recitation 14: environment diagrams

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Why bother?  

  * To formalize the scoping rules we've sorta ignored til now.

  * This is how scheme is implemented!  An environment is a list 
    of frames, a frame is a list of bindings, and a binding is a 
    list/pair of name & value! (We'll see this later in the term).

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Just follow the rules, no thinking required!

  * If it's a name, start at the current frame and find the closest
    binding (walk up the chain of frames as necessary).  If you don't 
    find it, error!

  * If it's a define, create a binding for this variable in the
    current frame.  If a binding already exists in the current frame,
    replace it.

  * If it's a set!, start at the current frame and find the closest
    binding of that variable (walk up the chain of frames as necessary).
    Change that binding to the new value.  If you don't find a binding,
    error!

  * If it's a lambda, create a double bubble.  First part points to
    the code (params & body).  Second part points to the current
    environment (where we are when we create the procedure).

  * If it's a procedure application (a combination):

     1. Evaluate all the subexpressions.

     2. Hang a new frame from the environment pointed to by the 
        environment pointer of the procedure we are applying.

     3. Create bindings in the new frame for the parameters listed in
        the code part of the procedure.

     4. Evaluate the body of the procedure in the new frame.

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Notes:

  * We start with a global environment that has all the built-in stuff
    defined.  It's sometimes handy to draw the built-in's we use.

  * As we're evaluating stuff, we always have a current environment
    (pointer to one frame that in turn points upwards to other frames,
    stopping at the global environment).

  * Where to use different colors: Every procedure is a different
    color.  When we apply a procedure, draw the new frame in the 
    same color as the procedure being applied.  (Check: All blue 
    frames should point to the same place as the environment pointer 
    of the blue procedure, etc.)

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(define (fact n)
  (if (= n 1) 
      1   
      (* n (fact (- n 1)))))
(fact 3)  -->

---------------------------------

(define x 0)
(define f
  (lambda (y)
    (define x (+ y 10))
    x))
(define g
  (lambda (y)
    (set! x (+ y 10))
    x))
(f 5)  -->
x      -->
(g 5)  -->
x      -->

---------------------------------

(define x 3)
((lambda (x y) (+ (x 1) y))
 (lambda (z) (+ x 2))
 3)  -->

---------------------------------

(define x 4)
(let ((x (+ 2 1))
      (y (square x)))
  (* x y))  --> 

DESUGARS TO:

((lambda (x y) (* x y))
 (+ 2 1)
 (square x)) --> 

---------------------------------

(define x 5)
(let ((x (lambda (x) (+ 6 x))))
  (set! x (x 7))
  x)  --> 

---------------------------------

(define a 5)
(define foo
  (let ((a 10))
    (lambda (x)
      (+ x a))))
(define (bar a) (foo 20))
(bar 100)  --> 

---------------------------------

(define (make-count-proc f)
  (let ((count 0))
    (lambda (x)
      (if (eq? x 'count) 
	  count
	  (begin (set! count (+ count 1))
		 (f x))))))

(define sqrt* (make-count-proc-2 sqrt))
(define square* (make-count-proc-2 square))

(sqrt* 4)  --> 
(sqrt* 'count)  --> 

(square* 4)  --> 
(square* 'count)  --> 

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