Adds new examples

2_84.scm

@@ -0,0 +1,28 @@
+(define (level-number levels name)
+  (define levels '(integer rational real complex))
+  (if (eq? (car levels) name)
+    0
+    (+ 1 (level-number (cdr levels) name))))
+
+(define (raise-to level x)
+  (if (= level (level-number x))
+      x
+      (raise-to level (raise x))))
+
+(define (apply-generic op . args)
+  (let ((type-tags (map type-tag args)))
+    (let ((proc (get op type-tags)))
+      (if proc
+        (apply proc (map contents args))
+        (if (= (length args) 2)
+          (let* ((type1 (car type-tags))
+                (type2 (cadr type-tags))
+                (level1 (level-number type1))
+                (level2 (level-number type2))
+                (a1 (car args))
+                (a2 (cadr args)))
+            (cond ((<= level1 level2) (apply-generic op (raise-to level2 a1) a2))
+                  (else level1 level2) (apply-generic op a1 (raise-to level1 a2)))
+          (error "Method not found for provided types"
+                             (list op type-tags)))))))
+; NOT TESTED

2_87.scm

@@ -0,0 +1,10 @@
+(define (install-polynomial-package)
+  (define (zero-poly? p)
+    (define (zero-termlist? terms)
+      (or (empty-termlist? terms)
+        (and (=zero? (coeff (first-term terms)))
+             (zero-termlist? (rest-terms terms)))))
+    (zero-termlist? (term-list p)))
+  (put '=zero? '(polynomial) (lambda (p) (zero-poly? p)))
+
+(define (=zero? x) (apply-generic '=zero? x))

2_88.scm

@@ -0,0 +1,164 @@
+(define put 2d-put!)
+; 2d-get doesn't work because it uses eq?
+(define (get x-key y-key)
+  (let ((1d-table (2d-get-alist-x x-key)))
+    (let ((type-f (assoc y-key 1d-table)))
+      (if type-f (cdr type-f) false))))
+
+(define (apply-generic op . args)
+  (let ((type-tags (map type-tag args)))
+    (let ((proc (get op type-tags)))
+      (if proc
+          (apply proc (map contents args))
+          (error "No method for these types"
+                 (list op type-tags))))))
+
+(define (type-tag datum)
+  (cond ((pair? datum) (car datum))
+        ((number? datum) 'scheme-number)
+        (else (error "Bad tagged datum -- TYPE-TAG" datum))))
+(define (contents datum)
+  (cond ((pair? datum) (cdr datum))
+        ((number? datum) datum)
+        (else (error "Bad tagged datum -- CONTENTS" datum))))
+(define (attach-tag type-tag contents)
+  (if (number? contents)
+      contents
+      (cons type-tag contents)))
+
+(define (add x y) (apply-generic 'add x y))
+(define (sub x y) (apply-generic 'sub x y))
+(define (mul x y) (apply-generic 'mul x y))
+(define (div x y) (apply-generic 'div x y))
+(define (equ? x y) (apply-generic 'equ? x y))
+(define (=zero? x) (apply-generic '=zero? x))
+
+;; scheme number package
+(define (install-scheme-number-package)
+  (define (tag x)
+    (attach-tag 'scheme-number x))
+  (put 'add '(scheme-number scheme-number)
+       (lambda (x y) (tag (+ x y))))
+  (put 'sub '(scheme-number scheme-number)
+       (lambda (x y) (tag (- x y))))
+  (put 'mul '(scheme-number scheme-number)
+       (lambda (x y) (tag (* x y))))
+  (put 'div '(scheme-number scheme-number)
+       (lambda (x y) (tag (/ x y))))
+  (put 'equ? '(scheme-number scheme-number) =)
+  (put '=zero? '(scheme-number)
+       (lambda (x) (= x 0)))
+  (put 'make 'scheme-number
+       (lambda (x) (tag x)))
+  'done)
+(define (make-scheme-number n)
+  ((get 'make 'scheme-number) n))
+
+(define (install-polynomial-package)
+  ;; internal procedures
+  ;; representation of poly
+  (define (make-poly variable term-list)
+    (cons variable term-list))
+  (define (variable p) (car p))
+  (define (term-list p) (cdr p))
+  (define (variable? x) (symbol? x))
+  (define (same-variable? v1 v2)
+    (and (variable? v1) (variable? v2) (eq? v1 v2)))
+  ;; representation of terms and term lists
+  (define (adjoin-term term term-list)
+    (if (=zero? (coeff term))
+        term-list
+        (cons term term-list)))
+  (define (the-empty-termlist) '())
+  (define (first-term term-list) (car term-list))
+  (define (rest-terms term-list) (cdr term-list))
+  (define (empty-termlist? term-list) (null? term-list))
+  (define (make-term order coeff) (list order coeff))
+  (define (order term) (car term))
+  (define (coeff term) (cadr term))
+
+  (define (add-poly p1 p2)
+    (if (same-variable? (variable p1) (variable p2))
+        (make-poly (variable p1)
+                   (add-terms (term-list p1)
+                              (term-list p2)))
+        (error "Polys not in same var -- ADD-POLY"
+               (list p1 p2))))
+  (define (add-terms L1 L2)
+    (cond ((empty-termlist? L1) L2)
+          ((empty-termlist? L2) L1)
+          (else
+           (let ((t1 (first-term L1)) (t2 (first-term L2)))
+             (cond ((> (order t1) (order t2))
+                    (adjoin-term
+                     t1 (add-terms (rest-terms L1) L2)))
+                   ((< (order t1) (order t2))
+                    (adjoin-term
+                     t2 (add-terms L1 (rest-terms L2))))
+                   (else
+                    (adjoin-term
+                     (make-term (order t1)
+                                (add (coeff t1) (coeff t2)))
+                     (add-terms (rest-terms L1)
+                                (rest-terms L2)))))))))
+  (define (sub-poly p1 p2)
+    (if (same-variable? (variable p1) (variable p2))
+        (make-poly (variable p1)
+                   (add-terms (term-list p1)
+                              (negate-terms (term-list p2))))
+        (error "Polys not in same var -- SUB-POLY"
+               (list p1 p2))))
+  (define (negate-terms terms)
+    (if (empty-termlist? terms)
+      '()
+      (let ((first (first-term terms)))
+        (adjoin-term (make-term (order first) (- (coeff first)))
+                     (negate-terms (rest-terms terms))))))
+  (define (mul-poly p1 p2)
+    (if (same-variable? (variable p1) (variable p2))
+        (make-poly (variable p1)
+                   (mul-terms (term-list p1)
+                              (term-list p2)))
+        (error "Polys not in same var -- MUL-POLY"
+               (list p1 p2))))
+  (define (mul-terms L1 L2)
+    (if (empty-termlist? L1)
+        (the-empty-termlist)
+        (add-terms (mul-term-by-all-terms (first-term L1) L2)
+                   (mul-terms (rest-terms L1) L2))))
+  (define (mul-term-by-all-terms t1 L)
+    (if (empty-termlist? L)
+        (the-empty-termlist)
+        (let ((t2 (first-term L)))
+          (adjoin-term
+           (make-term (+ (order t1) (order t2))
+                      (mul (coeff t1) (coeff t2)))
+           (mul-term-by-all-terms t1 (rest-terms L))))))
+  ;; interface to rest of the system
+  (define (tag p) (attach-tag 'polynomial p))
+  (put 'add '(polynomial polynomial)
+       (lambda (p1 p2) (tag (add-poly p1 p2))))
+  (put 'sub '(polynomial polynomial)
+       (lambda (p1 p2) (tag (sub-poly p1 p2))))
+  (put 'mul '(polynomial polynomial)
+       (lambda (p1 p2) (tag (mul-poly p1 p2))))
+  (define (zero-poly? p)
+    (define (zero-termlist? terms)
+      (or (empty-termlist? terms)
+        (and (=zero? (coeff (first-term terms)))
+             (zero-termlist? (rest-terms terms)))))
+    (zero-termlist? (term-list p)))
+  (put '=zero? '(polynomial) (lambda (p) (zero-poly? p)))
+  (put 'make 'polynomial
+       (lambda (var terms) (tag (make-poly var terms))))
+  'done)
+
+(define (make-polynomial var terms)
+  ((get 'make 'polynomial) var terms))
+
+; tests
+(install-scheme-number-package)
+(install-polynomial-package)
+
+(sub (make-polynomial 'x '((3 1) (2 2) (1 3) (0 1))) (make-polynomial 'x '((2 3) (1 2) (0 1))))
+