The two **boolean** values are `true`

and `false`

. They stand for the
**logical** values of the same name. They appear mainly as values of the
conditions in `if`

-statements and `while`

-loops.

This chapter contains sections describing the operations that are available for the boolean values (see Comparisons of Booleans, Operations for Booleans).

Further this chapter contains a section about the function `IsBool`

(see
IsBool). Note that it is a convention that the name of a function that
tests a property, and returns `true`

and `false`

according to the
outcome, starts with `Is`

, as in `IsBool`

.

, `bool1` = `bool2``bool1` <> `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`

,
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 = false); true gap> true <> 17; true

, `bool1` < `bool2`

,`bool1` <= `bool2`

, `bool1` > `bool2``bool1` >= `bool2`

The operators `<`

, `<=`

, `>`

, and `=>`

evaluate to `true`

if the
boolean value `bool1` is less than, less than or equal to, greater than,
and greater than or equal to the boolean value `bool2`. The ordering of
boolean values is defined by `true < false`

.

You can compare boolean values with objects of other types. Integers, rationals, cyclotomics, permutations, and words are smaller than boolean values. Objects of the other types, i.e., functions, lists, and records are larger.

gap> true < false; true gap> false >= true; true gap> 17 < true; true gap> true < [17]; true

`bool1` 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

,
which is interpreted as `b1` or `b2` or `b3``(`

. `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 Print("aha\n"); fi;
aha # no error, because
````l[i]`

is not evaluated

`bool1` 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

, which is interpreted as `b1` and `b2` and
`b3``(`

. `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;
false # is no error, because
````17`

is never looked at

`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> not true; false gap> not false; true

`IsBool( `

`obj` )

`IsBool`

returns `true`

if `obj`, which may be an object of an arbitrary
type, is a boolean value and `false`

otherwise. `IsBool`

will signal an
error if `obj` is an unbound variable.

gap> IsBool( true ); true gap> IsBool( false ); true gap> IsBool( 17 ); false

gap3-jm

11 Mar 2019