Precedence rules

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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.

  1. [x:= E] (textual substitution)
  2. ~, - (negation or complement, unary minus)
  3. *, /, mod, div (multiplication, division, mod, integer division)
  4. +, - (addition, substraction)
  5. =, <, >, /=, <=, >= (conventional relational operators. These are conjunctional.
  6. &, | (and, or)
  7. =>, <=, /=>, /<= (implication, consequence, anti-implication, anti-consequence)
  8. ==, =/= (equivalence, inequivalence --for boolean operands only)