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[?] Evaluate the following function f[x__Integer]:=x[[2]]; f[{7,8}]?

Doesn't x__Integer mean that the allowed arguments for f are just the lists of integers? (The Mathematica Book says so on p. 273 sect. 2.3 .8).

Or, am I really forced to write

f[x_ /; VectorQ[x, IntegerQ]] := x[[2]]

or for in a generalizable form:

f[x_ /; VectorQ[x, (Head[#] == Integer)& ]] := x[[2]] ?

As it looks to me, it would be useful if the Documentation Center would contain a Tutorial which collects the usual idioms for argument specifications of functions including user-defined heads and default arguments.

PS: My system is Mathematica 11.1 under Windows 10. See the attached file umTest1.nb for experimentation.

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POSTED BY: Ulrich Mutze
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Neil,

Thank you very much for your perfect answer.

And, also the Mathematica Book speaks of sequences and not of lists, in accordance with your answer.

Regards,

Ulrich
POSTED BY: Ulrich Mutze

Ulrich,

Your list of integers has Head of List, not Head of Integer so your function does not match a list of integers. Your definition should look like this:

f[{x__Integer}] := {x}[[2]]

or (a bit more cryptically:

f[{x__Integer}] :=  ##2 &[x]

The reason is that you have a list of integers which you can match with 

{x__Integer}

x will take on the value of a Sequence of Integers (not a list). Since it is a sequence and not a list you can either make it a list by doing {x} and then process it. or you can treat it as a sequence (second example).

Regards,

Neil
POSTED BY: Neil Singer
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