\DOC all

\TYPE {all : ('a -> bool) -> 'a list -> bool}

\SYNOPSIS
Tests whether a predicate holds throughout a list.

\DESCRIBE
{all P [x1,...,xn]} equals {P x1 andalso .... andalso P xn}.
{all P []} yields {true}.

\FAILURE
If {P x0,...,P x(j-1)} all evaluate to {true} and {P xj} raises an
exception {e}, then {all P [x0,...,x(j-1),xj,...,xn]} raises {e}.

\EXAMPLE
{
- all (equal 3) [3,3,3];
> val it = true : bool

- all (equal 3) [];
> val it = true : bool

- all (fn _ => raise Fail "") [];
> val it = true : bool

- all (fn _ => raise Fail "") [1];
! Uncaught exception:
! Fail  ""
}


\SEEALSO
Lib.all2, Lib.exists, Lib.first.
\ENDDOC