Associative operators x*(y*z) == (x*y)*z .

Binary operators, such as x+y, x>y

Commutative operators x*y = y*x.

composite operators, like a-b which is a+(-b)

Equivalence relations = reflexive, transitive and symmetric.

Flags for type of operator

Left binding like +: 1+2+3 -> (1+2)+3

Trinary ops such as ?: and or higher like [x,y,z,w]

No arguments to operator

Non standard operators, like array access. These will typically require the PrintRulesI interface to print and require special parsing options.

prefix operators -x

Reflective relations x=x for all x.

Right binding like =: 1=2=3 -> 1=(2=3)

self inverse operators like -(-x) !(!x)

postfix operators x%

Symmetric relation x=y implies y=x.

three argument operators like java's cond?tval:fval

Transitive relations x=y and y=z implies x=z

Unary operators, such as -x !x ~x

For non commutative operators printing can be determined by the left or right binding. For example (a-b)-c is printed as a-b-c (flag set). But a/b/c could be ambiguous so (a/b)/c is printed with brackets (flag not set).