Download OCaml Functions and Java List Concatenation with Abstract Syntax Trees and more Papers Computer Science in PDF only on Docsity! 1. Gives the types of the following Ocaml functions. (All are type-correct.) (a) let a x y = x+y (b) let b (x,y) = x+y (c) let c (x,y) = x (d) let d x = match x with (a,b) -> a (e) let e x = hd x + 1 (f) let f x y = match x with [] -> 0 | a::b -> a+y (g) let g (a,b) (c,d) = (a+d, b^c) (Recall that ^ is the string concatenation operation.) (h) let rec h x = match x with [] -> 0 | (a,b)::r -> a + (h r) 2. Define the following Ocaml functions: (a) genlist m n = [m; m+1; ... ; n] (or [] if m>n) (b) concatWithComma [s1; s2; ...; sn] = s1 ^ “,” ^ s2 ^ ... ^ sn (c) compress: int list -> (int * int) list replaces runs of the same integer with a pair giving the count and the number. E.g. compress [1;1;5;6;6;6;3] = [(2,1); (1,5); (3,6); (1,3)] (d) apply: string -> int list -> int applies the operator described by the string argument to the elements in the int list. The string argument can be either “times” or “plus”. apply “times” [2;3;4] = 24 Assume the int list argument is non-empty. 3. Suppose we are given the following type definition: type btree = leaf of int | node of int * btree * btree Define the following functions in Ocaml: (a) preorder: btree -> int list gives the preorder listing of the labels of the tree. E.g. let t = node(1, node(2, leaf(4), leaf(5)), node(3, leaf(6), leaf(7))) preorder t => [1; 2; 4; 5; 3; 6; 7] (b) followpath: btree -> boolean list -> int list gives the list of integers in the tree on the path described by the boolean list, where “true” means follow the left child and “false” means follow the right child. You may assume that the path described by the boolean list actually exists in the tree. E.g. followpath t [true; false] => [1; 2; 5] (c) height: btree -> int gives the height of a tree, defined as the length of the longest path from the root to a leaf node. height t;; => 2 (d) balanced: btree -> boolean returns true if for every internal node, the heights of its children differ by no more than 1. balanced t => true let t1 = node(1, leaf(2), node(3, leaf(6), leaf(7))) => true let t2 = node(1, leaf(2), node(3, leaf(6), node(8, leaf(7), leaf(9))) => false 4. Given this Java class definition: class List { public int h; public List t; public int hd () { return h; } public List tl () { return t; } public List (int h, List t) {this.h = h; this.t = t; } } The empty list is represented by null. Define the Java function to concatenate two lists: public static append (L1, L2) { } 5. Given the grammar: E -> E + T | T T -> T * P | P P -> id | ( E ) and an Ocaml type for trees:
