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planet/SICP/code10.tm

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<TeXmacs|2.1.2>
<style|<tuple|generic|no-page-numbers|british|s7>>
<\body>
<section*|Representing Sequences>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define one-through-four (list 1 2 3 4))
<|unfolded-io>
(1 2 3 4)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(car one-through-four)
<|unfolded-io>
1
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(cdr one-through-four)
<|unfolded-io>
(2 3 4)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(car (cdr one-through-four))
<|unfolded-io>
2
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(cons 10 one-through-four)
<|unfolded-io>
(10 1 2 3 4)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(cons 5 one-through-four)
<|unfolded-io>
(5 1 2 3 4)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (list-ref items n)
\ \ (if (= n 0)
\ \ \ \ \ \ (car items)
\ \ \ \ \ \ (list-ref (cdr items) (- n 1))))
<|unfolded-io>
list-ref
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define squares (list 1 4 9 16 25))
<|unfolded-io>
(1 4 9 16 25)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(list-ref squares 3)
<|unfolded-io>
16
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (length items)
\ \ (if (null? items)
\ \ \ \ \ \ 0
\ \ \ \ \ \ (+ 1 (length (cdr items)))))
<|unfolded-io>
length
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define odds (list 1 3 5 7))
<|unfolded-io>
(1 3 5 7)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(length odds)
<|unfolded-io>
4
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(append squares odds)
<|unfolded-io>
(1 4 9 16 25 1 3 5 7)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(append odds squares)
<|unfolded-io>
(1 3 5 7 1 4 9 16 25)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (scale-list items factor)
\ \ (if (null? items)
\ \ \ \ \ \ ()
\ \ \ \ \ \ (cons (* (car items) factor)
\ \ \ \ \ \ \ \ \ \ \ \ (scale-list (cdr items) factor))))
<|unfolded-io>
scale-list
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(scale-list (list 1 2 3 4 5) 10)
<|unfolded-io>
(10 20 30 40 50)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(map abs (list -10 2.5 -11.6 17))
<|unfolded-io>
(10 2.5 11.6 17)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(map (lambda (x) (* x x))
\ \ \ \ \ (list 1 2 3 4))
<|unfolded-io>
(1 4 9 16)
</unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
<section*|Hierarchical Structures>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (count-leaves x)
\ \ (cond ((null? x) 0) \
\ \ \ \ \ \ \ \ ((not (pair? x)) 1)
\ \ \ \ \ \ \ \ (else (+ (count-leaves (car x))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (count-leaves (cdr x))))))
<|unfolded-io>
count-leaves
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define x (cons (list 1 2) (list 3 4)))
<|unfolded-io>
((1 2) 3 4)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(length x)
<|unfolded-io>
3
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(count-leaves x)
<|unfolded-io>
4
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(list x x)
<|unfolded-io>
(((1 2) 3 4) ((1 2) 3 4))
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(length (list x x))
<|unfolded-io>
2
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(count-leaves (list x x))
<|unfolded-io>
8
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (scale-tree tree factor)
\ \ (cond ((null? tree) ())
\ \ \ \ \ \ \ \ ((not (pair? tree)) (* tree factor))
\ \ \ \ \ \ \ \ (else (cons (scale-tree (car tree) factor)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (scale-tree (cdr tree)
factor)))))
<|unfolded-io>
scale-tree
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(scale-tree (list 1 (list 2 (list 3 4) 5) (list 6 7))
\ \ \ \ \ \ \ \ \ \ \ \ 10)
<|unfolded-io>
(10 (20 (30 40) 50) (60 70))
</unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
<section*|Sequences as Conventional Interfaces>
<subsection*|Sequence Operations>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (square x) (* x x))
<|unfolded-io>
square
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(map square (list 1 2 3 4 5))
<|unfolded-io>
(1 4 9 16 25)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (filter predicate sequence)
\ \ (cond ((null? sequence) ())
\ \ \ \ \ \ \ \ ((predicate (car sequence))
\ \ \ \ \ \ \ \ \ (cons (car sequence)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (filter predicate (cdr sequence))))
\ \ \ \ \ \ \ \ (else (filter predicate (cdr sequence)))))
<|unfolded-io>
filter
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(filter odd? (list 1 2 3 4 5))
<|unfolded-io>
(1 3 5)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (accumulate op initial sequence)
\ \ (if (null? sequence)
\ \ \ \ \ \ initial
\ \ \ \ \ \ (op (car sequence)
\ \ \ \ \ \ \ \ \ \ (accumulate op initial (cdr sequence)))))
<|unfolded-io>
accumulate
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(accumulate + 0 (list 1 2 3 4 5))
<|unfolded-io>
15
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(accumulate * 1 (list 1 2 3 4 5))
<|unfolded-io>
120
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(accumulate cons () (list 1 2 3 4 5))
<|unfolded-io>
(1 2 3 4 5)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (enumerate-interval low high)
\ \ (if (\<gtr\> low high)
\ \ \ \ \ \ ()
\ \ \ \ \ \ (cons low (enumerate-interval (+ low 1) high))))
<|unfolded-io>
enumerate-interval
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(enumerate-interval 2 7)
<|unfolded-io>
(2 3 4 5 6 7)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (enumerate-tree tree)
\ \ (cond ((null? tree) ())
\ \ \ \ \ \ \ \ ((not (pair? tree)) (list tree))
\ \ \ \ \ \ \ \ (else (append (enumerate-tree (car tree))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (enumerate-tree (cdr
tree))))))
<|unfolded-io>
enumerate-tree
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(enumerate-tree (list 1 (list 2 (list 3 4)) 5))
<|unfolded-io>
(1 2 3 4 5)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (fib n)
\ \ (cond ((= n 0) 0)
\ \ \ \ \ \ \ \ ((= n 1) 1)
\ \ \ \ \ \ \ \ (else (+ (fib (- n 1))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (fib (- n 2))))))
<|unfolded-io>
fib
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (list-fib-squares n)
\ \ (accumulate cons
\ \ \ \ \ \ \ \ \ \ \ \ \ \ ()
\ \ \ \ \ \ \ \ \ \ \ \ \ \ (map square
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (map <hlink|fib|#define_fib>
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (enumerate-interval 0
n)))))
<|unfolded-io>
list-fib-squares
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(list-fib-squares 10)
<|unfolded-io>
(0 1 1 4 9 25 64 169 441 1156 3025)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (product-of-squares-of-odd-elements sequence)
\ \ (accumulate *
\ \ \ \ \ \ \ \ \ \ \ \ \ \ 1
\ \ \ \ \ \ \ \ \ \ \ \ \ \ (map <hlink|square|#define_square>
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (filter odd? sequence))))
<|unfolded-io>
product-of-squares-of-odd-elements
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(product-of-squares-of-odd-elements (list 1 2 3 4 5))
<|unfolded-io>
225
</unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
<subsection*|Nested Mappings>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (square x) (* x x))
<|unfolded-io>
square
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (smallest-divisor n)
\ \ (find-divisor n 2))
<|unfolded-io>
smallest-divisor
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (find-divisor n test-divisor)
\ \ (cond ((\<gtr\> (square test-divisor) n) n)
\ \ \ \ \ \ \ \ ((divides? test-divisor n) test-divisor)
\ \ \ \ \ \ \ \ (else (find-divisor n (+ test-divisor 1)))))
<|unfolded-io>
find-divisor
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (divides? a b)
\ \ (= (remainder b a) 0))
<|unfolded-io>
divides?
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (prime? n)
\ \ (= n (smallest-divisor n)))
<|unfolded-io>
prime?
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (flatmap proc seq)
\ \ (accumulate append () (map proc seq)))
<|unfolded-io>
flatmap
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (prime-sum? pair)
\ \ (prime? (+ (car pair) (cadr pair))))
<|unfolded-io>
prime-sum?
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (make-pair-sum pair)
\ \ (list (car pair) (cadr pair) (+ (car pair) (cadr pair))))
<|unfolded-io>
make-pair-sum
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (prime-sum-pairs n)
\ \ (map make-pair-sum
\ \ \ \ \ \ \ (filter prime-sum?
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (flatmap
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (lambda (i)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (map (lambda (j) (list i j))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (enumerate-interval 1 (-
i 1))))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (enumerate-interval 1 n)))))
<|unfolded-io>
prime-sum-pairs
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(prime-sum-pairs 4)
<|unfolded-io>
((2 1 3) (3 2 5) (4 1 5) (4 3 7))
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (remove item sequence)
\ \ (filter (lambda (x) (not (= x item)))
\ \ \ \ \ \ \ \ \ \ sequence))
<|unfolded-io>
remove
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (permutations s)
\ \ (if (null? s) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ; empty set?
\ \ \ \ \ \ (list ()) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ; sequence
containing empty set
\ \ \ \ \ \ (flatmap (lambda (x)
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (map (lambda (p) (cons x p))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (permutations (remove x
s))))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ s)))
<|unfolded-io>
permutations
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(permutations (list 1 2 3))
<|unfolded-io>
((1 2 3) (1 3 2) (2 1 3) (2 3 1) (3 1 2) (3 2 1))
</unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</body>
<\initial>
<\collection>
<associate|page-medium|papyrus>
<associate|page-screen-margin|false>
</collection>
</initial>
<\references>
<\collection>
<associate|auto-1|<tuple|?|?>>
<associate|auto-2|<tuple|?|?>>
<associate|auto-3|<tuple|?|?>>
<associate|auto-4|<tuple|?|?>>
<associate|auto-5|<tuple|?|?>>
</collection>
</references>
<\auxiliary>
<\collection>
<\associate|toc>
<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Representing
Sequences> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-1><vspace|0.5fn>
<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Hierarchical
Structures> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-2><vspace|0.5fn>
<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Sequences
as Conventional Interfaces> <datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-3><vspace|0.5fn>
<with|par-left|<quote|1tab>|Sequence Operations
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-4>>
<with|par-left|<quote|1tab>|Nested Mappings
<datoms|<macro|x|<repeat|<arg|x>|<with|font-series|medium|<with|font-size|1|<space|0.2fn>.<space|0.2fn>>>>>|<htab|5mm>>
<no-break><pageref|auto-5>>
</associate>
</collection>
</auxiliary>
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