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#lang sicp
(#%require (only racket/base print-as-expression print-mpair-curly-braces))
(print-as-expression #f)
(print-mpair-curly-braces #f)
;; Chapter 4
;; Metalinguistic Abstraction
;; 4.3
;; Variations on a Scheme -- Nondeterministic Computing
;; Amb and Search
#| (define (prime-sum-pair list1 list2) |#
#| (let |#
#| ((a (an-element-of list1)) |#
#| (b (an-element-of list2))) |#
#| (require (prime? (+ a b))) |#
#| (list a b))) |#
#| (define (require p) |#
#| (if (not p) (amb))) |#
#| (define (an-element-of items) |#
#| (require (not (null? items))) |#
#| (amb (car items) (an-element-of (cdr items)))) |#
#| (define (an-integer-starting-from n) |#
#| (amb n (an-integer-starting-from (+ n 1)))) |#
#| 4.35 |#
#| (define (an-integer-between low high) |#
#| (require (<= low high)) |#
#| (amb low (an-integer-between (+ low 1) high)) |#
#| (define (a-pythagorean-triple-between low high) |#
#| (let ((i (an-integer-between low high))) |#
#| (let ((j (an-integer-between i high))) |#
#| (let ((k (an-integer-between j high))) |#
#| (require (= (+ (* i i) (* j j)) (* k k))) |#
#| (list i j k))))) |#
#| 4.36 |#
#| (define (a-pythagorean-triple-bad) |#
#| (let ((i (an-integer-starting-from 1))) |#
#| (let ((j (an-integer-starting-from i))) |#
#| (let ((k (an-integer-starting-from j))) |#
#| (require (= (+ (* i i) (* j j)) (* k k))) |#
#| (list i j k))))) |#
;; there is not a valid k for every value of i j
;; the procedure would get stuck trying new values
;; of k forever
#| (define (a-pythagorean-triple) |#
#| (let ((i (an-integer-starting-from 1))) |#
#| (let ((j (an-integer-starting-from i))) |#
#| (let ((k (an-integer-between j (+ i j)))) |#
#| (require (= (+ (* i i) (* j j)) (* k k))) |#
#| (list i j k))))) |#
#| 4.37 |#
#| (define (a-pythagorean-triple-between low high) |#
#| (let |#
#| ((i (an-integer-between low high)) |#
#| (hsq (* high high))) |#
#| (let ((j (an-integer-between i high))) |#
#| (let ((ksq (+ (* i i) (* j j)))) |#
#| (require (>= hsq ksq)) |#
#| (let ((k (sqrt ksq))) |#
#| (require (integer? k)) |#
#| (list i j k)))))) |#
;; this version explores fewer possibilities
;; Examples of Nondeterministic Programs
(define (distinct? items)
(cond
((null? items) true)
((null? (cdr items) true))
((member (car items) (cdr items)) false)
(else (distinct? (cdr items)))))
#| (define (multiple-dwelling) |#
#| (let |#
#| ((baker (amb 1 2 3 4 5)) |#
#| (cooper (amb 1 2 3 4 5)) |#
#| (fletcher (amb 1 2 3 4 5)) |#
#| (miller (amb 1 2 3 4 5)) |#
#| (smith (amb 1 2 3 4 5))) |#
#| (require |#
#| (distinct? (list baker cooper fletcher miller smith))) |#
#| (require (not (= baker 5))) |#
#| (require (not (= cooper 1))) |#
#| (require (not (= fletcher 5))) |#
#| (require (not (= fletcher 1))) |#
#| (require (< miller cooper)) |#
#| (require (not (= (abs (- smith fletcher)) 1))) |#
#| (require (not (= (abs (- fletcher cooper)) 1))) |#
#| (list |#
#| (list 'baker baker) |#
#| (list 'cooper cooper) |#
#| (list 'fletcher fletcher) |#
#| (list 'miller miller) |#
#| (list 'smith smith)))) |#
#| 4.38 |#
#| (define (multiple-dwelling-mod) |#
#| (let |#
#| ((baker (amb 1 2 3 4 5)) |#
#| (cooper (amb 1 2 3 4 5)) |#
#| (fletcher (amb 1 2 3 4 5)) |#
#| (miller (amb 1 2 3 4 5)) |#
#| (smith (amb 1 2 3 4 5))) |#
#| (require |#
#| (distinct? (list baker cooper fletcher miller smith))) |#
#| (require (not (= baker 5))) |#
#| (require (not (= cooper 1))) |#
#| (require (not (= fletcher 5))) |#
#| (require (not (= fletcher 1))) |#
#| (require (< miller cooper)) |#
#| (require (not (= (abs (- fletcher cooper)) 1))) |#
#| (list |#
#| (list 'baker baker) |#
#| (list 'cooper cooper) |#
#| (list 'fletcher fletcher) |#
#| (list 'miller miller) |#
#| (list 'smith smith)))) |#
#| 4.39 |#
#| (define (multiple-dwelling-reorder) |#
#| (let |#
#| ((baker (amb 1 2 3 4 5)) |#
#| (cooper (amb 1 2 3 4 5)) |#
#| (fletcher (amb 1 2 3 4 5)) |#
#| (miller (amb 1 2 3 4 5)) |#
#| (smith (amb 1 2 3 4 5))) |#
#| (require (< miller cooper)) |#
#| (require (not (= (abs (- smith fletcher)) 1))) |#
#| (require (not (= (abs (- fletcher cooper)) 1))) |#
#| (require |#
#| (distinct? (list baker cooper fletcher miller smith))) |#
#| (require (not (= baker 5))) |#
#| (require (not (= cooper 1))) |#
#| (require (not (= fletcher 5))) |#
#| (require (not (= fletcher 1))) |#
#| (list |#
#| (list 'baker baker) |#
#| (list 'cooper cooper) |#
#| (list 'fletcher fletcher) |#
#| (list 'miller miller) |#
#| (list 'smith smith)))) |#
#| 4.40 |#
#| (define (multiple-dwelling-quick) |#
#| (let |#
#| ((baker (amb 1 2 3 4 5))) |#
#| (require (not (= baker 5))) |#
#| (let ((cooper (amb 1 2 3 4 5))) |#
#| (require (not (= cooper 1))) |#
#| (require (not (= cooper baker))) |#
#| (let ((fletcher (amb 1 2 3 4 5))) |#
#| (require (not (= (abs (- fletcher cooper)) 1))) |#
#| (require (not (= fletcher 1))) |#
#| (require (not (= fletcher 5))) |#
#| (require (not (= fletcher baker))) |#
#| (require (not (= fletcher cooper))) |#
#| (let ((miller (amb 1 2 3 4 5))) |#
#| (require (< miller cooper)) |#
#| (require (not (= miller baker))) |#
#| (require (not (= miller cooper))) |#
#| (require (not (= miller fletcher))) |#
#| (let ((smith (amb 1 2 3 4 5))) |#
#| (require (not (= (abs (- smith fletcher)) 1))) |#
#| (require (not (= smith baker))) |#
#| (require (not (= smith cooper))) |#
#| (require (not (= smith fletcher))) |#
#| (require (not (= smith miller))) |#
#| (list |#
#| (list 'baker baker) |#
#| (list 'cooper cooper) |#
#| (list 'fletcher fletcher) |#
#| (list 'miller miller) |#
#| (list 'smith smith)))))))) |#
#| 4.41 |#
(define (with-next value prev proc)
(if (null? value)
(prev)
(proc (car value) (cdr value))))
(define (require test this next)
(lambda (x value)
(if (not (test x))
(this value)
(next x value))))
(#%provide multiple-dwelling-scheme)
(define (multiple-dwelling-scheme)
(define (fail) (error "No solution"))
(define (bakerfunc bakers)
(with-next bakers fail
(require (lambda (b) (not (= b 5))) bakerfunc
(lambda (baker bakers)
(define (cooperfunc coopers)
(with-next coopers (lambda () bakerfunc bakers)
(require (lambda (c) (not (= c 1))) cooperfunc
(require (lambda (c) (not (= c baker))) cooperfunc
(lambda (cooper coopers)
(define (fletcherfunc fletchers)
(with-next fletchers (lambda () (cooperfunc coopers))
(require (lambda (f) (not (= (abs (- f cooper)) 1))) fletcherfunc
(require (lambda (f) (not (= f 1))) fletcherfunc
(require (lambda (f) (not (= f 5))) fletcherfunc
(require (lambda (f) (not (= f baker))) fletcherfunc
(require (lambda (f) (not (= f cooper))) fletcherfunc
(lambda (fletcher fletchers)
(define (millerfunc millers)
(with-next millers (lambda () (fletcherfunc fletchers))
(require (lambda (m) (< m cooper)) millerfunc
(require (lambda (m) (not (= m baker))) millerfunc
(require (lambda (m) (not (= m cooper))) millerfunc
(require (lambda (m) (not (= m fletcher))) millerfunc
(lambda (miller millers)
(define (smithfunc smiths)
(with-next smiths (lambda () (millerfunc millers))
(require (lambda (s) (not (= (abs (- s fletcher)) 1))) smithfunc
(require (lambda (s) (not (= s baker))) smithfunc
(require (lambda (s) (not (= s cooper))) smithfunc
(require (lambda (s) (not (= s fletcher))) smithfunc
(require (lambda (s) (not (= s miller))) smithfunc
(lambda (smith smiths)
(list
(list 'baker baker bakers)
(list 'cooper cooper coopers)
(list 'fletcher fletcher fletchers)
(list 'miller miller millers)
(list 'smith smith smiths))))))))))
(smithfunc (list 1 2 3 4 5)))))))))
(millerfunc (list 1 2 3 4 5))))))))))
(fletcherfunc (list 1 2 3 4 5)))))))
(cooperfunc (list 1 2 3 4 5))))))
(bakerfunc (list 1 2 3 4 5)))
#| 4.42 |#
#| 4.43 |#
#| 4.44 |#
#| 4.45 |#
#| 4.46 |#
#| 4.47 |#
#| 4.48 |#
#| 4.49 |#
;; Implementing the Amb Evaluator
#| 4.50 |#
#| 4.51 |#
#| 4.52 |#
#| 4.53 |#
#| 4.54 |#
|
