does NOT comment his code
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Re: [Caml-list] Objects or modules ?

[Nicolas FRANCOIS]

Thanks for the pointers. Exactly what I was looking for.

\bye

-- 

                   Nicolas FRANCOIS
            http://nicolas.francois.free.fr
 A TRUE Klingon programmer does NOT comment his code
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Re: [Caml-list] Objects or modules ?

[Francois Pottier]

On Sat, Jun 29, 2002 at 03:14:58AM +0200, Nicolas FRANCOIS wrote:
> I'd like to make a library managing mathematical data structures, for
> example integers, polynoms, fractions, and more if anyone is interested. I
> started on the module point of view, mainly to learn how to use modules
> and functors.

You may be interested in having a look at the FOC project's publications:

  http://www.lip6.fr/reports/lip6.2000.014.html
  http://calfor.lip6.fr/~foc/

They are writing a large library of mathematical structures in O'Caml.
I would recommend getting in touch with them for more information.

-- 
François Pottier
Francois.Pottier@inria.fr
http://pauillac.inria.fr/~fpottier/
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