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MathGroup Archive 2005

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Re: Types in Mathematica, a practical example

  • To: mathgroup at smc.vnet.net
  • Subject: [mg62845] Re: Types in Mathematica, a practical example
  • From: "Steven T. Hatton" <hattons at globalsymmetry.com>
  • Date: Tue, 6 Dec 2005 23:10:13 -0500 (EST)
  • References: <200512051841.NAA21133@smc.vnet.net> <dn36n9$2tv$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

I'm still working on my first pot of coffee, so I can claim full mental
acuity.  Nonetheless, I will offer my observations.

Andrzej Kozlowski wrote:

> It seems to me that you are looking here at Mathematica from the
> wrong view point. Although Mathematica is not a strict "functional"
> language, it is "functional" at least in the sense that it is
> "functions" and not "objects" that play the central role (I am being
> deliberately vague here but I have run out of patience with long
> discussions of programming languages and  general design issues.). 

You aren't obligated to participate in this discussion, as I'm sure you
know.  I will acknowledge that discussing Mathematica in terms of a
programming language can be a bit frustrating.  Part of that is due to the
inexact way in which it is documented at the fundamental level.

> In 
> this case the issue is with the function Plus and not with the nature
> or "type" of x etc. Plus has the attribute Listable, which is
> responsible for the behaviour you see (and it does [not?] really matter if
> Mathematica assumes that x is a number or not, for the same thing
> will happen, for example,  if you use the string "x" instead of the
> symbol  x). Hence the natural way to deal with your problem is by
> temporarily blocking the Listable attribute

Here I will say that Plus could be viewed as an instance of a class Symbol
with a member variable Listable.  I would probably implement attributes as
a single bit field. [10101110], or whatever, where one means the attribute
is set.

> like this: 
> 
> In[10]:=
> a = {{1, 2}, {3, 4}};
> 
> In[11]:=
> Block[{Plus}, x - a /. x -> a]

That is certainly an interesting trick.  If I understand correctly, you have
basically shadowed the "definition" of Plus, and within the context of the
Block, "Plus" is just a vacant symbol.

> Out[11]=
> {{0, 0}, {0, 0}}
> 
> As far as I am concerned this works just as I would wish and I see no
> benefit in adding any kind of "types" to deal with this sort of
> problems.

This really is the kind of answer I was trying to get at by bringing up the
topic of typing.  That is to say, in other languages we expect certain
kinds of behavior.  Some of these behaviors are based on a type system in
the other language.  What we have here is a person who came to Mathematica
with certain expectations of behavior which seem "type related". Your
suggestions seems like an insightfull means of accomplishing the original
objective of Ingolf's example.

As for adding any kind of type system to Mathematica, that could mean
different things.  It could mean modifying the core Mathematica language to
add a type system.  That is not something I expect to happen in the next
few thousand years, at least not in the sense of types in C++, etc.  It
could also mean implementing a type system using the current Mathematica
language.  That is something which people (e.g., Roman Maeder) have done,
by their own definition of types.  It also seems to be something WRI is
promoting in their training courses.

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