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RE: [Axiom-developer] [MutualRecursion] (new)
From: |
Page, Bill |
Subject: |
RE: [Axiom-developer] [MutualRecursion] (new) |
Date: |
Tue, 18 Jan 2005 13:43:11 -0500 |
Ralf,
On Tuesday, January 18, 2005 12:22 PM you wrote:
>
> Do you find the attached file relevant?
>
----------
#include "aldor"
#include "aldorio"
define Parity: Category == with {
parity: Integer -> Boolean;
}
Odd: Parity == add {
parity(n:Integer): Boolean == {
(n>0) => parity(n-1)$Even;
(n<0) => parity(n+1)$Even;
false;
}
}
Even: Parity == add {
parity(n: Integer): Boolean == {
n>0 => parity(n-1)$Odd;
n<0 => parity(n+1)$Odd;
true;
}
}
main(): () == {
import from Integer;
stdout << "parity( 10)$Even=" << parity( 10)$Even << newline;
stdout << "parity( 8)$Odd =" << parity( 8)$Odd << newline;
stdout << "parity(-1111)$Odd =" << parity(-111)$Odd << newline;
}
main();
-----
Yes I do find it very relevant. Thank you!
I have tried for about 1/2 an hour without success to write
this same category in Axiom. Perhaps someone with more
experience with the Axiom compiler can help?
> It actually compiles with Aldor 1.0.2 and runs with the output
>
> aldor -grun -laldor EvenOdd.as
> parity( 10)$Even=T
> parity( 8)$Odd =F
> parity(-1111)$Odd =T
>
> I wonder how the Aldor compiler handles such mutual recursive
> structures. Perhaps Peter Broadbery knows.
I would also like to know.
>
> Maybe this example is easy, because both domains are in the
> same file> Do you know a good example where it makes sense
> to put the domains much more away from each other?
I can not give a simple example right now but I suspect that
this happens very frequently in Axiom's algebra.
>
> BTW, who reads address@hidden
address@hidden is the email address of the
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> What if I write a mail to this address?
If you send mail to this address you should delete the part
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>
> Bill Page wrote:
> > Here is an example of defining functions by mutual
> recursion in Axiom
> >
> > We start with a "bootstrap" definition of
> 'parity(n)\$Even'. All that is
> > really needed here is a package that exports a function
> named 'parity'
> > with the right signature. This particular function will
> never be called
> > and will be re-defined later. It's only purpose is as a
> placeholder to
> > allow the later definition of **ODD**.
> >
> > \begin{axiom}
> > )abbrev package EVEN Even
> > Even(): E == I where
> > E == with
> > parity: Integer -> Boolean
> > I == add
> > parity(n) == true
> > \end{axiom}
> >
> > Now we can define 'parity(n)\$Odd'. It depends on **EVEN**.
> >
> > \begin{axiom}
> > )abbrev package ODD Odd
> > Odd(): E == I where
> > E == with
> > parity: Integer -> Boolean
> > I == add
> > parity(n:Integer) ==
> > -- output("ODD",n::OutputForm)$OutputPackage
> > (n>0) => parity(n-1)$Even
> > (n<0) => parity(n+1)$Even
> > false
> > \end{axiom}
> >
> > But the bootstrap definition of **EVEN** is incomplete. It really
> > depends (recusively) on **ODD**. So finally we need the
> full (re-)definition
> > of 'parity(n)\$Even'
> >
> > \begin{axiom}
> > )abbrev package EVEN Even
> > Even(): E == I where
> > E == with
> > parity: Integer -> Boolean
> > I == add
> > parity(n) ==
> > -- output("EVEN",n::OutputForm)$OutputPackage
> > n>0 => parity(n-1)$Odd
> > n<0 => parity(n+1)$Odd
> > true
> > \end{axiom}
> >
> > Now we can test the new functions:
> >
> > \begin{axiom}
> > parity(10)$Even
> > parity(8)$Odd
> > parity(-1111)$Odd
> > \end{axiom}
> >
> > --
> > forwarded from
>
http://page.axiom-developer.org/zope/mathaction/MutualRecursion#msg200501172
address@hidden