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SICP 05/07: use S7 Scheme session

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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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140
SICP/code07.tm
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@ -1,18 +1,22 @@
<TeXmacs|2.1.2>
<style|<tuple|generic|no-page-numbers|chinese>>
<style|<tuple|generic|no-page-numbers|chinese|s7>>
<\body>
<subsection*|1.3.1>
<\session|scheme|default>
<\unfolded-io|Scheme] >
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (cube x) (* x x x))
<|unfolded-io>
cube
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum-integers a b)
\ \ (if (\<gtr\> a b)
@ -24,7 +28,9 @@
sum-integers
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum-cubes a b)
\ \ (if (\<gtr\> a b)
@ -36,7 +42,9 @@
sum-cubes
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (pi-sum a b)
\ \ (if (\<gtr\> a b)
@ -48,25 +56,33 @@
pi-sum
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(sum-integers 1 3)
<|unfolded-io>
6
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(sum-cubes 1 3)
<|unfolded-io>
36
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(pi-sum 1 3)
<|unfolded-io>
0.3333333333333333
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum term a next b)
\ \ (if (\<gtr\> a b)
@ -80,13 +96,17 @@
sum
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (inc n) (+ n 1))
<|unfolded-io>
inc
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum-cubes-2 a b)
\ \ (sum cube a inc b))
@ -94,23 +114,25 @@
sum-cubes-2
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(sum-cubes-2 1 3)
<|unfolded-io>
36
</unfolded-io>
<\input|Scheme] >
\;
</input>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (identity x) x)
<|unfolded-io>
identity
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (sum-integers-2 a b)
\ \ (sum identity a inc b))
@ -118,13 +140,17 @@
sum-integers-2
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(sum-integers-2 1 10)
<|unfolded-io>
55
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (pi-sum-2 a b)
\ \ (define (pi-term x)
@ -140,47 +166,61 @@
pi-sum-2
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(* 8 (pi-sum-2 1 1000))
<|unfolded-io>
3.139592655589783
</unfolded-io>
<\input|Scheme] >
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
<subsection*|1.3.2>
<\session|scheme|default>
<\unfolded-io|Scheme] >
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (square x) (* x x))
<|unfolded-io>
square
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
((lambda (x y z) (+ x y (square z))) 1 2 3)
<|unfolded-io>
12
</unfolded-io>
<\input|Scheme] >
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
<subsection*|1.3.3>
<\session|scheme|default>
<\unfolded-io|Scheme] >
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (average x y) (/ (+ x y) 2))
<|unfolded-io>
average
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (search f neg-point pos-point)
\ \ (let ((midpoint (average neg-point pos-point)))
@ -204,7 +244,9 @@
search
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (close-enough? x y)
\ \ (\<less\> (abs (- x y)) 0.001))
@ -212,7 +254,9 @@
close-enough?
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (half-interval-method f a b)
\ \ (let ((a-value (f a))
@ -234,13 +278,17 @@
half-interval-method
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(half-interval-method sin 2.0 4.0)
<|unfolded-io>
3.14111328125
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(half-interval-method (lambda (x) (- (* x x x) (* 2 x) 3))
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1.0
@ -250,17 +298,17 @@
1.89306640625
</unfolded-io>
<\input|Scheme] >
\;
</input>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define tolerance 0.00001)
<|unfolded-io>
0.00001
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (fixed-point f first-guess)
\ \ (define (close-enough? v1 v2)
@ -282,13 +330,17 @@
fixed-point
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fixed-point cos 1.0)
<|unfolded-io>
0.7390822985224024
</unfolded-io>
<\unfolded-io|Scheme] >
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fixed-point (lambda (y) (+ (sin y) (cos y)))
\ \ \ \ \ \ \ \ \ \ \ \ \ 1.0)
@ -296,7 +348,9 @@
1.2587315962971173
</unfolded-io>
<\input|Scheme] >
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>