TagSet and the listability of Plus[ ]
- To: mathgroup at smc.vnet.net
- Subject: [mg61234] TagSet and the listability of Plus[ ]
- From: "Trevor Baca" <trevorbaca at gmail.com>
- Date: Thu, 13 Oct 2005 01:39:41 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
This is a question about overriding Plus[ ] for a particular type of
expression.
Say you define a foo to be the list of an integer and a string:
FooQ[expr_] := MatchQ[expr, {_Integer, _String}].
Then, for example, with ...
f1 = {3, "bar"};
f2 = {4, "tick"};
... we see that Plus[ ] does what it always does and threads across
lists ...
f1 + f2
{4, bar+tick}.
But let's say that we want to define addition on foo as the arithmetic
sum of the *first* parts but with the string join of the *second*
parts. Here's a not terribly successful strategy with TagSet:
Unprotect[Plus];
Plus /: m_?FooQ + n_?FooQ := {First[m] + First[n],
StringJoin[Last[m], Last[n]]};
Protect[Plus]
This interprets correctly and we see
DownValues[Plus]
{HoldPattern[m_?FooQ + n_?FooQ] :> {First[m] + First[n], Last[m] <>
Last[n]}}.
However, when we try ...
f1 + f2
... we get ...
{7, bar+tick}
... rather than ...
{7, bartick}
... unfortunately.
I'm pretty sure the reason for this is that the interpreter looks at f1
+ f2 and immediately produces the full form ...
List[7, Plus["bar", "tick"]]
... which means that the clever downvalue for Plus[ ] does absolutely
nothing.
A reasonable solution is to use a head other than list, as in
foo[3, bar] + foo[4, tick]
... in which case upvalues work fine:
foo[a_, b_] + foo[j_, k_] ^:= foo[a+j, StringJoin[b, k]].
But now I've developed something of a small obsession to override Plus
without introducing a special head.
Any suggestions?