RE: [Axiom-developer] [MutualRecursion] (new)

[Page, Bill]

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

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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
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