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|
(load "load")
;;; Problem 6.4
(define algebra-3
(rule-simplifier
(list
;; Sums
(rule (+ (? a)) none (? a))
(rule (+ (?? a) (+ (?? b)))
none
(+ (?? a) (?? b)))
(rule (+ (+ (?? a)) (?? b))
none
(+ (?? a) (?? b)))
(rule (+ (?? a) (? y) (? x) (?? b))
(expr<? x y)
(+ (?? a) (? x) (? y) (?? b)))
;; Products
(rule (* (? a)) none (? a))
(rule (* (?? a) (* (?? b)))
none
(* (?? a) (?? b)))
(rule (* (* (?? a)) (?? b))
none
(* (?? a) (?? b)))
(rule (* (?? a) (? y) (? x) (?? b))
(expr<? x y)
(* (?? a) (? x) (? y) (?? b)))
;; Distributive law
(rule (* (? a) (+ (?? b)))
none
(+ (?? (map (lambda (x) `(* ,a ,x)) b))))
;; Numerical simplifications below
(rule (+ 0 (?? x)) none (+ (?? x)))
(rule (+ (? x number?) (? y number?) (?? z))
none
(+ (? (+ x y)) (?? z)))
(rule (* 0 (?? x)) none 0)
(rule (* 1 (?? x)) none (* (?? x)))
(rule (* (? x number?) (? y number?) (?? z))
none
(* (? (* x y)) (?? z)))
;; Collect terms
(rule (+ (?? s) (? x) (? x) (?? e))
none
(+ (?? s) (* 2 (? x)) (?? e)))
(rule (+ (?? s) (* (?? x)) (* (?? x)) (?? e))
none
(+ (?? s) (* 2 (?? x)) (?? e)))
(rule (+ (?? s) (? x) (?? m) (* (? n number?) (? x)) (?? e))
none
(+ (?? s) (?? m) (* (? (+ 1 n)) (? x)) (?? e)))
(rule (+ (?? s) (* (? n number?) (?? x)) (* (? p number?) (?? x)) (?? e))
none
(+ (?? s) (* (? (+ n p)) (? x)) (?? e)))
)))
#| Test!
(algebra-3 '(+ x (* 4 x)))
;Value 15: (* 5 x)
(algebra-3 '(+ (* 8 1 f 34) (* 3 f)))
;Value 16: (* 275 x)
(algebra-3 '(+ x x))
;Value 42: (* 2 x)
(algebra-3 '(+ 4 s u s p))
;Value 39: (+ 4 p u (* 2 s))
(algebra-3 '(+ 1 2))
;Value: 3
(algebra-3 '(+ (* -2 h) (* 2 h)))
;Value: 0
(algebra-3 '(+ h (* 4 h)))
;Value 83: (* 5 h)
(algebra-3 '(+ (* w h) (* 4 h)))
;Value 84: (+ (* 4 h) (* h w))
(algebra-3 '(+ (* -1 h) (* 2 h)))
;Value 85: (h)
(algebra-3 '(+ x (* a x)))
;Value 86: (+ x (* a x))
(algebra-3 '(+ y (* x -2 w) (* x 4 y) (* w x) z (* 5 z) (* x w) (* x y 3)))
;Value 87: (+ y (* 6 z) (* 7 (x y)))
|#
;;; Problem 6.5
|
