forall

expression forall iterator

The given expression is evaluated for all the values taken on by the given iterator. If all the evaluations result in True, the overall expression results in True. If one or more evaluations result in False the overall expression results in False. For example:

  (even(i) forall i in {2 4 6 8}) = True
  (even(i) forall i in {2..4}) = False

Note that the name space of the iterator contains the given expression. In other words, the following are equivalent:

  b := even(i) forall i in S

and

  b := True
  for i in S
    b := b and even(i)
  loop

Herman Venter

This is Slim documentation as snarfed on 27 May 1999 by dB.