Description
Throughout this chapter, we have used the SML/NJ language system in an interactive mode. For longer examples, it makes more sense to store your function definitions in a file [which you will submit]. Once you have created a file containing a definition or definitions, you can load it into an ML session by using the predefined use function. For example, if you have created a file called assign1.sml in the current directory, you can run your ML language system and type use “assign1.sml”; after the prompt. The ML language system will read the contents of the file just as if you had typed it one line at a time. After use finishes, you can continue typing interactive ML expressions, for example, to test the function definitions in your file.
Exercise 1
Exercise 2
Exercise 7 Write a function cycle1 of type ‘a list -> ‘a list whose output list is the same as the input list, but with the first element of the list moved to the end. For example, cycle1 [1,2,3,4] should return [2,3,4,1].
Exercise 8 Write a function sort3 of type real * real * real -> real list that returns a list of three numbers, in sorted order with the smallest first.
Exercise 9 Write a function del3 of type ‘a list-> ‘a list whose output is the same as the input list, but with the third element deleted. Your function need not behave well on lists with lengths less than 3.
Exercise 10 Write a function sqsum of type int -> int that takes a non-negative integer n and returns the sum of the squares of all the integers 0 through n. Your function need not behave well on inputs less than zero.
Exercise 11 Write a function ‘a list * int -> ‘a list that takes a list and an integer n as input and returns the same list, but with the first element cycled to the end of the list n times. (Make use of your cycle1 function from a previous exercise.) For example, cycle([1,2,3,4,5,6],2) should return the list [3,4,5,6,1,2].
Exercise 13 Write a function max of type int list -> int that returns the largest element of a list of integers, Your function need not behave well if the list is empty. Hint: Write a helper function maxhelper that takes as a second parameter the largest element seen so far. Then you can complete the exercise by defining
fun max x = maxhelper (tl x, hd x);
Exercise 14 Write a function isPrime of type int -> bool that returns true if and only if its integer parameter is a prime number. Your function need not behave well if the parameter is negative.
Write a function cube of type int -> int that returns the cube of its parameter.
Write a function cuber of type real -> real the returns the cube of its parameter.
Write a function min3 of type int * int * int -> int that returns the smallest of three integers.
Exercise 4
