Interpreter Project

Part 3: Primitive Procedures

car, cdr, cons, +, -, *, <, >, =, etc.

Part 3 was due at 9:55 am Thursday, April 25th
All parts due: NOON on Sunday, May 12th

Quick link: Summary page

Wrapping up Part 2: Test and handin37 and update37

Remember, each step of the interpreter assumes that you have successfully completed the previous step. By writing comprehensive tests (in i-tests.rkt), you can be sure that the code you have written so far works properly. The responsibility for testing each section is yours.

If you are still working on Part 2, please let me know if you need help. It is important that you don't fall behind.

To get the code for Part 3 and some wrap-up tests from Part 2, you will first need to run update37. Once you have done so, you will have created a new directory (cs37/labs/i-3) which has the new i-tests and interpreter pieces.

To join your old code and tests (from cs37/labs/i-2) with the new code and tests in cs37/labs/i-3, follow these steps:

  1. Change to the i-3 directory: cd ~/cs37/labs/i-3
  2. Run the merge script to join your old files and the new files together ./merge
Assuming you successfully merged your old and new files together, you should have a new interpreter.rkt and i-tests.rkt file in your cs37/labs/i-3 directory.

The wrap-up tests for Part 2 simulate the interactions with the interpreter which are shown below. Your interpreter should successfully run the tests in i-tests.rkt, but it is strongly recommended that you type some or all of the code in by hand to verify that the interactions are working properly:

> (repl)            ; or (read-eval-print-loop) if you like typing
INTERPRETER> (set! x 5)
set! cannot set undefined identifier:  x
> (repl)
INTERPRETER> (define x 5)
INTERPRETER> (set! x 8)
INTERPRETER> (define z 'hello)
INTERPRETER> (define y z)
INTERPRETER> (set! z "testing...1...2...3...")

If your code passes all the tests, you should turn in your completed version of Part 2 using handin37.

Introduction to Part 3: Primitives

In today's portion, you will add the ability to evaluate expressions that use Racket's primitive procedures. We will not write our own implementations of these primitive procedures; rather, when a user of our interpreter asks to evaluate an expression with a primitive procedure, we will call the Racket primitive. This will save us from having to write our own versions of procedures like +, <, and cons. Recall that this is exactly what we did with F♭: when we wanted to add two numbers we just used the built-in + function already in Haskell.

In order to properly handle expressions which involve calls to primitive procedures, it is important to recall the rule of evaluation for Racket procedure applications. Assume that x has been defined as 8 and y has been defined as 9. When Racket encounters an expression such as (= x y), Racket first determines the type of the expression to be a procedure application. Racket knows the expression is a procedure application because:

  1. the expression is a list, and
  2. the first element of the list is not a special form, such as quote or define (which we implemented in Part 2) or begin or if (which we will implement in Part 4) or any other special form you implement in Part 6.

To evaluate (= x y), Racket first evaluates = to get the primitive implementation for numerical equality tests. (To see that Racket really does this, type = on a line by itself in Racket: it evaluates to #<procedure:=>.) Next, Racket evaluates the variable x to get 8 and it evaluates the variable y to get 9. (You handled evaluation of variables in Part 2.) Now that all of the elements of the list (= x y) have been evaluated, we apply the procedure #<procedure:=> to the arguments 8 and 9 (to get #f).

Since the name apply has already been taken by the real Racket interpreter, we will call our apply function i‑apply (short for interpreter-apply).

(Partially) implementing i-apply

In order to implement primitive functions, we will begin by working on the implementation necessary for handling procedure applications. (See the summary page for details.) We will start by writing the definitions of the tester and selector functions for applications:

(application? exp)    
(operator exp)
(operands exp)
The function application? should return #t if the expression is a procedure application. Use the definition provided in the introduction, but do not worry if the expression is a special form for now, we will deal with this case later. Note that the application? is trivial to write. The selector functions operator and operand should be clear, as well. For example:
(application? '(cons 1 y)) ; => #t
(application? '(newline))  ; => #t
(application? 'cons)       ; => #f
(operator '(cons 1 y))     ; => cons
(operands '(cons 1 y))     ; => (1 y)
(operands '(newline))      ; => ()

Note that you want (application? '()) to return #f.

Once we know that an expression is a procedure application, we have to evaluate each of the procedure arguments. To do this, we will write a helper function called eval-operands that evaluates each element in the list of the operands, and returns a new list containing the evaluated operands. (This list of evaluated operands will become the args parameter to the function i-apply.)

eval-operands should perform as follows:

(define env1 (extend-env '(a b c) '(1 0 8) empty-env))
(eval-operands '(a 9 b c a) env1) ; => (1 9 0 8 1)

Before continuing with our implementation of i-apply, we need to look at how primitive functions will be implemented in our interpreter.


Now that we can evaluate the operands in a procedure application, we need to determine the appropriate procedure to apply by evaluating the first element in the list (e.g. +, as shown in the introduction). For primitive functions, this means that we will need have each of the primitive procedure names bound to their implementations in the global environment.

We could bind the symbol car directly to the procedure which implements it, and we could bind the symbol cons directly to the procedure that implements it, and so forth. But, we would like a way of determining whether the symbol is bound to a primitive procedure or a user-defined procedure (created with lambda which we will implement in Part 5). To do this, we will "tag" each primitive procedure with the symbol primitive followed by the procedure's name and its implementation. We will do this using the procedure make-primitive:

(define make-primitive
  (lambda (name proc)
    (list 'primitive name proc)))

;; for example
(make-primitive 'car car) ; => (primitive car #<procedure:car>)
We could actually write our own implementations of each of Racket's primitive procedures. For example, we could say:
(define addition
  (lambda (x y)
     (cond ((< x 0) (addition (add1 x) (sub1 y))) 
           ((= x 0) y)
           ((= y 0) x)
           (else (addition (sub1 x) (add1 y))))))

(make-primitive '+ addition)
Doing this for each of Racket's primitives would be tedious. In fact, you'd probably end up using Racket's primitives to implement yours, and your versions would be slower than Racket's versions. It's important to note that using Racket's primitives to implement your primitives is not "cheating". If you were writing a Racket interpreter in C or Java, you'd use Java's implementation of + when writing the Racket implementation of + wouldn't write it from scratch why do you feel the need to do so here?

Since we will just use Racket's implementation for each of the primitives that we would like in our interpreter, we could simply say:

(make-primitive '= =) ; => (primitive = #<procedure:=>)
(make-primitive 'cons cons) ; => (primitive cons #<procedure:cons>)

See the code included in this part's interpreter.rkt file to see how this is actually done.

Write the tester and selector functions for primitives (see the summary page for details):

primitive-procedure?       ;is the procedure the result of calling make-primitive?
primitive-name             ;returns the name of the primitive
primitive-implementation   ;returns the implementation of the primitive
Once these have been completed, you should test the new version of setup-env which I have provided for you.

This new version of setup-env will add the definitions of many primitives to the global environment. In addition, the list primitive-procedures provides an easy way for you to add other primitive functions in the future, should you wish to do so. (You will likely need to do this in Part 6 to create your meta-circular interpreter). Be sure you understand how primitives work in our interpreter.

Completing primitive procedure application

To complete the implementation for primitive procedure application, you will need the definitions for i-apply and apply-primitive-procedure, which I have provided below:

(define i-apply
   (lambda (proc vals)   ;; note: these "vals" have already been evaluated
      ((primitive-procedure? proc) (apply-primitive-procedure proc vals))
      (else (error "unknown procedure type" proc)))))

(define apply-primitive-procedure
   (lambda (proc vals)
     (apply (primitive-implementation proc) vals)))
You can then add the following line to our conditional test in i-eval:
((application? exp) (eval-application exp env))
This leaves you to write eval-application, which will evaluate a procedure application in an environment.

Since the application? test is a very general test -- it matches both procedure applications and special forms -- be sure you place the test after you have exhausted all of the tests for special forms.

Part 3 Conclusion

Your interpreter should now handle the following tests. You must write your own tests that follow the format provided in the i-tests.rkt file.

INTERPRETER> (define x 8)
INTERPRETER> (define y (+ x 1))
INTERPRETER> (define lst (cons x (cons '(x y z) (cons y null))))
(8 (x y z) 9)
INTERPRETER> (define z (+ (car lst) (car (cdr (cdr lst)))))
INTERPRETER> (= (+ x y) z)
INTERPRETER> (define w *)

You should have completed this by 9:55 am Thursday, April 25th.
Continue to part 4.