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SICP 05/07: use S7 Scheme session

This commit is contained in:
Darcy Shen 2024-05-15 10:48:51 +08:00
parent a8150764c3
commit 5fb52afc54
2 changed files with 162 additions and 58 deletions
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78
SICP/code05.tm
View File

@ -1,12 +1,14 @@
<TeXmacs|2.1.2> <TeXmacs|2.1.2>
<style|<tuple|generic|no-page-numbers|british|reduced-margins>> <style|<tuple|generic|no-page-numbers|british|reduced-margins|s7>>
<\body> <\body>
<section*|Orders of Growth> <section*|Orders of Growth>
<\session|scheme|default> <\session|s7|default>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (expt-1 b n) (define (expt-1 b n)
\ \ (if (= n 0) \ \ (if (= n 0)
@ -18,19 +20,25 @@
expt-1 expt-1
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(expt-1 1 0) (expt-1 1 0)
<|unfolded-io> <|unfolded-io>
1 1
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(expt-1 2 3) (expt-1 2 3)
<|unfolded-io> <|unfolded-io>
8 8
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (expt-2 b n) (define (expt-2 b n)
\ \ (define (expt-iter b counter product) \ \ (define (expt-iter b counter product)
@ -52,21 +60,27 @@
expt-2 expt-2
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(expt-2 3 3) (expt-2 3 3)
<|unfolded-io> <|unfolded-io>
27 27
</unfolded-io> </unfolded-io>
<\input|Scheme] > <\input>
\<gtr\>\
<|input>
\; \;
</input> </input>
</session> </session>
<section*|Exponentiation> <section*|Exponentiation>
<\session|scheme|default> <\session|s7|default>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (fast-expt b n) (define (fast-expt b n)
\ \ (define (even? n) \ \ (define (even? n)
@ -86,17 +100,27 @@
fast-expt fast-expt
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fast-expt 3 3) (fast-expt 3 3)
<|unfolded-io> <|unfolded-io>
27 27
</unfolded-io> </unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session> </session>
<section*|Greatest Common Divisors> <section*|Greatest Common Divisors>
<\session|scheme|default> <\session|s7|default>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (gcd a b) (define (gcd a b)
\ \ (if (= b 0) \ \ (if (= b 0)
@ -108,11 +132,19 @@
gcd gcd
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(gcd 10 20) (gcd 10 20)
<|unfolded-io> <|unfolded-io>
10 10
</unfolded-io> </unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session> </session>
</body> </body>
@ -129,3 +161,21 @@
<associate|auto-3|<tuple|?|?>> <associate|auto-3|<tuple|?|?>>
</collection> </collection>
</references> </references>
<\auxiliary>
<\collection>
<\associate|toc>
<vspace*|1fn><with|font-series|<quote|bold>|math-font-series|<quote|bold>|Orders
of Growth> <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>|Exponentiation>
<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>|Greatest
Common Divisors> <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>
</associate>
</collection>
</auxiliary>

140
SICP/code07.tm
View File

@ -1,18 +1,22 @@
<TeXmacs|2.1.2> <TeXmacs|2.1.2>
<style|<tuple|generic|no-page-numbers|chinese>> <style|<tuple|generic|no-page-numbers|chinese|s7>>
<\body> <\body>
<subsection*|1.3.1> <subsection*|1.3.1>
<\session|scheme|default> <\session|s7|default>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (cube x) (* x x x)) (define (cube x) (* x x x))
<|unfolded-io> <|unfolded-io>
cube cube
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum-integers a b) (define (sum-integers a b)
\ \ (if (\<gtr\> a b) \ \ (if (\<gtr\> a b)
@ -24,7 +28,9 @@
sum-integers sum-integers
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum-cubes a b) (define (sum-cubes a b)
\ \ (if (\<gtr\> a b) \ \ (if (\<gtr\> a b)
@ -36,7 +42,9 @@
sum-cubes sum-cubes
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (pi-sum a b) (define (pi-sum a b)
\ \ (if (\<gtr\> a b) \ \ (if (\<gtr\> a b)
@ -48,25 +56,33 @@
pi-sum pi-sum
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(sum-integers 1 3) (sum-integers 1 3)
<|unfolded-io> <|unfolded-io>
6 6
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(sum-cubes 1 3) (sum-cubes 1 3)
<|unfolded-io> <|unfolded-io>
36 36
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(pi-sum 1 3) (pi-sum 1 3)
<|unfolded-io> <|unfolded-io>
0.3333333333333333 0.3333333333333333
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum term a next b) (define (sum term a next b)
\ \ (if (\<gtr\> a b) \ \ (if (\<gtr\> a b)
@ -80,13 +96,17 @@
sum sum
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (inc n) (+ n 1)) (define (inc n) (+ n 1))
<|unfolded-io> <|unfolded-io>
inc inc
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum-cubes-2 a b) (define (sum-cubes-2 a b)
\ \ (sum cube a inc b)) \ \ (sum cube a inc b))
@ -94,23 +114,25 @@
sum-cubes-2 sum-cubes-2
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(sum-cubes-2 1 3) (sum-cubes-2 1 3)
<|unfolded-io> <|unfolded-io>
36 36
</unfolded-io> </unfolded-io>
<\input|Scheme] > <\unfolded-io>
\; \<gtr\>\
</input> <|unfolded-io>
<\unfolded-io|Scheme] >
(define (identity x) x) (define (identity x) x)
<|unfolded-io> <|unfolded-io>
identity identity
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum-integers-2 a b) (define (sum-integers-2 a b)
\ \ (sum identity a inc b)) \ \ (sum identity a inc b))
@ -118,13 +140,17 @@
sum-integers-2 sum-integers-2
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(sum-integers-2 1 10) (sum-integers-2 1 10)
<|unfolded-io> <|unfolded-io>
55 55
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (pi-sum-2 a b) (define (pi-sum-2 a b)
\ \ (define (pi-term x) \ \ (define (pi-term x)
@ -140,47 +166,61 @@
pi-sum-2 pi-sum-2
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(* 8 (pi-sum-2 1 1000)) (* 8 (pi-sum-2 1 1000))
<|unfolded-io> <|unfolded-io>
3.139592655589783 3.139592655589783
</unfolded-io> </unfolded-io>
<\input|Scheme] > <\input>
\<gtr\>\
<|input>
\; \;
</input> </input>
</session> </session>
<subsection*|1.3.2> <subsection*|1.3.2>
<\session|scheme|default> <\session|s7|default>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (square x) (* x x)) (define (square x) (* x x))
<|unfolded-io> <|unfolded-io>
square square
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
((lambda (x y z) (+ x y (square z))) 1 2 3) ((lambda (x y z) (+ x y (square z))) 1 2 3)
<|unfolded-io> <|unfolded-io>
12 12
</unfolded-io> </unfolded-io>
<\input|Scheme] > <\input>
\<gtr\>\
<|input>
\; \;
</input> </input>
</session> </session>
<subsection*|1.3.3> <subsection*|1.3.3>
<\session|scheme|default> <\session|s7|default>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (average x y) (/ (+ x y) 2)) (define (average x y) (/ (+ x y) 2))
<|unfolded-io> <|unfolded-io>
average average
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (search f neg-point pos-point) (define (search f neg-point pos-point)
\ \ (let ((midpoint (average neg-point pos-point))) \ \ (let ((midpoint (average neg-point pos-point)))
@ -204,7 +244,9 @@
search search
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (close-enough? x y) (define (close-enough? x y)
\ \ (\<less\> (abs (- x y)) 0.001)) \ \ (\<less\> (abs (- x y)) 0.001))
@ -212,7 +254,9 @@
close-enough? close-enough?
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (half-interval-method f a b) (define (half-interval-method f a b)
\ \ (let ((a-value (f a)) \ \ (let ((a-value (f a))
@ -234,13 +278,17 @@
half-interval-method half-interval-method
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(half-interval-method sin 2.0 4.0) (half-interval-method sin 2.0 4.0)
<|unfolded-io> <|unfolded-io>
3.14111328125 3.14111328125
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(half-interval-method (lambda (x) (- (* x x x) (* 2 x) 3)) (half-interval-method (lambda (x) (- (* x x x) (* 2 x) 3))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.0
@ -250,17 +298,17 @@
1.89306640625 1.89306640625
</unfolded-io> </unfolded-io>
<\input|Scheme] > <\unfolded-io>
\; \<gtr\>\
</input> <|unfolded-io>
<\unfolded-io|Scheme] >
(define tolerance 0.00001) (define tolerance 0.00001)
<|unfolded-io> <|unfolded-io>
0.00001 0.00001
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (fixed-point f first-guess) (define (fixed-point f first-guess)
\ \ (define (close-enough? v1 v2) \ \ (define (close-enough? v1 v2)
@ -282,13 +330,17 @@
fixed-point fixed-point
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fixed-point cos 1.0) (fixed-point cos 1.0)
<|unfolded-io> <|unfolded-io>
0.7390822985224024 0.7390822985224024
</unfolded-io> </unfolded-io>
<\unfolded-io|Scheme] > <\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fixed-point (lambda (y) (+ (sin y) (cos y))) (fixed-point (lambda (y) (+ (sin y) (cos y)))
\ \ \ \ \ \ \ \ \ \ \ \ \ 1.0) \ \ \ \ \ \ \ \ \ \ \ \ \ 1.0)
@ -296,7 +348,9 @@
1.2587315962971173 1.2587315962971173
</unfolded-io> </unfolded-io>
<\input|Scheme] > <\input>
\<gtr\>\
<|input>
\; \;
</input> </input>
</session> </session>