Examples of associativity

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These laws follow directly from the commutativity and associativity of the union operator for bags.
We impose right associativity so that words have a unique type representation.
We did not consider rewriting modulo some equational theories such as associativity and commutativity.
In the world of strings this has a rough analogue in the associativity of concatenation, which does not hold for graph construction.
This statement follows from the associativity of substitution.
The associativity of signature morphisms follows directly from their set-theoretic definition.
To avoid further ambiguity, operators with the same precedence must have the same associativity.
All these observations also hold for rewriting modulo associativity and commutativity.
The unit laws allow some parsers to be simplified, and the associativity law allows parentheses to be eliminated in repeated sequencings.
Parentheses are only added where needed, ignoring associativity.
Connectives of the same polarity therefore associate, which, depending on the situation, may mean commutativity, associativity, neutrality, distributivity.
Note that in the parser implementation we are explicit about precedence and associativity of the operators; information which is not explicit in the grammar.
To resolve ambiguity, each operator is typically assigned a precedence and an associativity.
For several pre-defined operators which exhibit properties like associativity, commutativity and distributivity, the symbolic evaluator includes normalisation rules.
Exponentiation lacks the property of associativity, which we used for rewriting nested additions and multiplications.
This simpler notion also gives a direction to start out from in the above exercise for associativity of sequence.

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