HMWK1

Due: 1 March 2018, by end of class

1) Write a function called "ncopies", with the following type spec:

ncopies: string -> int -> string list

here is a couple of sample runs:

- ncopies 0 "x"   
val it = [] : string list
- ncopies 4 "x"
val it = [ "x", "x", "x", "x"] : string list


2)  Given the following data type:

datatype cTree = EMPTY |
                 NODE of string * int * cTree * cTree;

(where the node basically holds a string, and a count of how many times the string occurs)

you may presume that the append function is available (as defined in class).  

Write a function called detree with the type spec:
    detree : cTree -> string list

with the following sample runs:

- detree (NODE("x",2,(NODE("w",1,EMPTY,EMPTY),(NODE("y",3,EMPTY,EMPTY)));
val it = ["w", "x", "x", "y", "y", "y"] : string list

- detree EMPTY;
val it = [] : string list


3) Given a funtion called "concat", with type spec  concat: string list -> string

that works like this:

- concat ["x", "y", "z"]; 
val it = "xyz": string

and the functions:

fun curry f x y = f (x,y);
fun uncurry f (x,y) = f x y;

Determine the type specs of:

a) fun smush (a,b) = concat [a,b];

b) val smush2 = curry smush;


4) Finally, write a function which inserts strings into the cTree datatype.

Your function should have this typespec:  string -> cTree -> cTree


Note:  i) the strings should be stored in-order in the tree.
      ii) inserting another copy of a string should just increase the count field on that node.