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- #lang planet neil/sicp
- ;; Ex 2.83
- ;;
- ;; NB These procedures won't work because apply-generic is still the
- ;; version that uses generalised coercion which hasn't been implemented.
- ;; This version is using a raise strategy.
- (define (apply-generic op . args)
- (define (all-coercable? coerce-procs)
- (not (member #f coerce-procs)))
- (define (coerce-args coercion-procs args)
- (map (lambda (coerce-proc arg)
- (coerce-proc arg))
- coercion-procs
- args))
- ; attempt to coerce all args into a common type among the args
- (define (apply-with-coercion arg-types)
- ; attempt to coerce all args using each tag-type in turn
- ; it's a scoped procedure to keep the original arguments (arg-types) for error reporting
- (define (coerce-types tags)
- (if (null? tags) ; all targets exhausted
- (error "No method for these types - APPLY-GENERIC"
- (list op arg-types))
- (let* ((target-type (car tags))
- (arg-coercions (map ; get all the coercion procedures from the target
- (lambda (coerce-from)
- (if (eq? coerce-from target-type)
- identity
- (get-coercion coerce-from target-type)))
- arg-types)))
- (if (all-coercable? arg-coercions)
- ; the target type is valid if all the args can be coerced
- (apply apply-generic
- op
- (coerce-args arg-coercions args))
- ; target-type is not valid, so try the next one in the list
- (coerce-types (cdr tags)))))) ; try the next target type
- (coerce-types arg-types))
- (let* ((type-tags (map type-tag args))
- (proc (get op type-tags)))
- (if proc
- (apply proc (map contents args))
- (apply-with-coercion type-tags))))
- ;;
- ;; ======================================================================
- ;;
- ;; To test the exercises I need an implementation of put and get.
- ;; These are taken directly from section 3.3.3 of the book
- ;; http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-22.html#%_sec_3.3.3
- ;;
- ;; ======================================================================
- (define (make-table)
- (let ((local-table (list '*table*)))
- (define (lookup key-1 key-2)
- (let ((subtable (assoc key-1 (cdr local-table))))
- (if subtable
- (let ((record (assoc key-2 (cdr subtable))))
- (if record
- (cdr record)
- false))
- false)))
- (define (insert! key-1 key-2 value)
- (let ((subtable (assoc key-1 (cdr local-table))))
- (if subtable
- (let ((record (assoc key-2 (cdr subtable))))
- (if record
- (set-cdr! record value)
- (set-cdr! subtable
- (cons (cons key-2 value)
- (cdr subtable)))))
- (set-cdr! local-table
- (cons (list key-1
- (cons key-2 value))
- (cdr local-table)))))
- 'ok)
- (define (dispatch m)
- (cond ((eq? m 'lookup-proc) lookup)
- ((eq? m 'insert-proc!) insert!)
- ((eq? m 'table) local-table)
- (else (error "Unknown operation -- TABLE" m))))
- dispatch))
- (define operation-table (make-table))
- (define get (operation-table 'lookup-proc))
- (define put (operation-table 'insert-proc!))
- (define coercion-table (make-table))
- (define get-coercion (coercion-table 'lookup-proc))
- (define put-coercion (coercion-table 'insert-proc!))
- (define (square x) (* x x))
- (define (attach-tag type-tag contents)
- (if (eq? type-tag 'scheme-number)
- contents
- (cons type-tag contents)))
- (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) cdr datum)
- (else (error "Bad tagged datum -- CONTENTS" datum))))
- ;; ======================================================================
- ;;
- ;; The integer number package
- ;;
- ;; ======================================================================
- (define (install-integer-package)
- ;; internal procedures
- (define (tag x) (attach-tag 'integer x))
- ;; interface to rest of the system
- (put 'add '(integer integer) (lambda (x y) (tag (+ x y))))
- (put 'sub '(integer integer) (lambda (x y) (tag (- x y))))
- (put 'mul '(integer integer) (lambda (x y) (tag (* x y))))
- (put 'div '(integer integer) (lambda (x y) (tag (/ x y))))
- (put 'equ? '(integer integer) =)
- (put '=zero? '(integer integer) zero?)
- (put 'raise '(integer) (lambda (n) (make-rational n 1)))
- (put 'make 'integer (lambda (n) (tag n)))
- 'done)
- ;; ======================================================================
- ;;
- ;; The rational number package
- ;;
- ;; ======================================================================
- (define (install-rational-package)
- ;; internal procedures
- (define (numer x) (car x))
- (define (denom x) (cdr x))
- (define (make-rat n d) (let ((g (gcd n d)))
- (cons (/ n g) (/ d g))))
- (define (add-rat x y) (make-rat (+ (* (numer x) (denom y))
- (* (numer y) (denom x)))
- (* (denom x) (denom y))))
- (define (sub-rat x y) (make-rat (- (* (numer x) (denom y))
- (* (numer y) (denom x)))
- (* (denom x) (denom y))))
- (define (mul-rat x y) (make-rat (* (numer x) (numer y))
- (* (denom x) (denom y))))
- (define (div-rat x y) (make-rat (* (numer x) (denom y))
- (* (denom x) (numer y))))
- (define (equ-rat x y) (and (equ? (numer x) (numer y))
- (equ? (denom x) (denom y))))
- (define (=zero-rat x) (zero? (numer x)))
- (define (rational->real r) (make-real (/ (numer r) (denom r))))
- ;; interface to rest of the system
- (define (tag x) (attach-tag 'rational x))
- (put 'add '(rational rational) (lambda (x y) (tag (add-rat x y))))
- (put 'sub '(rational rational) (lambda (x y) (tag (sub-rat x y))))
- (put 'mul '(rational rational) (lambda (x y) (tag (mul-rat x y))))
- (put 'div '(rational rational) (lambda (x y) (tag (div-rat x y))))
- (put 'equ? '(rational rational) equ-rat)
- (put '=zero? '(rational) =zero-rat)
- (put 'raise '(rational) rational->real)
- (put 'make 'rational (lambda (n d) (tag (make-rat n d))))
- 'done)
- ;; ======================================================================
- ;;
- ;; The real number package
- ;;
- ;; ======================================================================
- (define (install-real-package)
- ;; internal procedures
- (define (tag x) (attach-tag 'real x))
- (define (real->complex r) (make-complex-from-real-imag r 0))
- ;; interface to rest of the system
- (put 'add '(real real) (lambda (x y) (tag (+ x y))))
- (put 'sub '(real real) (lambda (x y) (tag (- x y))))
- (put 'mul '(real real) (lambda (x y) (tag (* x y))))
- (put 'div '(real real) (lambda (x y) (tag (/ x y))))
- (put 'equ? '(real real) =)
- (put '=zero? '(real real) zero?)
- (put 'raise '(real) real->complex)
- (put 'make 'real (lambda (n) (tag n)))
- 'done)
- ;; ======================================================================
- ;;
- ;; The rectangular number package
- ;;
- ;; ======================================================================
- (define (install-rectangular-package)
- ;; internal procedures
- (define (real-part z) (car z))
- (define (imag-part z) (cdr z))
- (define (make-from-real-imag x y) (cons x y))
- (define (magnitude z)
- (sqrt (+ (square (real-part z))
- (square (imag-part z)))))
- (define (angle z)
- (atan (imag-part z) (real-part z)))
- (define (make-from-mag-ang r a)
- (cons (* r (cos a)) (* r (sin a))))
- ;; interface to the rest of the system
- (define (tag x) (attach-tag 'rectangular x))
- (put 'real-part '(rectangular) real-part)
- (put 'imag-part '(rectangular) imag-part)
- (put 'magnitude '(rectangular) magnitude)
- (put 'angle '(rectangular) angle)
- (put 'make-from-real-imag 'rectangular
- (lambda (x y) (tag (make-from-real-imag x y))))
- (put 'make-from-mag-ang 'rectangular
- (lambda (r a) (tag (make-from-mag-ang r a))))
- 'done)
- ;; ======================================================================
- ;;
- ;; The polar number package
- ;;
- ;; ======================================================================
- (define (install-polar-package)
- ;; internal procedures
- (define (magnitude z) (car z))
- (define (angle z) (cdr z))
- (define (make-from-mag-ang r a) (cons r a))
- (define (real-part z)
- (* (magnitude z) (cos (angle z))))
- (define (imag-part z)
- (* (magnitude z) (sin (angle z))))
- (define (make-from-real-imag x y)
- (cons (sqrt (+ (square x) (square y)))
- (atan y x)))
- ;; interface to the rest of the system
- (define (tag x) (attach-tag 'polar x))
- (put 'real-part '(polar) real-part)
- (put 'imag-part '(polar) imag-part)
- (put 'magnitude '(polar) magnitude)
- (put 'angle '(polar) angle)
- (put 'make-from-real-imag 'polar
- (lambda (x y) (tag (make-from-real-imag x y))))
- (put 'make-from-mag-ang 'polar
- (lambda (r a) (tag (make-from-mag-ang r a))))
- 'done)
- ;; ======================================================================
- ;;
- ;; The complex number package
- ;;
- ;; ======================================================================
- (define (install-complex-package)
- ;; imported procedures from rectangular and polar packages
- (define (make-from-real-imag x y) ((get 'make-from-real-imag 'rectangular) x y))
- (define (make-from-mag-ang r a) ((get 'make-from-mag-ang 'polar) r a))
- ;; internal procedures
- (define (tag z) (attach-tag 'complex z))
- (define (add-complex z1 z2) (make-from-real-imag (+ (real-part z1) (real-part z2))
- (+ (imag-part z1) (imag-part z2))))
- (define (sub-complex z1 z2) (make-from-real-imag (- (real-part z1) (real-part z2))
- (- (imag-part z1) (imag-part z2))))
- (define (mul-complex z1 z2) (make-from-mag-ang (* (magnitude z1) (magnitude z2))
- (+ (angle z1) (angle z2))))
- (define (div-complex z1 z2) (make-from-mag-ang (/ (magnitude z1) (magnitude z2))
- (- (angle z1) (angle z2))))
- (define (equ-complex z1 z2) (and (equ? (magnitude z1) (magnitude z2))
- (equ? (angle z1) (angle z2))))
- (define (=zero-complex z1) (zero? (magnitude z1)))
- ;; interface to rest of the system
- (put 'add '(complex complex) (lambda (z1 z2) (tag (add-complex z1 z2))))
- (put 'sub '(complex complex) (lambda (z1 z2) (tag (sub-complex z1 z2))))
- (put 'mul '(complex complex) (lambda (z1 z2) (tag (mul-complex z1 z2))))
- (put 'div '(complex complex) (lambda (z1 z2) (tag (div-complex z1 z2))))
- (put 'equ? '(complex complex) equ-complex)
- (put '=zero? '(complex) =zero-complex)
- (put 'make-from-real-imag 'complex (lambda (x y) (tag (make-from-real-imag x y))))
- (put 'make-from-mag-ang 'complex (lambda (r a) (tag (make-from-mag-ang r a))))
- (put 'real-part '(complex) real-part)
- (put 'imag-part '(complex) imag-part)
- (put 'magnitude '(complex) magnitude)
- (put 'angle '(complex) angle)
- 'done)
- ;; ======================================================================
- ;;
- ;; Generic procedures
- ;;
- ;; ======================================================================
- ; Constructors
- (define (make-integer n) ((get 'make 'integer) n))
- (define (make-real n) ((get 'make 'real) n))
- (define (make-rational n d) ((get 'make 'rational) n d))
- (define (make-complex-from-real-imag x y) ((get 'make-from-real-imag 'complex) x y))
- (define (make-complex-from-mag-ang r a) ((get 'make-from-mag-ang 'complex) r a))
- ; Selectors
- (define (real-part z) (apply-generic 'real-part z))
- (define (imag-part z) (apply-generic 'imag-part z))
- (define (magnitude z) (apply-generic 'magnitude z))
- (define (angle z) (apply-generic 'angle z))
- ; Operators
- (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))
- (define (raise x) (apply-generic 'raise x))
- ;; ======================================================================
- ;;
- ;; Package installation
- ;;
- ;; ======================================================================
- (define (install-number-packages)
- (install-integer-package)
- (install-polar-package)
- (install-rectangular-package)
- (install-rational-package)
- (install-real-package)
- (install-complex-package))
- (install-number-packages)
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