Manipulating Boards

In this assignment, we will start focusing on the boards. A natural representation for the board is a matrix (which Ocaml represents as an array of arrays). Each position of the matrix is one of our four possibilities:

type position = Plain | Water | Wall | Home
type board = position array array

Your task is to write the following functions:

Write a function getDims which takes a board and returns a pair of integers which are the number of rows and the number of columns in the board.
Write a function isSafe which takes a board and a pair of integers (i,j). The function should return true or false depending on whether the location (i,j) is safe or not. A location is safe if it is either Plain or Home, and unsafe otherwise.
Write a function getNeighbors which takes a board and a pair of integers (i,j). The function should return a list of all locations which are to the East, West, North, and South, unless of course the given input location is on an edge or corner.
Write a function getSafeNeighbors which takes a board and a pair of integers (i,j). The function should return a list of all neighboring locations which are also safe locations. You should and in fact must reuse the previous two functions to solve this one.
Create some boards, and test your code on them. Your samples and tests much be included with your submission.