The two main boolean values are true and false.
They stand for the logical values of the same name.
They appear as values of the conditions in if-statements
and while-loops.
Booleans are also important as return values of filters (see Filters)
such as IsFinite and IsBool.
Note that it is a convention that the name of a function that
returns true or false according to the outcome, starts with Is.
For technical reasons, also the value fail (see Fail)
is regarded as a boolean.
IsBool( obj ) C
tests whether obj is true, false or fail.
gap> IsBool( true ); IsBool( false ); IsBool( 17 ); true true false
fail V
The value fail is used to indicate situations when an operation could
not be performed for the given arguments, either because of shortcomings of
the arguments or because of restrictions in the implementation or
computability. So for example Position (see Position) will return fail
if the point searched for is not in the list.
fail is simply an object that is different from every other object than
itself.
For technical reasons, fail is a boolean value.
But note that fail cannot be used to form boolean expressions with
and, or, and not (see Operations for Booleans below),
and fail cannot appear in boolean lists (see Chapter Boolean Lists).
= bool2 <> bool2
The equality operator = evaluates to true if the two boolean values
bool1 and bool2 are equal, i.e., both are true or both are false or
both fail, and false otherwise. The inequality operator <> evaluates
to true if the two boolean values bool1 and bool2 are different and
false otherwise. This operation is also called the exclusive or, because
its value is true if exactly one of bool1 or bool2 is true.
You can compare boolean values with objects of other types. Of course they are never equal.
gap> true = false; false gap> false = (true = fail); true gap> true <> 17; true
< bool2
The ordering of boolean values is defined by true < false < fail.
For the comparison of booleans with other GAP objects,
see Section Comparisons.
gap> true < false; fail >= false; true true
The following boolean operations are only applicable to true and false.
or bool2
The logical operator or evaluates to true if at least one of the two
boolean operands bool1 and bool2 is true and to false otherwise.
or first evaluates bool1. If the value is neither true nor false
an error is signalled. If the value is true, then or returns true
without evaluating bool2. If the value is false, then or
evaluates bool2. Again, if the value is neither true nor false an
error is signalled. Otherwise or returns the value of bool2. This
short-circuited evaluation is important if the value of bool1 is
true and evaluation of bool2 would take much time or cause an error.
or is associative, i.e., it is allowed to write b1 or b2 or b3,
which is interpreted as (b1 or b2) or b3. or has the lowest
precedence of the logical operators. All logical operators have lower
precedence than the comparison operators =, <, in, etc.
gap> true or false;
true
gap> false or false;
false
gap> i := -1;; l := [1,2,3];;
gap> if i <= 0 or l[i] = false then # this does not cause an error,
> Print("aha\n"); fi; # because `l[i]' is not evaluated
aha
and bool2
The logical operator and evaluates to true if both boolean operands
bool1 and bool2 are true and to false otherwise.
and first evaluates bool1. If the value is neither true nor
false an error is signalled. If the value is false, then and
returns false without evaluating bool2. If the value is true,
then and evaluates bool2. Again, if the value is neither true nor
false an error is signalled. Otherwise and returns the value of
bool2. This short-circuited evaluation is important if the value of
bool1 is false and evaluation of bool2 would take much time or
cause an error.
and is associative, i.e., it is allowed to write b1 and b2 and
b3, which is interpreted as (b1 and b2) and b3. and has
higher precedence than the logical or operator, but lower than the
unary logical not operator. All logical operators have lower
precedence than the comparison operators =, <, in, etc.
gap> true and false; false gap> true and true; true gap> false and 17; # this does not cause an error, because `17' is never looked at false
and fil2
and can also be applied to filters. It returns a filter that when applied
to some argument x, tests fil1(x) and fil2(x).
gap> andfilt:= IsPosRat and IsInt;; gap> andfilt( 17 ); andfilt( 1/2 ); true false
not bool
The logical operator not returns true if the boolean value bool is
false and true otherwise. An error is signalled if bool does not
evaluate to true or false.
not has higher precedence than the other logical operators, or and
and. All logical operators have lower precedence than the comparison
operators =, <, in, etc.
gap> true and false; false gap> not true; false gap> not false; true
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GAP 4 manual
March 2006