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Separating Syntactic Analysis from Execution

The evaluator implemented above is simple, but it is very inefficient, because the syntactic analysis of expressions is interleaved with their execution. Thus if a program is executed many times, its syntax is analyzed many times. Consider, for example, evaluating (factorial 4) using the following definition of factorial:

(define (factorial n)
  (if (= n 1)
      (* (factorial (- n 1)) n)))

Each time factorial is called, the evaluator must determine that the body is an if expression and extract the predicate. Only then can it evaluate the predicate and dispatch on its value. Each time it evaluates the expression (* (factorial (- n 1)) n), or the subexpressions (factorial (- n 1)) and (- n 1), the evaluator must perform the case analysis in eval to determine that the expression is an application, and must extract its operator and operands. This analysis is expensive. Performing it repeatedly is wasteful.

We can transform the evaluator to be significantly more efficient by arranging things so that syntactic analysis is performed only once.[*] We split eval, which takes an expression and an environment, into two parts. The procedure analyze takes only the expression. It performs the syntactic analysis and returns a new procedure, the execution procedure, that encapsulates the work to be done in executing the analyzed expression. The execution procedure takes an environment as its argument and completes the evaluation. This saves work because analyze will be called only once on an expression, while the execution procedure may be called many times.

With the separation into analysis and execution, eval now becomes

(define (eval exp env)
  ((analyze exp) env))

The result of calling analyze is the execution procedure to be applied to the environment. The analyze procedure is the same case analysis as performed by the original eval of section [*], except that the procedures to which we dispatch perform only analysis, not full evaluation:

(define (analyze exp)
  (cond ((self-evaluating? exp) 
         (analyze-self-evaluating exp))
        ((quoted? exp) (analyze-quoted exp))
        ((variable? exp) (analyze-variable exp))
        ((assignment? exp) (analyze-assignment exp))
        ((definition? exp) (analyze-definition exp))
        ((if? exp) (analyze-if exp))
        ((lambda? exp) (analyze-lambda exp))
        ((begin? exp) (analyze-sequence (begin-actions exp)))
        ((cond? exp) (analyze (cond->if exp)))
        ((application? exp) (analyze-application exp))
         (error "Unknown expression type - ANALYZE" exp))))

Here is the simplest syntactic analysis procedure, which handles self-evaluating expressions. It returns an execution procedure that ignores its environment argument and just returns the expression:

(define (analyze-self-evaluating exp)
  (lambda (env) exp))

For a quoted expression, we can gain a little efficiency by extracting the text of the quotation only once, in the analysis phase, rather than in the execution phase.

(define (analyze-quoted exp)
  (let ((qval (text-of-quotation exp)))
    (lambda (env) qval)))

Looking up a variable value must still be done in the execution phase, since this depends upon knowing the environment.[*]

(define (analyze-variable exp)
  (lambda (env) (lookup-variable-value exp env)))

Analyze-assignment also must defer actually setting the variable until the execution, when the environment has been supplied. However, the fact that the assignment-value expression can be analyzed (recursively) during analysis is a major gain in efficiency, because the assignment-value expression will now be analyzed only once. The same holds true for definitions.

(define (analyze-assignment exp)
  (let ((var (assignment-variable exp))
        (vproc (analyze (assignment-value exp))))
    (lambda (env)
      (set-variable-value! var (vproc env) env)

(define (analyze-definition exp)
  (let ((var (definition-variable exp))
        (vproc (analyze (definition-value exp))))
    (lambda (env)
      (define-variable! var (vproc env) env)

For if expressions, we extract and analyze the predicate, consequent, and alternative at analysis time.

(define (analyze-if exp)
  (let ((pproc (analyze (if-predicate exp)))
        (cproc (analyze (if-consequent exp)))
        (aproc (analyze (if-alternative exp))))
    (lambda (env)
      (if (true? (pproc env))
          (cproc env)
          (aproc env)))))

Analyzing a lambda expression also achieves a major gain in efficiency: We analyze the lambda body only once, even though procedures resulting from evaluation of the lambda may be applied many times.

(define (analyze-lambda exp)
  (let ((vars (lambda-parameters exp))
        (bproc (analyze-sequence (lambda-body exp))))
    (lambda (env) (make-procedure vars bproc env))))

Analysis of a sequence of expressions (as in a begin or the body of a lambda expression) is more involved. [*] Each expression in the sequence is analyzed, yielding an execution procedure. These execution procedures are combined to produce an execution procedure that takes an environment as argument and sequentially calls each individual execution procedure with the environment as argument.

(define (analyze-sequence exps)
  (define (sequentially proc1 proc2)
    (lambda (env) (proc1 env) (proc2 env)))
  (define (loop first-proc rest-procs)
    (if (null? rest-procs)
        (loop (sequentially first-proc (car rest-procs))
              (cdr rest-procs))))
  (let ((procs (map analyze exps)))
    (if (null? procs)
        (error "Empty sequence - ANALYZE"))
    (loop (car procs) (cdr procs))))

To analyze an application, we analyze the operator and operands and construct an execution procedure that calls the operator execution procedure (to obtain the actual procedure to be applied) and the operand execution procedures (to obtain the actual arguments). We then pass these to execute-application, which is the analog of apply in section [*]. Execute-application differs from apply in that the procedure body for a compound procedure has already been analyzed, so there is no need to do further analysis. Instead, we just call the execution procedure for the body on the extended environment.

(define (analyze-application exp)
  (let ((fproc (analyze (operator exp)))
        (aprocs (map analyze (operands exp))))
    (lambda (env)
      (execute-application (fproc env)
                           (map (lambda (aproc) (aproc env))

(define (execute-application proc args) (cond ((primitive-procedure? proc) (apply-primitive-procedure proc args)) ((compound-procedure? proc) ((procedure-body proc) (extend-environment (procedure-parameters proc) args (procedure-environment proc)))) (else (error "Unknown procedure type - EXECUTE-APPLICATION" proc))))

Our new evaluator uses the same data structures, syntax procedures, and run-time support procedures as in sections [*],  [*], and [*].

Exercise. Extend the evaluator in this section to support the special form let. (See exercise [*].)  

Exercise. Alyssa P. Hacker doesn't understand why analyze-sequence needs to be so complicated. All the other analysis procedures are straightforward transformations of the corresponding evaluation procedures (or eval clauses) in section [*]. She expected analyze-sequence to look like this:

(define (analyze-sequence exps)
  (define (execute-sequence procs env)
    (cond ((null? (cdr procs)) ((car procs) env))
          (else ((car procs) env)
                (execute-sequence (cdr procs) env))))
  (let ((procs (map analyze exps)))
    (if (null? procs)
        (error "Empty sequence - ANALYZE"))
    (lambda (env) (execute-sequence procs env))))
Eva Lu Ator explains to Alyssa that the version in the text does more of the work of evaluating a sequence at analysis time. Alyssa's sequence-execution procedure, rather than having the calls to the individual execution procedures built in, loops through the procedures in order to call them: In effect, although the individual expressions in the sequence have been analyzed, the sequence itself has not been.

Compare the two versions of analyze-sequence. For example, consider the common case (typical of procedure bodies) where the sequence has just one expression. What work will the execution procedure produced by Alyssa's program do? What about the execution procedure produced by the program in the text above? How do the two versions compare for a sequence with two expressions?  

Exercise. Design and carry out some experiments to compare the speed of the original metacircular evaluator with the version in this section. Use your results to estimate the fraction of time that is spent in analysis versus execution for various procedures.

next up previous contents
Next: Variations on a Scheme Up: The Metacircular Evaluator Previous: Internal Definitions
Ryan Bender