• To: mathgroup at smc.vnet.net
• Subject: [mg88198] Question about OneIdentity
• From: Szabolcs Horvát <szhorvat at gmail.com>
• Date: Mon, 28 Apr 2008 04:38:08 -0400 (EDT)
• Organization: University of Bergen

```(Scroll down for the actual question)

I never really understood Flat and OneIdentity, and unfortunately

From the docs:

"""
OneIdentity is an attribute that can be assigned to a symbol f to
indicate that f[x], f[f[x]], etc. are all equivalent to x for the
purpose of pattern matching.

OneIdentity has an effect only if f has attribute Flat.
"""

There is also an example, listing the Attributes of Times and showing
that Times[a] evaluates to a.  However, this is misleading because this
behaviour cannot be caused by Times's attributes:

In[1]:= Attributes[f] = Attributes[Times]
Out[1]= {Flat, Listable, NumericFunction,
OneIdentity, Orderless, Protected}

In[2]:= f[a]
Out[2]= f[a]

If we assign the same attributes to f, f[a] will not evaluate to a.  Was
the technical writer also confused, or is the example supposed to
illustrate something different than what I understood?

** And now the actual question:

According to the text in the docs (f[x] is considered equivalent to x in
pattern matching) I would expect

MatchQ[1, f[1]]

to give True after evaluating SetAttributes[f, {Flat, OneIdentity}].
But it gives False.

** The application:

This came up in the following application:

fun[HoldPattern@Plus[terms__]] := doSomething[{terms}]

This function should handle a single term, too.  Of course, there are
workarounds, but I couldn't come up with anything as simple as the
pattern above (which unfortunately does not work).

```

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