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Re: How to declare Integers?

• To: mathgroup at smc.vnet.net
• Subject: [mg13167] Re: How to declare Integers?
• From: Sean Ross <seanross at worldnet.att.net>
• Date: Mon, 13 Jul 1998 07:42:17 -0400
• References: <000001bda94e$c10efc90$338e5981@sumba.cs.uwm.edu>
• Sender: owner-wri-mathgroup at wolfram.com

Le Van Tri wrote:
> 
> Dear Joe Oswald and Sean Ross,
> 
> About your idea of having variable typing instead of pattern matching in
> Mathematica
> I think that idea is nice but some what "obsolete" - by which I mean
> variable typing
> is obsolete by the coming out of pattern matching. Why ? In traditional
> languages
> like Fortran, C++, Lisp, Scheme, ML, ... variable typing was done statically
> at compile
> time. By using pattern matching, that could be done dynamically at run time.
> Which
> way is better ?

Perhaps the term variable "typing" is ill-advised since it sounds the
same as what is done in C++ or Fortran.  No, what we are after is
something like this:


Declare[symbol,Integer];

Sin[symbol Pi x]

and have it return zero for all x even with no explicit value assigned
to symbol.

I want to be able to tell mathematica that a certain symbol is Real,
Complex, Imaginary, greater than 2, Integer etc. and have every single
function in the language react appropriately taking that declaration as
an assumption.  I want Integrals to be appropriate to Real only or
Integer only arguments etc.  In essence I want global assumptions or
conditions on symbols with every built-in function looking at those
restrictions or assumptions and responding appropriately.

You can't do that yet with pattern matching.