CS450- Assignment 2 Implement a Memory Cell and Tail-Recursive Function Intersperse Solved

1.   Your goal is to implement a memory cell encoded with functions as data. Recall §2.1.3 of the SICP book, in particular the implementation of functions cons, car, and cdr.

A memory cell is a function value that expects exactly one argument: a list. According to the contents of the list, the memory cell should perform one of two operations:

•    Operation set. The argument is a list with exactly one element. The memory cell must return a new memory cell.

•    Operation get. The argument is an empty list. The memory cell returns the value contained in the memory cell.

The following two definitions can be used to interact with any memory cell:

(define (cell-get c) (c (list)))

(define (cell-set c x) (c (list x)))

(b)    Implement a read-write cell. Function rw-cell takes a number that initializes the memory cell. Operation set returns a new cell with the value given. Operation get returns the contents of the cell.

(c)     Implement a read-only cell. Function ro-cell takes a number and return a read-only cell. Operation set should not change the stored value and return a cell with the same contained value. Operation get returns the initial value.

2.   Implement a tail-recursive function intersperse that takes a list l and an element e and returns a list with the elements in list l interspersed with element e. The implementation must only use the list constructors and selectors that we covered in our class. That is, return a list where we add element e between each pair of elements in l.

3.   Implement a tail-recursive function find that takes as arguments a function predicate and a list l and returns either a pair index-element or #f. The implementation must only use the list constructors and selectors that we covered in our class. The objective of the function is to find a index-element in a list given some predicate. Function find calls function predicate over each element of the list until the predicate returns true. If predicate returns true, then function find returns a pair with the zero-based index of the element and the element.

Function predicate takes an integer (the zero based index in the list) and the element we are trying to find.

(a)    Implement function find.

(b)    Implement function member in terms of function find. Function member takes an element x and a list l and returns #t if the element x is in list l, otherwise it returns #f.

(c)     Implement function index-of in terms of function find. Function index-of takes a list l and an element x and returns the index of the first occurrence of element x in list l, otherwise it returns #f.

4.   Implement function uncurry which takes as argument a curried function f and returns a new function which takes as parameter a list of arguments which are then applied to f. The implementation must only use the list constructors and selectors that we covered in our class.

5.   Recall the AST we defined in Lecture 5. Implement function parse-ast that takes a datum and yields an element of the AST. You will need as auxiliary functions real? and symbol? from Racket’s standard library and functions lambda?, define-basic?, and define-func? from Homework Assignment 1 (Part II).

The function takes a datum that is a valid term. Your function should only handle functions declarations, definitions, variables, and numbers. Do not handle conditionals nor handle booleans.