Re: Determine if a parameter is a function

• To: mathgroup at smc.vnet.net
• Subject: [mg101863] Re: Determine if a parameter is a function
• From: Peter Breitfeld <phbrf at t-online.de>
• Date: Mon, 20 Jul 2009 06:00:23 -0400 (EDT)
• References: <h3kddu\$g35\$1@smc.vnet.net> <h3uv4g\$k8j\$1@smc.vnet.net>

```Yours is a fine solution, but why do you need AtomQ?

At the moment, after heavy trying, I use to test if f is not to be
considered a function:

KeineFunktion::nofun="Parameter  `1`  sollte eine Funktion sein.";
KeineFunktion[f_]:=
If[Not[
((DownValues[f] =!= {}) ||
(Intersection[Attributes[f],{NumericFunction}] =!= {}))) ],
Message[KeineFunktion::nofun, f]; True, False];

This passes nearly all usual cases, except "Set", which will be
considered a function, whereas e.g. SetDelayed, Rule or constants where
not. This is, because Set has DownValues.

One -- in my opinion not very complicated case -- is with functions
which are defined by SubValues. So

u[x_][y_]:=x^2+y

KeineFunktion[u[x]]        --> True
KeineFunktion[u]           --> True

but

KeineFunktion[u[x][#]&]    --> False    (not astonishing)

The length of "systemFunctions" you calculated is bigger than the length
calculated with my function, because I have them restricted to
NumericFunktion.

> Actually, after some work, I found a solution which appears more
> reliable (but who knows...):
>
> ClearAll[FunctionQ];
> FunctionQ[f_] := (functionQtest2[f] || functionQtest3[f]) &&
> functionQtest1[f];
>
> ClearAll[functionQtest1,functionQtest2,functionQtest3];
> functionQtest1[f_Symbol] := (Length[StringPosition[ToString
> [f::usage,OutputForm],"["]]>0);
> functionQtest1[___] := True;
> functionQtest3[f_] := (AtomQ[f] && (Head[f]===Symbol) && (!NumericQ
> [f]) && (
>     (DownValues[f]=!={})||(Attributes[f]=!={})
> ));
>
> The functionQtest1 test comes from a little heuristics about usage
> messages.
> Then, the following comes out:
>
> In:= FunctionQ[Red]
> Out= False
>
> In:= FunctionQ[\[ScriptCapitalA]]
> Out= False
>
> In:= FunctionQ[Log]
> Out= True
>
> In:= FunctionQ[Algebraics]
> Out= False
>
> In:= FunctionQ[Log[Sin[#]] &]
> Out= True
>
> In:= systemFunctions = Select[ToExpression /@ Names["System`*"],
> FunctionQ];
> In:= systemFunctions // Length
> Out= 1661
>
>
>
> On Jul 15, 1:09 pm, Peter Breitfeld <ph... at t-online.de> wrote:
>> Suppose I have a function eg
>>
>> myfunc[f_,x_]:= <some definitions>
>>
>> f should be a pure function like (#^2&) or Function[{x},x^2] or a named
>> function either self defined, like
>>
>> f[x_]:=x^2   or g[x_]=x^2
>>
>> or built-in like Sin, Log, ...
>>
>> How can I test if f is any of these, to be able to yield a message on
>> wrong input?
>>
>> I found that the pure-functions have Head Function, but all the others
>>
>> --
>> _________________________________________________________________
>> Peter Breitfeld, Bad Saulgau, Germany --http://www.pBreitfeld.de
>
>

--
_________________________________________________________________
Peter Breitfeld, Bad Saulgau, Germany -- http://www.pBreitfeld.de

```

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