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MathGroup Archive 1994

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Re: Defining a predicate

  • To: mathgroup at yoda.physics.unc.edu
  • Subject: Re: Defining a predicate
  • From: rubin at msu.edu (Paul A. Rubin)
  • Date: Fri, 24 Jun 94 15:29:51 EDT

>I want to define a predicate (TableauQ) to recognise a system (list) of
>equations, so that I set $PrePrint to apply TableForm to such a
>system. The following works:
>
>	TableauQ[_] := False
>	TableauQ[{_Equal..}] := True
>	$PrePrint = If[TableauQ[#], TableForm[#],#]&;
>
>However, the logic of providing a blanket False (TableauQ[_] :=
>False), which is then overridden when appropriate pattern matches,
>bothers me. Is the explicit False necessary?

Seems so.

>On p. 227 of the good book, Wolfram writes:
>
>	An important feature of Mma property-testing functions whose
>names end in Q is that they always return False if they cannot
>determine whether the expression has the given property.
>
>That behaviour also seems appropriate in my example. Is it possible
>to make user defined predicates exhibit the same behaviour?

If you mean establish a condition that all user-defined predicates with
names ending in 'Q' default to False if otherwise unresolved, it seems a bit
dangerous to want it.  Is MyFunQ a predicate or a user-defined function?
Obviously, you can impose on yourself the condition that anything ending in
'Q' be a predicate, but what happens when you load an externally developed
package?

In any event, I'm pretty sure you cannot make that a standard in Mma.  When
Mma goes to resolve a reference like MyFunQ[x], it looks for applicable
substitution rules, and specifically for rules associated with either
MyFunQ, x, or the Head of x.  A condition like f_[_] := False if the name of
f ends in 'Q' would have no symbol with which to be associated.

BTW, I did a little experiment implementing a predicate three different
ways.  My predicate checked for the Head "junk."  The first way was yours:
f1Q[_] := False; f1Q[_junk] := True.  The second, which bypasses the blanket
false but is logically equivalent, was:  f1Q[x_] := If[ Head[x] == junk,
True, False ].  The third was like the first but with undelayed assignment:
f1Q[_] = False; f1Q[_junk] = True.  The average of 10 applications to a list
of 200 critters, roughly half having head "junk," showed the second method
to take about 25% longer than the first, and the third to take about 60%
less time than the first.  I presume that's because the delayed assignment
(:=) has to be evaluated each time the function is referenced.  So you'll
pick up a little speed by dropping the colons.

>
>+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
>Michael Carter                      m.carter at econ.canterbury.ac.nz
>
>Department of Economics             voice: + 64 3 364 2524
>University of Canterbury            fax:   + 64 3 364 2635
>Private Bag 4800
>Christchurch
>NEW ZEALAND
>
**************************************************************************
* Paul A. Rubin                                  Phone: (517) 336-3509   *
* Department of Management                       Fax:   (517) 336-1111   *
* Eli Broad Graduate School of Management        Net:   RUBIN at MSU.EDU    *
* Michigan State University                                              *
* East Lansing, MI  48824-1122  (USA)                                    *
**************************************************************************
Mathematicians are like Frenchmen:  whenever you say something to them,
they translate it into their own language, and at once it is something
entirely different.                                    J. W. v. GOETHE






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