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Groups > comp.soft-sys.math.mathematica > #16641

Re: Do we need a When function?

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On 2014-3-10, 4:37 , Itai Seggev wrote:
> On Sat, Mar 08, 2014 at 02:42:31AM -0500, David Bailey wrote:
>> Dear All,
>>
>> Recently I wanted to create an expression that only evaluated when x was
>> a number. Obviously, one way to do that is to write something like:
>>
>>    If[x<1000000000000,f[x]]
>>
>> This will stay unevaluated until x is assigned to a number - as required
>> - but it is very ugly because it makes it hard to understand what is
>> going on.
>
> Why isn't this simply
>
> If[NumericQ[x], f[x]]   (*are NumberQ, if want an actual number type*)
>
> But I'm further confused by your statement that it stays unevlauate until x is
> assigned a number.  That's not true, it will evaluate to Null unless x is
> numeric prior to the start of evaluation.
>
>> More generally, it would be nice to write an expression that will only
>> evaluate when an expression is true. I solved that by writing a function
>> When:
>>
>> SetAttributes[When, HoldAll];
>> When[cond_, val_] := val /; cond
>>
>> However, my point is that this construction is sufficiently useful that
>> it should be built in to Mathematica, and my solution might not be
>> obvious to all users.
>>
>> Am I missing a simpler solution?
>>
>> Do others agree that this is an omission in the language?
>
> I'm not sure what your use case is.  F[x] will of course stay unevluated until
> x has some value which F knows what to do with...
>

Hello Itai,

What (I believe) David means is that

If[NumericQ[x], f[x]]

immediately evaluates to Null if the symbol x has no assigned value. 
When[NumericQ[x], f[x]] does not evaluate in this case, so later you can 
substitute in a number for x and have f[x] evaluate correctly in case 
f[x] only works with numbers, not symbols.

Then you could do something like

FindRoot[
  When[NumericQ[a], First@FindMaximum[Exp[-a x] x^2, {x, 1}] - 0.5],
  {a, 1}
]

without having to go to the trouble of defining

f[a_?NumericQ] := First@FindMaximum[Exp[-a x] x^2, {x, 1}]

first, and keeping in mind that the symbol f is defined (or Clear[]ing 
it afterwards).  This is potentially convenient when f would really be a 
one-time use function.

Szabolcs

P.S. Personally I am not convinced that When[] is necessary, but I felt 
the need to clarify since most responders seem to have missed the point 
of the suggestion.

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Re: Do we need a When function? Itai Seggev <itais@wolfram.com> - 2014-03-10 08:37 +0000
  Re: Do we need a When function? Szabolcs Horvát <szhorvat@gmail.com> - 2014-03-11 07:17 +0000
  Re: Do we need a When function? David Bailey <dave@removedbailey.co.uk> - 2014-03-13 07:11 +0000

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