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UpValues for expressions headed by a string

• To: mathgroup at smc.vnet.net
• Subject: [mg62896] UpValues for expressions headed by a string
• From: "Trevor Baca" <trevorbaca at Gmail.com>
• Date: Thu, 8 Dec 2005 00:04:25 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

This is a question about the limitations of using a string as the head
of an expression.

As an example we'll create two expressions (or data types): a foo
(which does what we want) and a bar (which doesn't).

If we define foo with

  fooQ[f_] := MatchQ[f, foo[_Integer]]

and then define wiggle on foo with

  foo /: wiggle[f_foo?fooQ] := First[f] + 10

then the results are exactly as expected:

  wiggle[foo[17]]
  27

But, if we (note the doublequotes and) define bar as headed with a
string in

  barQ[b_] := MatchQ[b, "bar"[_Integer]]

and then attempt to define wiggle on bar with

  "bar" /: wiggle[b_"bar"?barQ] := First[b] - 5

we get the error

  TagSetDelayed::"sym": "Argument "bar" at position 1 is expected to be
a symbol.

which makes sense because we're essentially trying to assign an upvalue
to the *string* "bar" (rather than to the *symbol* foo).

First question: is it possible to assign an upvalue to a string?

Second question: why doesn't unprotecting String with

  Unprotect[String];
  "bar" /: wiggle[b_"bar"?barQ] := First[b] - 5;
  Protect[String]

work?

Last, is it, in general, a bad idea to create data types headed with a
string, either because of situations like the one given here or for
some other, additional reasons?

Trevor.

• Follow-Ups:
  • Re: UpValues for expressions headed by a string
    • From: Sseziwa Mukasa <mukasa@jeol.com>