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RE: Help: Why no output?

• To: mathgroup at smc.vnet.net
• Subject: [mg34948] RE: [mg34941] Help: Why no output?
• From: "Wolf, Hartmut" <Hartmut.Wolf at t-systems.com>
• Date: Sat, 15 Jun 2002 02:27:30 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

> -----Original Message-----
> From: kzhang at flashmail.com [mailto:kzhang at flashmail.com]
To: mathgroup at smc.vnet.net
> Sent: Friday, June 14, 2002 8:39 AM
> Subject: [mg34948] [mg34941] Help: Why no output?
> 
> 
> The behavior of the following function is puzzling to me:
> 
> In[1]:=f[x_, n___Integer] := If[Length[{n}] == 1, n  , Length[x]]
> In[2]:=f[0.5]  (* Nothing returned. *)
> In[3]:=f[{1,2}] (* Nothing returned. The length of x should be
> returned *)
> (* However, with the modification to f, everything works as intended
> *)
> In[4]:=f[x_, n___Integer] := If[Length[{n}] == 1, 1*n  , Length[x]]
>                                                  ^^^^^^
> In[5]:=f[0.5]
> Out[5]:=0
> In[6]:=f[{1,2}]
> Out[6]:=2         
> 
> Could anyone help me understand why changing n to (1*n) in the If[]
> statement makes such difference? Why doesn't f[] defined in the In[1]
> work?
> 
> Thanks for your help.
> 
> Kezhao Zhang
>

Kezhao,

to resolve the puzzle we have to follow the evaluation sequence of e.g.
f[0.5] (or equally well f[{1,2}], both cases are quite the same). So the
decisive question is: what is the value of n___, when n is not given?

...




..well Pattern[n, BlankNullSequence[Integer]] just matches to the null
sequence!

...now we have to ask what happens to the right side of the transformation
rule?
That's simple, just replace n by nothing

f[0.5] --> If[Length[{}]==1, Length[0.5]]

n just has disappeared from the expression! The condition becomes False, but
the else-case is no more present, so Null is returned. That is the value of
f[0.5], but that is not printed.


This is much the same as

Unevaluated[If[Length[{n}]==1, n, Length[x]]] /. n -> Sequence[]

If you now consider that

In[7]:= 1*Sequence[]
Out[7]= 1

then you'll find the answer to your second question.

--
Hartmut