XmacsLabs
/
planet
mirror of https://gitee.com/XmacsLabs/planet.git
1
0
Fork 0
Code

SICP 10: 函数式编程三板斧

This commit is contained in:
Darcy Shen 2024-05-16 16:13:08 +08:00
parent 5fb52afc54
commit 494849a32c
2 changed files with 709 additions and 0 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

6
SICP/index.tm
View File

@ -24,6 +24,12 @@
<item>\<#76EE\>\<#6807\>\<#90AE\>\<#7BB1\>\<#FF1A\>shenda AT ustc.edu
</itemize>
<item>\<#7B2C\>10\<#8BFE\>\<#FF1A\>\<#51FD\>\<#6570\>\<#5F0F\>\<#7F16\>\<#7A0B\>\<#4E09\>\<#677F\>\<#65A7\>
\<#8BFE\>\<#4EF6\>\<#FF1A\><hlink|\<#5E7B\>\<#706F\>\<#7247\>10|slide10.tm>
\<#4EE3\>\<#7801\>\<#FF1A\><hlink|\<#4EE3\>\<#7801\>\<#6E05\>\<#5355\>10|code10.tm>
<item>\<#7B2C\>8\<#8BFE\>\<#FF1A\>\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#6570\>\<#636E\>\<#62BD\>\<#8C61\>
\<#8BFE\>\<#4EF6\>\<#FF1A\><hlink|\<#5E7B\>\<#706F\>\<#7247\>08|slide08.tm>

703
SICP/slide10.tm Normal file
View File

@ -0,0 +1,703 @@
<TeXmacs|2.1.2>
<style|<tuple|beamer|no-page-numbers|chinese|python|s7>>
<\body>
<\hide-preamble>
<assign|dfn|<macro|x|<strong|<arg|x>>>>
</hide-preamble>
<\slideshow>
<\slide>
\;
\;
\;
\;
<doc-data|<doc-title|\<#96F6\>\<#57FA\>\<#7840\>SICP
10>|<doc-author|<author-data|<author-name|>>>|<doc-author|<author-data|<author-name|\<#6C88\>\<#6D6A\>\<#718A\>\<#732B\>\<#513F\>>>>|<doc-author|<author-data|<author-name|MathAgape>>>|<doc-subtitle|\<#51FD\>\<#6570\>\<#5F0F\>\<#7F16\>\<#7A0B\>\<#4E09\>\<#677F\>\<#65A7\>>>
</slide>
<\slide>
<tit|\<#96F6\>\<#57FA\>\<#7840\>SICP\<#FF1A\>\<#7B2C\>10\<#8BFE\>>
<\wide-tabular>
<tformat|<cwith|2|-1|1|-1|cell-height|40px>|<cwith|2|-1|1|-1|cell-vmode|exact>|<table|<row|<\cell>
<\large>
<strong|\<#6570\>\<#636E\>\<#62BD\>\<#8C61\>\<#5BFC\>\<#5F15\>>
</large>
</cell>|<\cell>
<\large>
<strong|Introduction to Data Abstractio>n
</large>
</cell>>|<row|<\cell>
\<#5B9E\>\<#4F8B\>\<#FF1A\>\<#6709\>\<#7406\>\<#6570\>\<#7684\>\<#7B97\>\<#672F\>\<#8FD0\>\<#7B97\>
</cell>|<\cell>
Example: Arithmetic Operations for Rational Numbers
</cell>>|<row|<\cell>
\<#62BD\>\<#8C61\>\<#5C42\>\<#7EA7\>
</cell>|<\cell>
Abstraction Barriers
</cell>>|<row|<\cell>
\<#6570\>\<#636E\>\<#610F\>\<#5473\>\<#7740\>\<#4EC0\>\<#4E48\>
</cell>|<\cell>
What Is Meant by Data?
</cell>>|<row|<\cell>
<large|<strong|\<#5C42\>\<#6B21\>\<#6027\>\<#6570\>\<#636E\>\<#548C\><todo|\<#95ED\>\<#5305\>\<#6027\>\<#8D28\>>>>
</cell>|<\cell>
<large|<strong|Hierarchical Data and the Closure Property>>
</cell>>|<row|<\cell>
\<#5E8F\>\<#5217\>\<#7684\>\<#8868\>\<#793A\>
</cell>|<\cell>
Representing Sequences
</cell>>|<row|<\cell>
\<#5C42\>\<#6B21\>\<#6027\>\<#7ED3\>\<#6784\>
</cell>|<\cell>
Hierarchical Structures
</cell>>|<row|<\cell>
\<#5E8F\>\<#5217\>\<#4F5C\>\<#4E3A\>\<#4E00\>\<#79CD\>\<#7EA6\>\<#5B9A\>\<#7684\>\<#63A5\>\<#53E3\>
</cell>|<\cell>
Sequences as Conventional Interfaces
</cell>>>>
</wide-tabular>
\;
<strong|\<#5229\>\<#7528\>\<#51FD\>\<#6570\>\<#5F0F\>\<#7F16\>\<#7A0B\>\<#4E09\>\<#677F\>\<#65A7\>\<#FF08\>\<#6620\>\<#5C04\>/\<#8FC7\>\<#6EE4\>/\<#6298\>\<#53E0\>\<#FF09\>\<#548C\>\<#884D\>\<#751F\>\<#7B97\>\<#5B50\>\<#63CF\>\<#8FF0\>\<#6570\>\<#636E\>\<#5904\>\<#7406\>\<#903B\>\<#8F91\>\<#3002\>>
\;
</slide>
<\slide>
<tit|\<#5B9A\>\<#4E49\>\<#6570\>\<#636E\>\<#FF1A\>list>
\<#901A\>\<#8FC7\>\<#5B9A\>\<#4E49\>\<#4E00\>\<#7EC4\><strong|\<#903B\>\<#8F91\>\<#81EA\>\<#6D3D\>>\<#7684\>\<#9009\>\<#62E9\>\<#51FD\>\<#6570\>\<#548C\>\<#6784\>\<#9020\>\<#51FD\>\<#6570\>\<#FF0C\>\<#5B9A\>\<#4E49\>\<#6570\>\<#636E\>\<#3002\>
<\with|par-columns|2>
\<#6784\>\<#9020\>\<#5668\>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(list 1 2 3 4)
<|unfolded-io>
(1 2 3 4)
</unfolded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(cons 5 (list 1 2 3 4))
<|folded-io>
(5 1 2 3 4)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
()
<|folded-io>
()
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
\<#9009\>\<#62E9\>\<#5668\>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(car (list 1 2 3 4))
<|folded-io>
1
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(cdr (list 1 2 3 4))
<|folded-io>
(2 3 4)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(cadr (list 1 2 3 4))
<|folded-io>
2
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(list-ref (list 1 2 3 4) 3)
<|folded-io>
4
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
\<#6027\>\<#8D28\>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(list? (list 1))
<|folded-io>
#t
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(list? 1)
<|folded-io>
#f
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(eq? () ())
<|folded-io>
#t
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(eq? () (list 1))
<|folded-io>
#f
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(null? ())
<|folded-io>
#t
</folded-io>
<\input>
\<gtr\>\
<|input>
(length (list 1 2 3 4))
</input>
</session>
</with>
</slide>
<\slide>
<tit|\<#4E09\>\<#677F\>\<#65A7\>\<#4E4B\>\<#6620\>\<#5C04\>\<#FF1A\>map>
<scm|map>\<#662F\>S7 Scheme\<#7684\>\<#5185\>\<#7F6E\>\<#51FD\>\<#6570\>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (square x) (* x x))
<|folded-io>
square
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(map square (list 1 2 3 4 5))
<|folded-io>
(1 4 9 16 25)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(map (lambda (x) (* x x)) (list 1 2 3 4 5))
<|folded-io>
(1 4 9 16 25)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(map (lambda (x) (+ x 1)) (list 1 2 3 4 5))
<|folded-io>
(2 3 4 5 6)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(map (lambda (x) (append x "@liii.pro")) (list "da" "nian"))
<|folded-io>
("da@liii.pro" "nian@liii.pro")
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(map odd? (list 1 2 3 4 5))
<|folded-io>
(#t #f #t #f #t)
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</slide>
<\slide>
<tit|\<#4E09\>\<#677F\>\<#65A7\>\<#4E4B\>\<#8FC7\>\<#6EE4\>\<#FF1A\>filter>
<hlink|SRFI-1: List Library|https://srfi.schemers.org/srfi-1/srfi-1.html>\<#4E2D\>\<#5B9A\>\<#4E49\>\<#4E86\><scm|filter>\<#FF0C\>\<#6211\>\<#4EEC\>\<#9700\>\<#8981\>\<#81EA\>\<#5DF1\>\<#5B9E\>\<#73B0\>
<\with|par-columns|2>
\<#5B9E\>\<#73B0\>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (filter pred? seq)
\ \ (cond
\ \ \ ((null? seq) ())
\ \ \ ((pred? (car seq))
\ \ \ \ (cons (car seq)
\ \ \ \ \ \ \ \ \ \ (filter pred? (cdr seq))))
\ \ \ (else (filter pred? (cdr seq)))))
<|unfolded-io>
filter
</unfolded-io>
</session>
\<#5E94\>\<#7528\>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(filter odd? (list 1 2 3 4 5))
<|folded-io>
(1 3 5)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(filter even? (list 1 2 3 4 5))
<|folded-io>
(2 4)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(filter (lambda (x) (\<gtr\> x 3)) '(1 3 5))
<|folded-io>
(5)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(filter (lambda (x) (= x 3)) `(1 3 5))
<|folded-io>
(3)
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(filter (lambda (x) (\<gtr\> x 20))
\ (map (lambda (x) (* x x))
\ \ (list 1 2 3 4 5 6)))
<|folded-io>
(25 36)
</folded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</with>
</slide>
<\slide>
<tit|\<#4E09\>\<#677F\>\<#65A7\>\<#4E4B\>\<#6298\>\<#53E0\>\<#FF1A\>fold\<#548C\>fold-right>
<hlink|SRFI-1: List Library|https://srfi.schemers.org/srfi-1/srfi-1.html>\<#4E2D\>\<#5B9A\>\<#4E49\>\<#4E86\><scm|fold>\<#FF0C\>\<#6211\>\<#4EEC\>\<#9700\>\<#8981\>\<#81EA\>\<#5DF1\>\<#5B9E\>\<#73B0\>
<\with|par-columns|2>
\<#5B9E\>\<#73B0\>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (fold op initial seq)
\ (if (null? seq)
\ \ initial
\ \ (fold op
\ \ \ \ \ \ \ \ (op (car seq) initial)
\ \ \ \ \ \ \ \ (cdr seq))))
<|folded-io>
fold
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (fold-right op initial seq)
\ (if (null? seq)
\ \ initial
\ \ (op (car seq)
\ \ \ \ \ \ (fold-right op
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ initial
\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (cdr seq)))))
<|folded-io>
fold-right
</folded-io>
</session>
\<#5E94\>\<#7528\>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fold + 0 (list 1 2 3 4))
<|unfolded-io>
10
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fold-right + 0 (list 1 2 3 4))
<|unfolded-io>
10
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fold cons () (list 1 2 3 4))
<|unfolded-io>
(4 3 2 1)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(fold-right cons () (list 1 2 3 4))
<|unfolded-io>
(1 2 3 4)
</unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
</with>
</slide>
<\slide>
<tit|\<#7406\>\<#89E3\>\<#5DE6\>\<#6298\>\<#53E0\>fold>
\<#901A\>\<#8FC7\>\<#53EF\>\<#89C6\>\<#5316\>\<#7406\>\<#89E3\><scm|(fold
cons () (list 1 2 3))>
<\with|par-columns|4>
<\scm-code>
; Step 0
(fold cons\
\ \ ()
\ <tree|\<box\>|1|<tree|\<box\>|2|<tree|\<box\>|3|\<box\>>>>)
; Step 1
(fold cons\
\ \ <tree|\<box\>|1|\<box\>>
\;
\ <tree|\<box\>|2|<tree|\<box\>|3|\<box\>>>)
; Step 2
(fold cons \ <tree|\<box\>|2|<tree|\<box\>|1|\<box\>>>
\;
\ \ <tree|\<box\>|3|\<box\>>)
\;
; Step 3
(fold cons <tree|\<box\>|3|<tree|\<box\>|2|<tree|\<box\>|1|\<box\>>>>
())
</scm-code>
</with>
</slide>
<\slide>
<tit|\<#7406\>\<#89E3\>\<#53F3\>\<#6298\>\<#53E0\>fold-right\<#6B65\>\<#9AA4\>0-1>
\<#901A\>\<#8FC7\>\<#53EF\>\<#89C6\>\<#5316\>\<#7406\>\<#89E3\><scm|(fold-right
cons () (list 1 2 3))>
<\with|par-columns|2>
<\scm-code>
; Step 0
(fold-right cons () <tree|\<box\>|1|<tree|\<box\>|2|<tree|\<box\>|3|\<box\>>>>)
; Step 1
(cons 1
\ (fold-right cons () <tree|\<box\>|2|<tree|\<box\>|3|\<box\>>>)))
\;
\;
</scm-code>
</with>
</slide>
<\slide>
<tit|\<#7406\>\<#89E3\>\<#53F3\>\<#6298\>\<#53E0\>fold-right\<#6B65\>\<#9AA4\>2-3>
\<#901A\>\<#8FC7\>\<#53EF\>\<#89C6\>\<#5316\>\<#7406\>\<#89E3\><scm|(fold-right
cons () (list 1 2 3))>
<\with|par-columns|2>
<\scm-code>
; Step 2
(cons 1
\ (cons 2
\ \ (fold-right cons () <tree|\<box\>|3|\<box\>>)))
\;
\;
\;
\;
\;
\;
; Step 3
(cons 1 (cons 2 (cons 3 ()))))
<tree|\<box\>|1|<tree|\<box\>|2|<tree|\<box\>|3|\<box\>>>>
\;
</scm-code>
</with>
</slide>
<\slide>
<tit|\<#884D\>\<#751F\>\<#7B97\>\<#5B50\>\<#FF1A\>flatmap>
<\session|s7|default>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(define (flatmap f seq)
\ \ (fold-right append () (map f seq)))
<|unfolded-io>
flatmap
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(flatmap (lambda (x) (list x x)) (list 1 2 3 4))
<|unfolded-io>
(1 1 2 2 3 3 4 4)
</unfolded-io>
<\unfolded-io>
\<gtr\>\
<|unfolded-io>
(map (lambda (x) (list x x)) (list 1 2 3 4))
<|unfolded-io>
((1 1) (2 2) (3 3) (4 4))
</unfolded-io>
<\input>
\<gtr\>\
<|input>
\;
</input>
</session>
<\equation*>
map:<block|<tformat|<table|<row|<cell|1>|<cell|2>|<cell|3>|<cell|4>>>>><long-arrow|\<rubber-rightarrow\>|<scm|(lambda
(x) (list x x))>><block|<tformat|<table|<row|<cell|<subtable|<tformat|<table|<row|<cell|1>>|<row|<cell|1>>>>>>|<cell|<subtable|<tformat|<table|<row|<cell|2>>|<row|<cell|2>>>>>>|<cell|<subtable|<tformat|<table|<row|<cell|3>>|<row|<cell|3>>>>>>|<cell|<subtable|<tformat|<table|<row|<cell|4>>|<row|<cell|4>>>>>>>>>>
</equation*>
<\equation*>
flatmap:<block|<tformat|<table|<row|<cell|1>|<cell|2>|<cell|3>|<cell|4>>>>><long-arrow|\<rubber-rightarrow\>|<scm|(lambda
(x) (list x x))>><block|<tformat|<table|<row|<cell|1>|<cell|1>|<cell|2>|<cell|2>|<cell|3>|<cell|3>|<cell|4>|<cell|4>>>>>
</equation*>
</slide>
<\slide>
<tit|\<#884D\>\<#751F\>\<#7B97\>\<#5B50\>\<#FF1A\>flatmap\<#7684\>\<#5E94\>\<#7528\>>
<\session|s7|default>
<\folded-io>
\<gtr\>\
<|folded-io>
(define (remove item sequence)
\ \ (filter (lambda (x) (not (= x item)))
\ \ \ \ \ \ \ \ \ \ sequence))
<|folded-io>
remove
</folded-io>
<\folded-io>
\<gtr\>\
<|folded-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)))
<|folded-io>
permutations
</folded-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>
</slide>
<\slide>
<tit|\<#603B\>\<#7ED3\>>
<\itemize>
<item>\<#5B9A\>\<#4E49\>\<#6570\>\<#636E\>: list
<item>\<#4E09\>\<#677F\>\<#65A7\>\<#4E4B\>\<#6620\>\<#5C04\>map
<item>\<#4E09\>\<#677F\>\<#65A7\>\<#4E4B\>\<#8FC7\>\<#6EE4\>filter
<item>\<#4E09\>\<#677F\>\<#65A7\>\<#4E4B\>\<#6298\>\<#53E0\>fold/fold-right
<item>\<#884D\>\<#751F\>\<#7B97\>\<#5B50\>\<#FF1A\>\<#53C2\>\<#8003\><hlink|SRFI-1:
List Library|https://srfi.schemers.org/srfi-1/srfi-1.html>
<\itemize>
<item>flatmap
<item>find
<item>any (\<exists\>)
<item>every (\<forall\>)
<item>count
<item>reduce/reduce-right
</itemize>
</itemize>
</slide>
</slideshow>
</body>
<\initial>
<\collection>
<associate|info-flag|minimal>
<associate|marked-color|pastel yellow>
<associate|page-border|attached>
<associate|page-medium|paper>
<associate|page-offset|1>
<associate|page-packet|2>
<associate|page-screen-margin|false>
<associate|par-columns|1>
<associate|preamble|false>
</collection>
</initial>