CS 2420-20 Homework 14

Due: Thursday, March 8th, 2012 9:10am

This assignment is essentially the same as HW 13, but using the interpreter with environments.

Part 1 – Testing Numbers

Start with miniracket3.rkt (same password as before).

Add support for booleans as values and expressions, and also add an iszero form that has a single sub-expression. If the value of the iszero sub-expression is 0, then the result should be true. If the value of the sub-expression is any other number, then the result should be false.

For example, assuming that you name the new expression structure iszero, (evaluate (make-iszero (make-minus 7 7)) empty (hash)) should produce #t — assuming that your representation of a boolean value is a Racket boolean — while (evaluate (make-iszero (make-plus 7 7)) empty (hash)) should produce #f.

Part 2 – Adding Conditionals

Add an if form to the language. You will need to name the structure for if forms something other than if, perhaps branch.

For example, assuming that you name the new expression structure branch and that you represent Mini Racket booleans using Racket booleans, then (evaluate (make-branch (make-iszero 0) 1 0) empty (hash)) should produce 1, while (evaluate (make-branch (make-iszero 6) 1 0) empty (hash)) should produce 0.

As an extended example,

  (evaluate (make-app 'fact 6)
            empty
            (hash 'fact
                  (make-function 'n
                                 (make-branch (make-iszero 'n)
                                              1
                                              (make-times 'n (make-app 'fact
                                                                       (make-minus 'n 1))))
                                 empty)))

should produce 720.