Infix Math Operators

An entry in the last column indicates that the operator is usable only in LaTeX (L) or only in Plain TeX (P).

Symbol or Macro	Meaning	Reading	Precedence	Restrictions
\c	Logical Implication	implies	2
\cond	Conditionally Existent Term	then	3
\els	Definitional Otherwise	else	3
\Iff	Logical Equivalence	if and only if	4
\And	Logical Conjunction	and	5
\Or	Logical Disjunction	or	5
\ident	Identity	is identical to	6
=	Equality	equals	6
\in	Elementhood	belongs to	6
\i	Inclusion	subset of	6	P
\subset	Inclusion	subset of	6	L
‹	Inequality	less than	6
›	Inequality	greater than	6
\le	Inequality	less than or equal to	6
\ge	Inequality	greater than or equal to	6
\ne	Inequality	not equal to	6
\i \ne	Proper Inclusion	proper subset of	6	P
\subset\ne	Proper Inclusion	proper subset of	6	L
\notin	Non-membership	not an element of	6
\djn	Disjointness	does not intersect with	6
\orders	Order Relation	orders	6
,	Tuple Operator	comma	6
+	Addition	plus	9
-	Subtraction	minus	9
\cdot	Multiplication	times	13
\cap	Set Intersectionintersect	15
\cup	Set Unionunion	15
\dsj	Disjoint Union	disjoint union	15
\cmp	Functional Composition	composed with	15
\lilx	Cartesian Product	cross	15
\symdif	Symmetric Difference symmetric difference	17
\setdif	Set Difference	minus	17
\toThe	Exponentiation	to the power	17

These operators may of course be combined to form complex expressions but they must however be used within at least one pair of parentheses.

One apparent omission from this table is mention of left vs. right associativity. The parser however does not automatically group repeated operations to the left or to the right. Repeated operations are in general left to the user to define. In the case of operations tagged as having both the associative and commutative properties however the parser removes extra parentheses and the unifier attempts to match operands irrespective of where they occur in the sequence of operands. At present conjunction is tagged in this way by the prep program and no other operators are so tagged. In time more operators will be tagged by default and more properties will be built-in, but at this stage it is helpful to keep assumptions minimal in order to better understand the behavior of the system.

Another apparent omission from the table is functional evaluation. This is omitted partly because including it would usurp adjacent-writing which is the prime location on the parse tree, partly because with outer parentheses (f(x)) is cumbersome, and partly because the non-parenthetical Morse notation using an initial dot very works well.