Boolean Logic

TeXpr supports set of boolean algebra operators, allowing for logical comparisons, conditions, and bitwise-like logic within expressions.

Comparison Operators

These operators compare two values and always produce a boolean result (True/False).

Strict Type Safety

In a Numeric Context (e.g. 1 + (x > 0)), utilizing a boolean result will throw an error. Unlike some languages that implicitly convert true to 1.0, TeXpr enforces strict separation between numbers and booleans to prevent logical ambiguities.

Operator	Syntax	Alias	Description
Greater Than	>		Returns true if left > right.
Less Than	<		Returns true if left < right.
Greater/Equal	\ge	\geq	Returns true if left ≥ right.
Less/Equal	\le	\leq	Returns true if left ≤ right.
Equal	=	==	Returns true if values are equal.
Not Equal	\ne	\neq	Returns true if values are not equal.

Examples

x > 0        % True if x is positive
\pi \ge 3.14 % True
2 * x = y    % True if equation holds

Boolean Operators

Combine boolean comparisons using standard logical connectives.

Operator	Syntax	Alias	Description
AND	\land	\wedge, &	True if both operands are true.
OR	\lor	\vee, |	True if either operand is true.
NOT	\neg	\lnot, !	Inverts the truth value.
XOR	\oplus		True if exactly one operand is true.
Implication	\Rightarrow	\implies	True unless Left is true and Right is false.
Biconditional	\Leftrightarrow	\iff	True if both operands have the same value.

Logic Examples

% Range check
(x > 0) \land (x < 10)   % True if x is between 0 and 10

% Complex condition
(x = 0) \lor (y = 0)     % True if either x or y is zero

% De Morgan's Law
\neg(A \land B) \iff (\neg A \lor \neg B)  % Always True

Precedence

Operators are evaluated in the order below. Precedence matters for usage without parentheses:

x > 0 \land y < 10
% Parsed as: (x > 0) \land (y < 10) -> Correct

1. Groups: (...)
2. Arithmetic: ^, *, /, +, -
3. Comparisons: >, <, =, etc.
4. NOT: \neg
5. AND: \land
6. XOR: \oplus
7. OR: \lor
8. Implication: \Rightarrow
9. Biconditional: \Leftrightarrow

Type Behavior

• Numeric Context: Booleans cannot be used directly in arithmetic. 1 + true throws an EvaluatorException.
• Boolean Context: Comparison results are preserved as boolean types and can be used in logical operations (\land, \lor).

See Also

• Piecewise Functions - Using logic for conditional function definitions.