This section deals with logical values (`Booleans').

Booleans are primarily of importance as (return) values for (intrinsic) predicates. It is important to know that the truth-value of predicates is always evaluated left to right, that is, the left-most clause is evaluated first, and if that determines the value of the predicate evaluation is aborted; if not, the next clause is evaluated, etc. So, for example, if x is a Boolean, it is safe (albeit silly) to type:

> if x eq true or x eq false or x/0 eq 1 then
>    print "fine";
> else
>    print "error";
> end if;

Subsections

• Creation of Booleans
• Boolean Operators
• Functions on Booleans
• Iteration

The Boolean structure.

false

The Boolean elements.

True if both x and y are true, false otherwise.

True if x or y is true (or both are true), false otherwise.

True if either x or y is true (but not both), false otherwise.

Negate the truth value of x.

True if both x and y are true or both x and y are false, false otherwise.

True if either x is true and y is false, or x is false and y is true, otherwise false.

True if x is a Boolean value, false otherwise.

True if x is not a Boolean value, false otherwise.

Return a random Boolean.

A Boolean structure B may be used for enumeration: for x in B do, and x in B in set and sequence constructors.

> P := Booleans();
>  for x, y in P do
>     print (x ne y) eq (x xor y);
> end for;
true
true
true
true

> equal := true;
> for x, y in P do
>     if (x eq y) and not ((x and y) or (not x and not y)) then
>         equal := false;
>     end if;
> end for;
> print equal;
true