NAME

contextBoolean.pl - Implements a MathObject class for Boolean expressions

DESCRIPTION

Load this file:

loadMacros('contextBoolean.pl');

and then select the context:

Context('Boolean');

CONSTANTS

This constant recognizes two constants by default, T and F. The following are all equivalent:

$T = Compute('1');
$T = Boolean('T');
$T = Context()->T;
$T = context::Boolean->T;

VARIABLES

By default, this context has two variables, p and q. More variables can be added through the usual means of modifying context:

Context->variables->add( r => 'Boolean' );

OPERATORS

Changing the LaTeX representations of the boolean operators is handled through the operators or, and, xor, and not. Note the extra space following the LaTeX command.

Context->operators->set( not => { TeX => '\neg ' } );

Aliases and Alternatives

Modifications to the operators should be applied to the string versions of each operator: 'or', 'xor', 'and', and 'not'; rather than to any of the following aliases or alternatives.

OR

The 'or' operator is indicated by or, +, \\/, wedge, or unicode x{2228}.

AND

The 'and' operator is indicated by and, *, whitespace (as with implicit multiplication), /\\, vee, or unicode x{2227}.

XOR

The 'xor' operator is indicated by xor, \\<>, oplus, or unicodes x{22BB}, x{2295}.

NOT

The 'not' operator is indicated by not, -, !, ~, or unicodes x{00AC}, x{223C}.

A right-associative version of the 'not' operator is also available by using ' or ` following the expression to be negated.

OPERATOR PRECEDENCE

setPrecedence

This context supports two paradigms for operation precedence: equal (default) and oxan.

The default setting, equal, gives all boolean operations the same priority, meaning that parenthesis are the only manner by which an expression will evaluate operations to the right before those to the left.

$a = Compute("T or T and F"); # $a == F

The oxan setting priortizes or < xor < and < not.

Context()->setPrecedence('oxan');
$b = Compute("T or T and F"); # $b == T

REDUCTION

The context also handles reduceConstants with the following reduction rules:

'x||1'

$f = Formula('p or T')->reduce; # $f == T

'x||0'

$f = Formula('p or F')->reduce; # $f == Formula('p')

'x&&1'

$f = Formula('p and T')->reduce; # $f == Formula('p')

'x&&0'

$f = Formula('p and F')->reduce; # $f == F

'!!x'

$f = Formula('not not p')->reduce; # $f == Formula('p');

COMPARISON

Boolean Formula objects are considered equal whenever the two expressions generate the same truth table.

$f = Formula('not (p or q)');
$g = Formula('(not p) and (not q)');
# $f == $g is true