3.2 the environment model

3/2/jord/notes.org

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+* 3.2 the environment model of evaluation
+
+substitution has failed with the new power of assignment.
+
+the substitution model:
+  to apply a compound procedure to its arguments, eval the body of the
+  procedure with the formal params replaced by the corresponding
+  argument.
+
+a variable is no longer a name for a value. now it must designate a
+"place" where its value lies.
+
+these new structures are called /environments/.
+
+an environment is a sequence of /frames/.
+
+each frame is a table of /bindings/.	( a frame has at most one
+					    binding per variable)
+
+each frame has a pointer to its /enclosed environment/
+					(unless it is the /global/
+					    environment ) 
+
+a variable's value 
+  with respect to its environment is
+    the value given by 
+      the binding of the variable 
+        in the first frame
+          in the environment 
+            that contains a binding 
+              for that variable.
+  if no frame in the sequence 
+    specifies a binding
+      for the variable
+        then the variable is
+          /unbound/
+
+a binding overiding a different value in a higer frame is /shadowed/ 
+  by the other binding
+
+** 3.2.1 the rules for evaluation
+to evaluate a combination:
+  1. evaluate the subexpressions of the combinataion
+  2. apply the value of the operator subexpression to the values of
+     the operand subexpressions
+
+in the environment model of evaluation, a procedure is a pair
+consisting of:
+  - some code
+  - a pointer to an environment
+
+to apply a procedure to arguments, create a new environment containing
+a frame that binds the parameters to the values of the arguments
+
+the environment model of procedure application can be given by two
+rules:
+
+  - a procedure object is applied to a set of arguments by
+    constructing a frame, binding the formal parameters of the
+    procedure to the arguments of the call and then evaluating the
+    body of the procedure in the context of the new environment
+    constructed. the new frame has as its enclosing environment the
+    environment part of the procedure object being applied
+  - a procedure is created by evaluating a lambda expression relative
+    to a given environment. the resulting procedure object is a pair
+    consisting of the text of the lambda expression and a pointer to
+    the environment in which the procedure was created
+  - define creates a binding in the current frame, assigning the value
+    to the symbol
+  - (set! variable value) locates the binding of the variable in the
+    environment and changes that binding to a new value
+
+** 3.2.2 applying simple procedures
+
+#+BEGIN_SRC scheme
+  (define (square x)
+    (* x x))
+  (define (sum-of-squares x y)
+    (+ (square x) (square y)))
+  (define (f a)
+    (sum-of-squares (+ a 1) (* a 2)))
+  (f 5)
+#+END_SRC
+
+** 3.2.3 frames as the repository of local state
+
+#+BEGIN_SRC scheme
+  (define (make-withdraw balance)
+    (lambda (amount)
+      (if (>= balance amount)
+	  (begin (set! balance (- balance amount))
+		 balance)
+	  "insufficient funds")))
+  (define W1 (make-withdraw 100))
+  (W1 75)
+#+END_SRC
+
+** 3.2.4 internal definitions
+
+#+BEGIN_SRC scheme
+  (define (sqrt x)
+    (define (good-enuf? guess)
+      (< (abs (- (square guess) x)) 0.001))
+    (define (improve guess)
+      (average guess (/ x guess)))
+    (define (sqrt-iter guess)
+      (if (good-enuf? guess)
+	  guess
+	  (sqrt-iter (improve guess))))
+    (sqrt-iter 1.0))
+#+END_SRC
+
+with internal definitions:
+  - names of procedures do not interfere with others in the bigger
+    environment
+  - local procedures can access enclosing arguments via free vars