Re: TagSet and the listability of Plus[ ]

• To: mathgroup at smc.vnet.net
• Subject: [mg61451] Re: [mg61234] TagSet and the listability of Plus[ ]
• From: Trevor Bača <trevorbaca at gmail.com>
• Date: Wed, 19 Oct 2005 02:16:59 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```David,

Thanks very much; I like the infix circle-plus!

Trevor.

On 10/13/05, David Park <djmp at earthlink.net> wrote:
> Trevor,
>
> How about something like this?
>
> FooQ[expr_] := MatchQ[expr, {_Integer, _String}]
> f1 = {3, "bar"};
> f2 = {4, "tick"};
> f3 = {1, "one"};
>
> CirclePlus[args__?FooQ] :=
>   Fold[{First[#1] + First[#2], Last[#1] <> Last[#2]} &, {0, ""}, {args}]
>
> f1 \[CirclePlus] f2 \[CirclePlus] f3
> {8, bartickone}
>
> David Park
>
>
>
> From: Trevor Baca [mailto:trevorbaca at gmail.com]
To: mathgroup at smc.vnet.net
>
>
> 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?
>
>
>

--
Trevor BaÄ?a
trevorbaca at gmail.com

```

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