The preceding example illustrates some rules for pattern matching:

1. Function names and structure in the pattern must be matched exactly by the input.
   • (- ?x ?y) does not match (+ a b) .

   • The pattern (+ (- ?x) ?y) does not match the input (+ a b) .

2. A variable in the pattern will match anything in the input, but it must do so consistently.
   • The pattern (- ?x ?x)
     matches (- (sin theta) (sin theta))
     but not (- (sin theta) (cos theta)) .

     We implement this by letting a variable match anything the first time, but it can only match the same thing thereafter.

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