Matching and substitution can combined to transform an input from a pattern-pair: a list of matching pattern and output pattern.

; returns transformed input or #f
(define (transform pattern-pair input)
  (let ((bindings (match? (car pattern-pair)
                          input)))
    (and bindings
         (sublis bindings (cadr pattern-pair)))))

> (match? '(- ?x ?x) '(- z z))
((?x . z))

> (match? '(- (+ ?x ?y) (+ ?z ?y))
          '(- (+ (age tom) (age mary))
              (+ (age bill) (age mary))))
((?z age bill) (?y age mary) (?x age tom))

> (transform '((- (+ ?x ?y) (+ ?z ?y))
               (- ?x ?z))
             '(- (+ (age tom) (age mary))
                 (+ (age bill) (age mary))))
(- (age tom) (age bill))

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