Quiz 3 review and Recursion in AAQZ4

1. a: (list 7 “apple” 2) b: (list 4 4 4)

   what is (length (cons a b))

   = 1 + (length b)

   = 1 + 3

2. a : (list 9 “hello”) b : (list “a” 44 “b”)

   what is (second (cons a b))

   = (first (rest (cons a b)))

   = (first b)

   = “a”

3. ’(24 () v)

   (cons 24 (cons ’() (cons v ’())))

4. (define (whistly [l : (Listof Booleab)]) : String (match l [’() ’()] [(cons f r) … (cons f (whistly r)) …]))
5. Match case for langauge

   <exp>::= <real num>
          | {sub <expr> <rea num>}

Abstract Syntax Definitions Given

(define-type Exp (U ListNum Sub))

(struct LitNum ([n : Real]))

(struct Sub ([e : Exp] [n : Real])

        (define (parse [c : Sexp]) : Exp
                (match c
                 [(? real? n) (LitNum n)]
                 [(list 'sub x (? real? n)) (sub (parse x) n)]))

{bind [fact = {(n) > {if {< n 0 {* n {fact {+ n 1}}}}}}]}

fact is not in scope here but what if we pass in fact…

:{bind [fact = {(self n) > {if {< n 0 {* n {self self {+ n 1}}}}}}]}

{fact fact 4}}