lhs -> rhs or lhs rhs represents a rule that transforms lhs to rhs.
The character can be entered as -> or \[Rule].
lhs -> rhs evaluates rhs immediately.
You can apply rules using Replace.
The assignment lhs = rhs specifies that the rule lhs -> rhs should be used whenever it applies.
lhs rhs can be entered as lhs \[Rule] rhs or lhs -> rhs.
In StandardForm, Rule is printed using .
Rule is a scoping construct (see Section A.3.8).
Symbols that occur as pattern names in lhs are treated as local to the rule. This is true when the symbols appear on the right-hand side of /; conditions in lhs, and when the symbols appear anywhere in rhs, even inside other scoping constructs.
See The Mathematica Book: Section 2.4.1 and Section A.5.5.
Implementation Notes: see section A.9.3.
See also: Replace, Set, RuleDelayed, PolynomialReduce.
Related package: Utilities`FilterOptions`.