F# has a predened list datatype. Strictly speaking, however, it is not necessary, For instance, integer lists could be simulated by the following user dened datatype type ilist = E | L of int * ilist where the constructor E stands for the empty list and the constructor L builds a new list by adding a number in front of another list. Then one can represent, say, a list with elements 1,4,6,7, in that order, with the ilist value L(1, L(4, L(6, L(7, E)))). 1 Using pattern matching and recursion, implement the following functions manipulating ilist values

4. Write an F# function remove: int-> ilist-> ilist which, given an integer x and a list l, "removes" all the occurrences of x from l, that is, returns a list containing (in the same order) all and only the elements of l that differ from x. For example, remove 2 (L(1, L(2, L(3, L(3, L(2, E)))))) sL(1, L(3, L(3, E))); remove 5 (L(1, L(2, L(3, )))) is (L(1, L(2, L(3, E)))). 5. Write an F# function move: ilist-> ilist-> ilist which takes two lists and returns the result of inserting the values of the first list into the second, in reverse order. For example, move (L(1, L(2, L(3, E)))) (L(7,E)) is L(3, L(2, L(1, L(7,E))))