CS 227 Let and Letrec terminology and uses

* Problems
   The two main problems to be solved by let and letrec are preventing
    ____________________________ and _______________________________
* let
   The syntax of LET is as follows


   
   The value returned by
       (let ((y 1))
	 (let ((y (+ y 3))
	       (x (+ y 2)))
	   (+ x y)))
   is _____.   Why isn't it 10 or 4? _______________________________________.

   Suppose z is not defined yet.  What happens to
       (+ (let ((z (* 3.14 2.73)))
	    (f z z))
	  z)
   when it is executed? ____________________________________________________

   Why is the value of the following
       (let ((x 4))
	 (let ((x (* x x)))
	   (let ((x (* x x)))
	     (+ x x))))
   512? _______________________________________________________

* Environments
** in general
   An *environment* can be thought of as a _______________  or _______________
   that maps __________________ to ___________________.

   Draw a picture of an environment here:





   A *binding* is ________________________________, made by LET or LAMBDA.
   A variable in a LET or LAMBDA is *bound* by that LET or LAMBDA if
   __________________________________________________________________.
   Such variables are called *formal parameters*.
   A variable is *free* in an expression if it occurs _______________
   __________________________________________________________________.

   The bound free variables of the expression
      ((LAMBDA (f y)
	 (f a (f y z)))
       f 3)
   are ____________.  The bound variables are __________________.
** global
   The *initial global environment* maps names like _________________________
   but not keywords, like define and let, to their standard values

   The *user global environment* consists of the _____________________________
   plus our own __________________________ made using the keyword ____________.

** local
   the result of the following code
	    (define x 2)
	    (define square
		(lambda (x)
		   (* x x)))
            (square 3)
   is: __________________
   and then the result of the expression, x, is ________________
   
   Draw a line from the x's in (* x x) to the place that they refer.
   
** Nesting
   The result of the following code:
	(let ((+ cons))
	    (let ((z 3.14159))
		 (+ (- z 1) z)))
   is  ___________________________________

   Is a procedure name a variable?  ________________

   Draw a picture of the environment for
 
     ((lambda (f y)
        (f a (f y z)))
      + 3)

* Scope of a binding
   The *scope of a binding* is the _____________ of the program
   in which ___________________________________________.

** Hole
   A *hole in the scope* is an area of the program for which
   ________________________________________________________.

** Lexically scoped (Statically scoped)
   A programming language is *lexically scoped* if
   the scope of a binding can be determined ___________________________.

   A language is *dynamically scoped* if the scope of a binding
   can (in general) only be determined _______________________________.

** Closures
   A procedure object is formed by ___________________
   and is also called a ________________________.

   A closure remembers the procedure's parameters, it's code
   and ________________________________________.

   Consider the code...
	(DEFINE add2
	  (LET ((two   2))
	    (LAMBDA (x) (+ x two))))
   Fill in the details of the following for the evaluation of the DEFINE above
	Env0:
	    +  ~~~> [proecdure|args|...|Env0]
	  add2 ~~~>  [procedure | (x) | (+ x two) |_________]

	  (LET ((two   2))
	    (LAMBDA (x) (+ x two))))   ;; this happens when _________________

        Env1 (parent Env0):
           two ~~~> [___]

       	    (LAMBDA (x) (+ x two))))   ;; this happens when _________________

   Continuing from the above, fill in the details for the evaluation of
	(LET ((b   0.5))
	  (/ b (add2 b)))

        Env2 (parent _______):
	     b ~~~> [_____]

	  (/ b (add2 b))               ;; this is the _______________________

        Env3 (parent ________):
             x ~~~> [_______]

             (+ x two)                 ;; this is the body of _______________

   In the evaluation of (+ x two), the value of the variable two is found by
   looking in Env3, and then its parent environment: ______________.
   That environment is the parent of Env3 because _________________.

   What would be different if we had defined add2 as follows?
	(DEFINE add2
         (LAMBDA (x)
           (LET ((two   2))
             (+ x two))))

** letrec
   You need to use LETREC instead of LET to define _______________________.

   The main difference between LET and LETREC is ______________________
   ____________________________________________________________________.

   Give an example of using LETREC to avoid passing unchanging parameters.