scheme 核心概念(一)StorySense

1. Functional Language ?2. LISP ?3. Data type4. Forms & Eval5. Recursion6. Local Variables

scheme 核心概念(一)

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

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

Data Type

● booleans ○ (not #t) => #f

● numbers○ 1○ 3.14○ 1/2○ 1+i

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

Data Type

● Dotted pairs & lists○ (1 . 2) => pair○ (1 2) => list○ pair make list

■ cons■ car■ cdr

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

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

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)

Forms & Eval

● express value

● 7 => 7● (+ 1 2) => 3● (if #t 1 2) => 1 ● (define a (+ 1 (* 3 4))) => a● (lambda (x) (+ 1 x)) => #<procedure>

eval

Eval

● self-eval● symbol-eval● form-eval● special form-eval

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”

symbol-eval

找出跟這個符號關聯的元素

● ex :○ (define a 10)○ a => 10

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

form-eval

● ex :○ (+ 1 2) => 3○ (+ 1 (+ 1 1)) => 3○ (+ 1 (+ 1 2) 4 (/ 1 0)) => error

special form-eval

● define● lambda● if● set!● begin

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

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)) !!!

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”

set!

● side effect !!!● not pure function● (set! symbol new-value)● ex:

○ (define a 10)○ (set! a 20)○ a => 20

begin

● (begin form1 form2 form3 …. formN)● ex:

○ (if #t (begin (+ 1 1) (set! a "in begin") a) "false") => 100

Recursion

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

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

tail-recursive

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

fibonacci number

(define (fib n) (if (<= n 2) 1 (+ (fib (- n 1))

(fib (- n 2)))))

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)))

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))))))

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 '()))

Let It Be Lambda

● (let ((n1 v1) (n2 v2)

(n.. v…)) body)= ( (lambda (n1 n2 n…) (body)) v1 v2 v…)

Local Variables

● (define x 20)

● (let ((x 10)) (+ x 1))

● (let ((x 5)) (set! x 6) x)

Lexical Scope(define scope 5)(define (print-scope)

(display scope))

(let ((scope 100))(print-scope)) => (display 5)

state

● state(define (make-state init-value)

(let ((init init-value))init))

(define a (make-state 5))(define b (make-state 6))(+ a b)

Let Over Lambda & Closure(define inc-counter

(let ((counter 0))(lambda ()

(set! counter (+ 1 counter)) counter)))

> (inc-counter) => 1> (inc-counter) => 2

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

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")))))

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))

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)

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