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list data

list data. list 만들기 nil : list link :  * list -> list list 사용하기 empty? : list -> bool first : list ->  rest : list -> list. map over list. (define (map f lst) (if (empty? lst) nil (link (f (first lst)) (map f (rest lst))) ) ). (define (inc n) (+ n 1))

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list data

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  1. list data • list 만들기 • nil : list • link :  * list -> list • list 사용하기 • empty? : list -> bool • first : list ->  • rest : list -> list

  2. map over list (define (map f lst) (if (empty? lst) nil (link (f (first lst)) (map f (rest lst))) ) )

  3. (define (inc n) (+ n 1)) (map inc ‘(1 2 3)) (define (square n) (* n n)) (map square ‘(1 2 3))

  4. fold over list (define (accumulate op init lst) (if (empty? lst) init (op (first lst) (accumulate op init (rest lst))) ) )

  5. binary tree data • tree 만들기 • leaf :  -> tree • node : tree * tree -> tree • tree 사용하기 • leaf-val : tree ->  • is-leaf? : tree -> bool • left-subtree : tree -> tree • right-subtree : tree -> tree

  6. map over binary tree (define (map f tr) (if (is-leaf? tr) (leaf (f (leaf-val tr))) (node (map f (left-subtree tr)) (map f (right-subtree tr)) )) )

  7. fold over binary tree (define (accumulate op tr) (if (is-leaf? tr) (leaf-val tr) (op (accumulate op (left-subtree tr)) (accumulate op (right-subtree tr)) ) ) )

  8. boolean circuit data • boolean circuit 만들기 • one: circuit • zero: circuit • not : circuit -> circuit • and : circuit * circuit -> circuit • or : circuit * circuit -> circuit • boolean circuit 사용하기 • is-one? : circuit -> bool • is-zero? : circuit -> bool • is-not? : circuit -> bool • is-and? : circuit -> bool • is-or? : circuit -> bool • nth-circuit : circuit * nat -> circuit

  9. map over boolean circuit (define (map f circuit) (cond ((is-one? circuit) (f one)) ((is-zero? circuit) (f zero)) ((is-not? circuit) (not (map f (nth-child circuit 0)))) ((is-and? circuit) (and (map f (nth-child circuit 0)) (map f (nth-child circuit 1)))) ((is-or? circuit) (and (map f (nth-child circuit 0)) (map f (nth-child circuit 1)))) ) )

  10. fold over boolean circuit (define (eval c) (cond ((is-one? c) 1) ((is-zero? c) 0) ((is-not? c) (bool-not (eval (nth-circuit c 0)))) ((is-and? c) (bool-and (eval (nth-circuit c 0)) (eval (nth-circuit c 1)))) ((is-or? c) (bool-or (eval (nth-circuit c 0)) (eval (nth-circuit c 1)))) ) )

  11. cascading over list (define (sum-odd lst) (accumulate + 0 (filter odd? lst) ) ) (define (sum-odd-square lst) (accumulate + 0 (map square (filter odd? lst)) ) )

  12. cascading over tree (define (sum-odd-squares tr) (accumulate + 0 (map square (filter odd? (enlist-leaves tr) ) ) ) )

  13. symbolic expression data • 식 만들기 • const : int -> expr • var : string -> expr • sum : expr * expr -> expr • product : expr * expr -> expr • 식 사용하기 • is-const? : expr -> bool • is-var? : expr -> bool • is-sum? : expr -> bool • is-product? : expr -> bool • const-val: expr -> int • var-name: expr -> string • addend: expr * nat -> expr • augend: expr -> expr • multiplier: expr -> expr • multiplicand: expr -> expr

  14. example: symbolic differentiation (define (diff e x) (cond ((is-const? e) …) ((is-var? e) …) ((is-sum? e) …) ((is-product? e) ...) (else (error “diff expects expr”)) ) )

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