[SOLVED] ocaml project

Introduction

The goal of this project is to get you familiar with programming in OCaml. You will have to write a number of small functions, each of whose specification is given below. In our reference solution, each function’s implementation is typically 3-6 lines of code; in a couple of cases you will want to write a helper function which will add another 3-6 lines.

This project is due in one week!We recommend you get started right away, going from top to bottom, and the problems get increasingly more challenging.

Getting Started

Download the following archive file p2a.zipand extract its contents.

Along with files used to make direct submissions to the submit server (submit.jar, .submit, submit.rb), you will find the following project files:

• Your OCaml program – basics.ml
• Ruby script to run public tests- test_all.rb . To run a specific test, read README .

You may want to use functions from testUtils.mlfor printing debugging messages, but your actual submission in basics.mlshould not print any output nor should it depend on the testUtils.ml file in any way.

To run an individual test, you can type commands like ocaml testRecursion1.ml. The output from the test will be printed to the console. You should compare it to the corresponding .outto see if it is correct (this is what goTest.rbdoes).

Note that you must implement your functions with the exact parameter and return type specified, or else the submit server tests will fail.

For this project the only OCaml libraries you are allowed to use are those defined in the Pervasivesmodule loaded by default. You are not allowed to use library functions found in any other modules, particularly Listand Array.

Part 1: Simple functions

Write the following functions:

Name	Type	Return value	Example
head_divisor l	int list -> bool	true if the head of the list divides the second element of the list false otherwise	head_divisor [1;2] = true head_divisor [2;5] = false
tuple_addr t	int * int * int -> int	the sum of the tuple’s elements	tuple_addr (1,2,3) = 6 tuple_addr (-10,50,30) = 70
caddr_int	int list -> int	the second element of the list -1 if the list has 0 or 1 elements	caddr_int [1;2;3] = 2 caddr_int [1] = -1

Part 2: Simple Curried Functions

A curried function is one that takes multiple arguments “one at a time”. For example, the following function sub takes two arguments and computes their difference:

 let sub x y = x - y

The type of this function is int -> int -> int. Technically, this says that sub is a function that takes an int and returns a function that takes another int and finally returns the answer, also an int. In other words, we could write

 sub 2 1

and this will produce the answer 1. But we could also do something like this:

 let f = sub 2 in f 1

and this will also produce 1. Notice how we call sub with only one argument, so it returns a function f that takes the second argument. In general, you can think of a function f of the type

 t1 -> t2 -> t3 -> ... -> tn

as a function that takes n-1 arguments of types t1, t2, t3, …, tn-1 and produces a result of type tn. Such functions are written with OCaml syntax

 let f a1 a2 a3 ... = body

where a1 has type t1, a2 has type t2, etc.Implement the following simple, curried functions:

Name	Type	Return value	Example
mult_of_n x y	int -> int -> bool	whether x is a multiple of y	mult_of_n 5 5 = true mult_of_n 2 3 = false
triple_it x y z	‘a -> ‘b -> ‘c -> ‘a*’b*’c	a tuple containing the three arguments, in order	triple_it 5 5 5 = (5,5,5) triple_it “hello” “b” “a” = (“hello”,”b”,”a”)
maxpair (x,y) (m,n)	‘a*’b -> ‘a*’b -> ‘a*’b	(x,y) if it is larger than (m,n), according to lexicographic ordering (m,n) otherwise (see note about comparison functions below)	maxpair (1,2) (3,4) = (3,4) maxpair (1,2) (1,3) = (1,3)

The OCaml comparison functions (=,<=,>=,<, and >) are polymorphic, so you can give them any two arguments of the same type.

Part 3: Recursive Functions

The rest of the project asks that you implement a number of recursive functions, many of which compute on lists.

Name	Type	Return value	Example
power_of x y	int -> int -> bool	returns true if y is a power of x false otherwise	power_of 2 8 = true power_of 0 5 = false
prod l	int list -> int	the product of all elements in l 1 if l is empty	prod [5;6] = 30 prod [0;5;3] = 0
unzip l	(‘a*’b) list -> (‘a list)*(‘b list)	a pair of lists consisting of the all first and second elements, respectively, of the pairs in l	unzip [(1,2);(3,4)] = ([1;3],[2;4]) unzip [(3,7);(4,5);(6,9)] = ([3;4;6],[7;5;9])
maxpairall l	(int*int) list -> int*int	the largest pair in input list l, according to lexicographic ordering (0,0) if l is empty	maxpairall [(1,2);(3,4)] = (3,4) maxpairall [(1,2);(1,3);(0,0)] = (1,3)
addTail l x	‘a list -> ‘a -> ‘a list	a new list where x is appended to the end of l	addTail [1;2] 3 = [1;2;3]
get_val x n	int list -> int -> int	element of list x at index n (indexes start at 0) -1 if n is outside the bounds of the list	get_val [5;6;7;3] 1 = 6 get_val [5;6;7;3] 4 = -1
get_vals x y	int list -> int list -> int list	list of elements of list x at indexes in list y, -1 for any indexes in y are outside the bounds of x (as with get_vals) elements must be returned in order listed in y	get_vals [5;6;7;3] [2;0] = [7;5] get_vals [5;6;7;3] [2;4] = [7;-1]
list_swap_val b u v	‘a list -> ‘a -> ‘a -> ‘a list	list b with values u,v swapped change value of multiple occurrences of u and/or v, if found change value for u even if v not found in list, and vice versa	list_swap_val [5;6;7;3] 7 5 = [7;6;5;3] list_swap_val [5;6;3] 7 5 = [7;6;3]
index x v	‘a list -> ‘a -> int	index of rightmost occurrence of value v in list x (indexes start at 0) -1 if not found	index [1;2;2] 1 = 0 index [1;2;2;3] 2 = 2 index [1;2;3] 5 = -1
distinct l	‘a list -> ‘a list	a new list that contains the distinct elements of l, in the same order they appear in l	distinct [1;2;2] = [1;2] distinct [2;1;2;2;3] = [2;1;3]
find_new x y	‘a list -> ‘a list -> ‘a list	list of members of list x not found in list y maintain relative order of elements in result	find_new [4;3;7] [5;6;5;3] = [4;7] find_new [5;6;5;3] [4;3;7] = [5;6;5]
power_list l	int list -> bool	true if each consecutive element is a power of the previous, false otherwise return true for []	power_list [3;9;81] = true power_list [9;7;5] = false

Submission

You can submit your project in two ways:

• Submit your basics.ml file directly to the submit server by clicking on the submit link in the column “web submission”.