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Re: Types in Mathematica thread

• To: mathgroup at smc.vnet.net
• Subject: [mg62900] Re: Types in Mathematica thread
• From: "Steven T. Hatton" <hattons at globalsymmetry.com>
• Date: Thu, 8 Dec 2005 00:04:34 -0500 (EST)
• References: <dmp9na$hi2$1@smc.vnet.net> <dn37bp$35e$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

Jon Harrop wrote:

>> 7. Downvalues are "default" function structures, or "common" functions,
>> or "built-in function" structures, or "broadest class" functions.
>> Upvalues are "special case" functions, or "user-defined" functions /
>> modifications of built-in or default functions, or "narrow-case"
>> functions, or "context-dependent" functions. (This latter is especially
>> important for AI and for a general understanding of the universe.)
> 
> The fact that Mathematica distinguishes between up- and down-values is
> really incidental (a historical artefact). So I think you're
> over-analysing it.

They certainly have different roles during evaluation. UpValues make a lot
more sense when it comes to operator overloading than does unprotecting and
modifying builtin operators.  This is not only to avoid tinkering with the
implementation and possibly breaking something, it has significant
performance advantages.

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