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MathGroup Archive 2006

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Re: Clarification re. Curiosity concerning transformation rules for List

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70962] Re: [mg70947] Clarification re. Curiosity concerning transformation rules for List
  • From: "Chris Chiasson" <chris at chiasson.name>
  • Date: Fri, 3 Nov 2006 01:39:06 -0500 (EST)
  • References: <200611021148.GAA15676@smc.vnet.net> <acbec1a40611020647h4cc56eaas403a8ff2b7cda3ad@mail.gmail.com>

heh, actually, one can't even Block List - interesting

On 11/2/06, Chris Chiasson <chris at chiasson.name> wrote:
> Your question was clear the last time. You could easily Block List,
> and then its definitions and attributes would be yours to modify
> inside the Block.
>
> I am not aware of any function or scoping construct that would allow
> you to keep the present definitions for List and append your own such
> that all the rules would be active at the same time. (though I could
> think of several uses for a scoping construct with this capability -
> special message handling would be one application)
>
> I guess the short answer to your question is: no.
>
> A lot of stuff would probably break if List were to have that
> definition assigned.
>
> On 11/2/06, Andrew Moylan <andrew.j.moylan at gmail.com> wrote:
> > I recently wrote:
> >
> > ----
> > Since the List symbol is locked, I am curious about the possibility (or
> > otherwise) of giving definitions for which the left-hand-side of the
> > transformation rule contains only the List symbol. Here's an arbitrary,
> > explicit example:
> >
> > Is it possible to make a definition such that: any list of two
> > identical elements evaluates to the empty list? E.g. {x_, x_} -> {}.
> >
> > I can't see any way this transformation rule can be added. It's not
> > possible to modify the DownValues for List; and there are no
> > first-level symbols to which an UpValue can be added. Does anyone have
> > any ideas?
> > ----
> >
> > I received some replies suggesting that I use my proposed rule
> > {x_,x_}->{} in combination with ReplaceAll to effect the transformation
> > on a case-by-case basis. However, I am interested in whether it is
> > possible to add a _definition_ so that the rule is _always_ applied.
> >
> > I think I can clarify by way of an example:
> >
> > Unprotect[Power];
> > Power[x_, x_] = 0;
> >
> > Now 4^3 evaluates to 64 as usual, but 4^4 evaluates to 0. However, the
> > following fails because List has attribute Locked (as well as attribute
> > Protected):
> >
> > Unprotect[List];
> >
> > This doesn't mean that transformation rules involving lists cannot ever
> > be defined. We can use UpValues. For example:
> >
> > AppendTo[UpValues[hello], {hello, x_} -> 0]
> >
> > Now pairs with the symbol hello as their first element evaluate to
> > zero: {hello, 1} evaluates to 0. But other lists are not affected: {1,
> > 2} evaluates to {1, 2}.
> >
> > However, the only way it was possible to add that definition was by
> > attaching it as an UpValue for hello. Since there are no symbols in the
> > rule {x_,x_}->{} (except List, which is locked), is it possible to make
> > this definition? Is there a "global" set of transformation rules,
> > always applied, but not attached to any particular symbol?
> >
> > I hope this is clearer, instead of less clear ;-).
> >
> > Cheers,
> >
> > Andrew
> >
> >
>
>
> --
> http://chris.chiasson.name/
>


-- 
http://chris.chiasson.name/


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