Sequence and boolean And

Question

I'm trying to figure out if a calculation result it's a valid result. As it return a matrix, I need to test that every element it's a number, so I thought this could work...

numericTable = Range[12] ~Partition ~ 4;
check=( NumberQ/@Flatten@numericTable) /.List->Sequence ;
And[check]

This should return True or False depending if exist or not a non-numerical element in the matrix. But it returns

Sequence[True,True,True,True,True,True,True,True,True,True,True,True]

So I don't understand anything, because...

In[]:= Sequence[True,True,True,True,True,True,True,True,True,True,True,True]===check
And[Sequence[True,True,True,True,True,True,True,True,True,True,True,True]]
Out[]= True
Out[]= True

Where's the catch ???

Answer 1

As in the comments above, we see that the HoldAll attribute is causing the "problem".

Note that if we unset HoldAll it works:

Unprotect@And;
ClearAttributes[And, HoldAll];
Protect@And;

Then:

And[check]

True

EDIT: based on Oleksandr R.'s comment, I must stress that I showed this only to illustrate the "problem". It is not a good idea to unset HoldAll for And, as noted below in his comment. So as in my comment to the question above, you can just use Evaluate to get the result:

And[Evaluate@check]

to get to the same result.

(END EDIT)

You could directly apply And on what you constructed:

And @@ (NumberQ /@ Flatten@numericTable)

but better check MrWizard's answer for a direct solution of your problem.

Answer 2

In addition to HoldAll as highlighted by Pinguin Dirk the other component of the behavior is that And directly returns single arguments:

And[73]

73

Combined, And[check] spits out check which at the top level evaluates to Sequence[True, . . .].

One problem with your method for checking the matrix is that it does not short-circuit on a non-numeric value, and therefore it may waste time. That is, NumberQ is applied to every element even if the very first one is non-numeric. A faster approach is to use the built-in MatrixQ:

MatrixQ[numericTable, NumberQ]

True