quiz3-soln-fall11 - (x,y:t> if k = 1 then y...

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CMSC330 Fall 2011 Quiz #3 Solutions 1. (8 pts) OCaml Types and Type Inference a. (3 pts) Give the type of the following OCaml expression fun x -> [ x 1 ] Type = (int->’a) -> (‘a list) b. (3 pts) Write an OCaml expression with the following type ‘a list -> ‘a Code = fun (x::y) -> x fun x -> match x with h::t -> h c. (2 pts) Give the value of the following OCaml expressions. If an error exists, describe the error. (fun x -> fun y -> x+y) 6 4 Value = 10 2. (16 pts) OCaml Programming a. (8 pts) Write a curried function findKth which when given a number k and a list lst of int (key, value) pairs , returns the kth value in the list. You may use map or fold if you wish, but it is not required. You may assume lst contains at least k pairs. Example: findKth 1 [(1,2);(5,9);(9,3)] = 2 // since 2 is 1st value findKth 2 [(1,2);(5,9);(9,3)] = 9 // since 9 is 2nd value let rec findKth k lst = match lst with
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Unformatted text preview: (x,y)::t -> if k = 1 then y else (findKth (k-1) t) b. (8 pts) Using either map or fold and an anonymous function, write a curried function findGreaterThan which when given a number n and a list of ints lst, returns a list of all elements of lst greater than n (maintaining their relative ordering). You may assume (x > y) returns true when x is larger than y. Example: findGreaterThan 20 [33;18;21;19] = [33;21] findGreaterThan 65 [33;18;21;19] = let findGreaterThan v lst = List.rev (fold (fun a h -> if (h > v) then (h::a) else a) lst) 3. (6 pts) Context Free Grammars Consider the following grammar: S & E+E | E*E E & 0 | 1 | n | (S) a. (2 pts) What is the set of strings accepted by this grammar? Arithmetic expressions involving + and *. b. (4 pts) Provide a leftmost derivation of the string “(n+1)*n” for this grammar. S & E*E & (S)*E & (E+E)*E & (n+E)*E & (n+1)*E & (n+1)*n...
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