Re: [Maxima-discuss] rules and patterns

[Richard F. <fa...@be...>]

On 2/19/2014 11:52 AM, Mark wrote:
> On 02/19/2014 08:13 PM, Robert Dodier wrote:
>> On 2014-02-19, Mark <zei...@ya...> wrote:
>>
>>> Apart from the maxima manual, is there any other recommended how-to
>>> documentation for using rules and patterns in Maxima?
>> No, but feel free to post any questions about rules & patterns to the mailing list.
>>
>>> I tried working with the 2nd eds. of Macsyma's user guide, but there are
>>> differences between Macsyma and Maxima for me right away. E.g. if I
>>> simply copy-cut-and-paste the famous example to implement the factorial
>>> using rules (pg. 220), then, tellsimpafter() is not applied recursively,
>>> but only once.

1. I wrote the pattern matcher circa 1969 at MIT.

2. WGD changed it, substituting his own version, in the Symbolics 
version in 1986.
   (according to comments not in the Maxima code)

3. Apparently the semantics in this case differ.  I do not know if this 
was intentional or not.

4. The use of tellsimpafter shown in the user manual is not how it is 
intended to be used.
It might be too strong to say the example is a bug, but perhaps it is.  
I do not know who wrote the user
manual, but the IDEA behind tellsimpafter is that it should be used when 
there is some
perhaps quite powerful built-in simplification mechanism in Macsyma that 
you don't want to
coerce or over-ride,  but that you wanted to advise in a kind of final 
checkup.  That is, if
the built-in simplifier left some form unchanged, then you could turn to 
your own program.

e.g. tellsimpafter(integrate(EXP,x),  f(x))     would be used only if 
the built-in integrate command
did not work, but you knew how to integrate EXP.
Tellsimpafter COULD be used to modify a simplifier that you constructed 
yourself with layers of
tellsimp() and perhaps tellsimpafter() interlayered.  Sounds like a bad 
design, but in the case here,
where the rule set strictly defines the domain (positive integers vs 
anything else), the ordering
of the rules doesn't matter!

The use of tellsimpafter to define a new function is inappropriate 
generally.  The use of tellsimpafter
to modify the simplification of function foo, where the replacement 
contains foo is an invitation to
disaster -- or at least it seemed to me, in 1969.  So I disallowed 
re-simplification. Allowing
re-simplification is probably a change of  a dozen characters or so,  
and WGD presumably did that,
realizing that my fear was not especially well founded, and that 
potentially infinite recursion
could be stopped by appropriate ordering of rules.   I assume that WGD 
also modernized the
code in various ways.

To me, the appropriate code for a rule-based factorial that just leaves 
non-integers or negative
numbers hanging  would be

  posintp(n):=is(integerp(n) and n>0)$
  matchdeclare(int,posintp)$

tellsimp(fact(0),1)$
tellsimp(fact(int),int*fact(int-1))$

There is no reason to use tellsimpAFTER here.   Why did the user-guide 
author use it?



>> That sounds interesting, but as I don't have the Macsyma user guide at
>> hand, I can't try out that example. Care to post the code in question?
> Before I do that, may I ask if you would think that the docs for the
> pattern matcher in Macsyma should be one-to-one usable also for Maxima?
I would have thought so.  It could be that WGD introduced other 
differences.  I noticed
one, which is that tellsimp(exp1,exp2,cond)  is acceptable.   the third 
argument cond  is
a conditional which is evaluated, and if false, inhibits the rule.

So any examples that you encounter that use that feature will not work 
in Maxima
currently.

I haven't spotted any examples in the Macsyma user manual and its 
on-line help
system neglects to mention this feature.

In the Macsyma system then, only one rule would be needed...

matchdeclare(int,true);
tellsimp(fact(int),int*fact(int-1),   integerp(int) and int>0);

this is not acceptable to Maxima.

>
> This is the code from pg. 220 of Macsyma User's Guide 2nd. Ed. (Google
> tells you to get it from
> http://www.cs.berkeley.edu/~fateman/macsyma/docs/userg.pdf)
Yes, that's a place to find it.  You can also find the reference manual 
in that directory.
Nice of Google to find it for you.
>
> (c1) posintp(n):=is(integerp(n) and n>0)$
> (c2) matchdeclare(int,posintp)$
> (c3) tellsimpafter(fact(0),1)$
> (c4) tellsimpafter(fact(int),int*fact(int-1))$
> (c5) fact(-1)
> (d5) fact(- 1)
> (c6) fact(0.5)
> (d6) fact(0.5)
> (c7) fact(0)
> (d7) 1
> (c8) fact(5)
> (d8) 120
>
> This makes sense to me, if I should think of tellsimpafter() to work
> recursively until the rule cannot be applied any more.
As far as I can recall, that's not the way the original author thought 
it should work, but it is the way WGD
changed it  (Bill Dubuque, where are you?)
>
> Now this is what happens if I (, admittedly, completely blindly) type in
> the same lines into a freshly started Maxima
>
> <snip>;
>
> (%i9) fact(5);
> (%o9) 5*fact(4)
>
> (d8) vs. (%o9) is what I was asking about.
>
> Mark
>
>