We have emphasized the use of design patterns in writing programs. We would like to use patterns automatically to generate, improve, or transform programs, equations, and other tree-like data structures.

We will use rewrite rules, each consisting of an input pattern and an output pattern.

• Input Pattern: (- (- ?x ?y))
• Output Pattern: (- ?y ?x)
• Rewrite Rule: ( (- (- ?x ?y)) (- ?y ?x))
• Example Input: (- (- (sin theta) z))
• Bindings: ((?y z) (?x (sin theta)))
• Output: (- z (sin theta))

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