midterm1-fall12-blank

# Fill in the description string of the runtest

• Notes
• 10

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Fill in the description string of the run_test function with a short explanation of why the test case is interesting. i. let test () : bool = [1;0;2;0;3] = (interspserse 0 [1;2;3]) ;; run_test "comes from the problem description" test ii. let test () : bool = _________ = (intersperse _________ _______________________) ;; run_test "___________________________________________________" test iii. let test () : bool = _________ = (intersperse _________ _______________________) ;; run_test "___________________________________________________" test iv. let test () : bool = _________ = (intersperse _________ _______________________) ;; run_test "___________________________________________________" test 2

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(12 points) Step 4 is implementing the program . Fill in the body of the intersperse function to com- plete the design. Do not use any list library functions (such as fold , or @ ) to solve this problem. If you would like to use a helper function in your answer, you must define it. let rec intersperse (c:______________) (l:______________) : ______________ = 3
2. List Processing (20 points) For each of the following programs, write the value computed for r : a. let rec h (l:int list) : int = begin match l with | [] -> 0 | x::xs -> x * (h xs) end let r : int = h [1;2;3] b. let rec g (l:’a list) : ’a list = begin match l with | [] -> [] | [x] -> [x] | x::y::xs -> if x < y then x::(g (y::xs)) else y::(g (x::xs)) end let r : int list = g [1;3;2;0] c. let rec f (p: ’a -> bool) (l:’a list) : ’a list * ’a list = begin match l with | [] -> ([], []) | x::xs -> let (l,r) = f p xs in if p x then (x::l, r) else (l, x::r) end let r : (int list * int list) = f ( fun (x:int) -> x > 0) [0;1;2;-3;4] 4

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The last two programs refer to the following definitions. let rec transform (f: ’a -> ’b) (x: ’a list): ’b list = begin match x with | [] -> [] | h :: t -> (f h) :: (transform f t) end let rec fold (combine: ’a -> ’b -> ’b) (base: ’b) (x: ’a list): ’b = begin match x with | [] -> base | h :: t -> combine h (fold combine base t) end d. let k (x: ’a list) : ’a list = fold ( fun (h:’a) (v:’a list) -> v @ [h]) [] x let r : int list = k [1;3;2;4] e. let j (x : int list list) : int list = let transformer (l:int list) : int = fold ( fun (x:int) (v:int) -> x + v) 0 l in transform transformer x let r : int list = j [[1;2;3];[4;5];[]] 5
3. Types (16 points) For each OCaml value or function definition below, fill in the blank where the type annotation could go or write “ill typed” if there is a type error. If an expression can have multiple types, give

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• Fall '09
• int list, int tree

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