How to abort evaluation of a sequence of inputs?

Question

By default pressing Alt+. or calling Abort[] within the evaluation causes abort of the currently evaluating input. But when working in the FrontEnd we usually send to the kernel a sequence of inputs. For example, if we type the following three expressions on separate lines in one Cell and then press Shift+Enter we get infinite evaluation:

f := CheckAbort[Pause[.1], Abort[]]
While[True, f]
While[True, f]
While[True, f]

To stop this infinite evaluation we must to press Alt+. three times.

How to define the function f in the example above in such a way that pressing Alt+. one time will abort the evaluation of the full sequence of inputs without quitting the kernel?

EDIT

I think that if the FrontEnd creates an input queue for MathKernel it probably can also cancel this queue.

Answer 1

Sasha's suggestion to just use four cells is valid, because that's basically what the FrontEnd does anyway, submitting several distinct evaluations to the Kernel. If you insist in using one cell, wrap it in parens (CompoundExpression), which causes those four lines to be treated as one evaluation (note the need for ; too):

(
   f := CheckAbort[Pause[.1], Abort[]];
   While[True, f];
   While[True, f];
   While[True, f]
)

Then, one abort issued will abort the evaluation as a whole.