This document discusses core concepts in Scheme programming language, including functional programming, LISP, data types, forms and evaluation, recursion, and local variables. It provides examples of different data types in Scheme like booleans, numbers, characters, strings, symbols, and lists. It also explains evaluation of self-evaluating forms, symbols, function calls, and special forms. Examples of recursion and local variables using let and lambda are presented.

1. scheme 核心概念(一)
StorySense

2. scheme 核心概念(一)
1.
2.
3.
4.
5.
6.
Functional Language ?
LISP ?
Data type
Forms & Eval
Recursion
Local Variables

3. Functional Language ?
● 函數式語言
● 特性：
○
○
○
○
○
First-class and higher-order functions
Pure functions
Recursion
Strict versus non-strict evaluation
Type systems

4. LISP ?
●
●
●
●
●
●
LISt Processor 列表處理語言
John McCarthy 約翰·麥卡錫 1958年於MIT基於Lambda calculus所設計的程
式語言
最初LISP語言的概念上的設計，後續有很多不同實現與版本，統稱為LISP家
族
Common Lisp
Clojure
Scheme
○
○
○
極簡主義
目前版本R7S7
主流的scheme的直譯器或是編譯器
■
■
■
Racket
chicken
guile

5. Data Type
● booleans
○ (not #t) => #f
● numbers
○ 1
○ 3.14
○ 1/2
○ 1+i

6. Data Type
● characters
○ #a
● strings
○ "hello scheme"
● symbol
○ a ,abc ,this-is-symbol
○ 字母或是符號的組合
○ 用於關聯值或是函數或是其他元素

7. Data Type
● Dotted pairs & lists
○ (1 . 2) => pair
○ (1 2) => list
○ pair make list
■ cons
■ car
■ cdr

8. Dotted pairs & lists
● (cons 1 2) => (1 . 2)
● (car (cons 1 2)) => 1
● (cdr (cons 1 2)) => 2
○ (quote ()) or ‘() => ()
○ (cons (cons 1 2) 3) => ((1 . 2) . 3)
○ (cons 1 (cons 2 3)) => (1 2 . 3)
cdr 的部分是pair，就不會顯示dot
○ (cons 4 ‘()) => (4) *這是pair
○ (cons 5 (cons 4 ‘())) => (5 4) *這是list

9. Dotted pairs & lists
●
●
●
●
(pair? (cons 1 2)) => #t
(list? (cons 1 2)) => #f
(pair? (cons 1 (cons 2 '()))) => #t
(list? (cons 1 (cons 2 '()))) => #t

10. Pair & List operation
● car
● cdr
● ex:
○
○
○
○
○
l => ((1 2) 3 ((5 6) 7))
(car l) => (1 2)
(cdr l) => (3 ((5 6) 7))
(car (cdr l)) => 3
*(cadr l) => 3
(car (car (cdr (cdr l)))) => (5 6) *(caaddr l) => (5 6)

11. Forms & Eval
● express
●
●
●
●
●
eval
value
7 => 7
(+ 1 2) => 3
(if #t 1 2) => 1
(define a (+ 1 (* 3 4))) => a
(lambda (x) (+ 1 x)) => #<procedure>

12. Eval
●
●
●
●
self-eval
symbol-eval
form-eval
special form-eval

13. self-eval
數字 or 字串 or 真假值
● 自我求值
● 直接回傳值
● ex :
○ 7 => 7
○ “hello” => “hello”

14. symbol-eval
找出跟這個符號關聯的元素
● ex :
○ (define a 10)
○ a => 10

15. form-eval
● (f a b c)
○ f 為函數位置
○ a b c 為參數位置
○ 先將所有參數依序求值
○ 再將函數求值，確定函數的過程
○ 將參數帶入函數中求值
○ 回傳值

16. form-eval
● ex :
○ (+ 1 2) => 3
○ (+ 1 (+ 1 1)) => 3
○ (+ 1 (+ 1 2) 4 (/ 1 0)) => error

17. special form-eval
●
●
●
●
●
define
lambda
if
set!
begin

18. define
●
●
●
●
在環境中把symbol與value關聯起來
先對value部分求值
(define symbol value)
ex:
○
○
○
○
(define a 10)
(define b (+ 1 2))
(define a’ a)
(define copy-car car)
■ (copy-car (cons 1 2)) => 1

19. lambda
● lambda calculation !!!
● (lambda args body)
● ex:
○
○
○
○
○
○
○
(lambda (x) (+ 1 x))
((lambda (x) (+ 1 x)) 5) => 6
(define inc (lambda (x) (+ 1 x)))
(inc 5) => 6
(define (inc x) (+ 1 x))
(inc 5) => 6
TRY (lambda (x) (/ x 0)) !!!

20. if
● control structure
● (if test true-block false-block)
● ex:
○
○
○
○
(if #t 1 2) => 1
(if (> 1 2) “y” “n”) => “n”
(if (= 1 1) “y” “n”) => “y”
(if (> 2 1) “y” (/ 1 0)) => “y”

21. set!
●
●
●
●
side effect !!!
not pure function
(set! symbol new-value)
ex:
○ (define a 10)
○ (set! a 20)
○ a => 20

22. begin
● (begin form1 form2 form3 …. formN)
● ex:
○ (if #t (begin
(+ 1 1)
(set! a "in begin")
a)
"false") => 100

23. Recursion
●
●
●
●
scheme沒有 for ???
tail recursion
tail-call-optimization
need example

24. list-sum
(define (list-sum lis)
(if (null? lis)
0
(+ (car lis)
(list-sum (cdr lis)))))

25. tail-recursive
(define (lsum lis acc)
(if (null? lis)
acc
(lsum (cdr lis)
(+ acc (car lis)))))
(define (list-sum lis)
(lsum lis 0))

26. fibonacci number
(define (fib n)
(if (<= n 2)
1
(+ (fib (- n 1))
(fib (- n 2)))))

27. fibonacci number tail-recursive
(define (fib-tail-helper a b n)
(if (= n 0)
b
(fib-tail-helper b (+ a b) (- n 1))))
(define (fib-tail n)
(fib-tail-helper 1 1 (- n 2)))

28. remove
(define (remove x ls)
(if (null? ls)
'()
(if (eq? x (car ls))
(append '() (remove x (cdr ls)))
(append (list (car ls)) (remove x (cdr ls))))))

29. remove tail-recursive
(define (remove-tail-helper x ls acc)
(if (null? ls)
acc
(if (eq? x (car ls))
(remove-tail-helper x (cdr ls) acc)
(remove-tail-helper x (cdr ls) (append acc (list (car ls)))))))
(define (remove-tail x ls)
(remove-tail-helper x ls '()))

30. Let It Be Lambda
● (let ((n1 v1)
(n2 v2)
(n.. v…))
body)
= ( (lambda (n1 n2 n…) (body))
v1 v2 v…)

31. Local Variables
● (define x 20)
● (let ((x 10))
(+ x 1))
● (let ((x 5))
(set! x 6)
x)

32. Lexical Scope
(define scope 5)
(define (print-scope)
(display scope))
(let ((scope 100))
(print-scope)) => (display 5)

33. state
● state
(define (make-state init-value)
(let ((init init-value))
init))
(define a (make-state 5))
(define b (make-state 6))
(+ a b)

34. Let Over Lambda & Closure
(define inc-counter
(let ((counter 0))
(lambda ()
(set! counter (+ 1 counter))
counter)))
> (inc-counter) => 1
> (inc-counter) => 2

35. Let Over Lmabda Over Let Over Lmabda
(define (make-adder)
(let ((n 2))
(define add2
(lambda (x)
(+ x n)))
add2))
>(define my-add (make-adder))
> (my-add 2) => 4
> (my-add 8) => 10

36. Example: Stack class
(define (make-stack)
(let ((stack '()))
(define (push val)
(set! stack (cons val stack))
stack)
(define (pop)
(let ((tmp (car stack)))
(set! stack (cdr stack))
tmp))
(define (top)
(car stack))
(define (is-empty?)
(null? stack))
(lambda (op)
(cond ((eq? op 'push) push)
((eq? op 'pop) pop)
((eq? op 'top) top)
((eq? op 'empty?) is-empty?)
(else "error")))))

37. Example: Stack class
(define stack (make-stack))
(define top (stack 'top))
(define empty? (stack 'empty?))
(define push-stack (stack 'push))
(define pop-stack (stack 'pop))

38. Example: Stack class
> (push-stack 5) => (5)
> (top) => 5
> (push-stack 6) => (6 5)
> (pop-stack) => 6
> (top) => 5
> (push-stack 1) => (1 5)
> (push-stack 2) =>(2 1 5)
> (push-stack 3) =>(3 2 1 5)

39. Learn Lisp in Scheme
● 請原諒投影片很爛的code hightlight
● Question & Feedback make me
more perfect
contact me : ts771164@gmail.com (odie)

40. Thanks for your listening
next time - scheme 核心概念(二)