CS 2420-20 Homework 13

Due: Tuesday, March 6th, 2012 9:10am

Part 1 – Testing Numbers

Start with miniracket2.rkt (password required; check your e-mail).

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)) (hash)) should produce #t — assuming that your representation of a boolean value is a Racket boolean — while (evaluate (make-iszero (make-plus 7 7)) (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) (hash)) should produce 1, while (evaluate (make-branch (make-iszero 6) 1 0) (hash)) should produce 0.

As an extended example,

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

should produce 720.