The precedence rules are designed to make formula
manipulation easier by reducing the need for parentheses in many circumstances.
There are other reasons for some of the precedences, as well. In the table
below, we give the precedences from tightest to loosest binding, showing
also the symbols we use for the symbols in this html document. We give
also some of the arithmetic operators.
- [x:= E] (textual substitution)
- ~, - (negation or complement,
- *, /, mod, div (multiplication,
division, mod, integer division)
- +, - (addition, substraction)
- =, <, >, /=, <=, >=
(conventional relational operators. These are conjunctional.
- &, | (and, or)
- =>, <=, /=>, /<= (implication,
consequence, anti-implication, anti-consequence)
- ==, =/= (equivalence,
inequivalence --for boolean operands only)