No Code. Theoretical analysis Only

Define the following operations for our previous modeling of lists as Cartesians: (a) length of a list (len function): This function returns the number of elements that a list contains. (b) index set of a list (inds function): The set of indices of the elements in the list, from 1 to and including the length of the list. If the list is empty the index set is the empty set. (c) element set (elems function): This function returns the set of distinct elements of the list. If the list is empty then the element set is empty. (d) The list indexing operation 11), where if the list is empty then the operation is undefined, i.e. ends in the result chaos