1. David Evans http://www.cs.virginia.edu/evans
Lecture 25:
The
Metacircular Evaluator
Eval
Apply
CS200: Computer Science
University of Virginia
Computer Science
David Evans

2. Menu Metacircular Evaluator Core Review Implementing Environments
26 March 2003
CS 200 Spring 2003

3. Environmental Model of Evaluation
To evaluate a combination, evaluate all the subexpressions and apply the value of the first subexpression to the values of the other subexpressions.
To apply a compound procedure to a set of arguments, evaluate the body of the procedure in a new environment. The parent of the new environment is the procedure’s environment; the frame is a new frame that contains places with the formal parameters bound to the arguments.
26 March 2003
CS 200 Spring 2003

4. meval (define (meval expr env) (cond ((self-evaluating? expr) expr)
((variable? expr) (environment-lookup-name expr env))
((lambda? expr)
(make-procedure (lambda-parameters expr)
(lambda-body expr) env))
((application? expr)
(mapply (meval (application-operator expr) env)
(map (lambda (subexpr) (meval subexpr env))
(application-operands expr))))
(else (error "Unknown expression: " exp))))
26 March 2003
CS 200 Spring 2003

5. mapply (define (mapply procedure operands) (cond
((primitive-procedure? procedure)
(apply-primitive procedure operands))
((compound-procedure? procedure)
(meval-sequence
(procedure-body procedure)
(extend-environment
(procedure-parameters procedure)
operands
(procedure-environment procedure))))
(else (error “Can’t apply: " procedure))))
26 March 2003
CS 200 Spring 2003

6. Environments
26 March 2003
CS 200 Spring 2003

7. (nest 3) (define nest (lambda (x) (+ x x)))) > ((nest 3) 4)
From Lecture 19:
global
environment
(define nest
(lambda (x)
(+ x x))))
> ((nest 3) 4)
+ : #<primitive:+>
nest:
x : 3
parameters: x body:
(lambda (x) (+ x x))
x : 3
(nest 3)
((lambda (x) (+ x x)) 4)
x : 4
26 March 2003
CS 200 Spring 2003
(+ x x)

8. Representing Environments
An environment is a frame and a parent.
x : 4
(define (make-new-environment frame env)
(cons frame env))
26 March 2003
CS 200 Spring 2003

9. Environment Procedures
(define (first-frame env)
(car env))
(define (enclosing-environment env)
(cdr env))
26 March 2003
CS 200 Spring 2003

10. Representing Frames (define (make-empty-frame) (list))
A frame is a list of name-value pairs.
y : 3
x : 4
(define (make-empty-frame)
(list))
26 March 2003
CS 200 Spring 2003

11. Environmental Model of Evaluation
To evaluate a combination, evaluate all the subexpressions and apply the value of the first subexpression to the values of the other subexpressions.
To apply a compound procedure to a set of arguments, evaluate the body of the procedure in a new environment. The parent of the new environment is the procedure’s environment; the frame is a new frame that contains places with the formal parameters bound to the arguments.
26 March 2003
CS 200 Spring 2003

12. mapply (define (mapply procedure operands) (cond
((primitive-procedure? procedure)
(apply-primitive procedure operands))
((compound-procedure? procedure)
(meval-sequence
(procedure-body procedure)
(extend-environment
(procedure-parameters procedure)
operands
(procedure-environment procedure))))
(else (error “Can’t apply: " procedure))))
26 March 2003
CS 200 Spring 2003

13. extend-environment (define (extend-environment names values env)
(make-new-environment
(map (lambda (name value)
(cons name value))
names values)
env))
26 March 2003
CS 200 Spring 2003

14. meval (define (meval expr env) (cond ((self-evaluating? expr) expr)
((variable? expr) (environment-lookup-name expr env))
((lambda? expr)
(make-procedure (lambda-parameters expr)
(lambda-body expr) env))
((application? expr)
(mapply (meval (application-operator expr) env)
(map (lambda (subexpr) (meval subexpr env))
(application-operands expr))))
(else (error "Unknown expression: " exp))))
26 March 2003
CS 200 Spring 2003

15. environment-lookup-name
(define (environment-lookup-name name env)
(if (null? env) (error "No binding " name)
(if (frame-contains? name
(first-frame env))
(frame-lookup-name name
(environment-lookup-name name
(enclosing-environment env)))))
26 March 2003
CS 200 Spring 2003

16. frame procedures (define (frame-contains? name frame)
(insertlg (lambda (var result)
(if (eq? (car var) name) #t result))
frame #f))
(define (frame-lookup-name name frame)
(if (null? frame) (error "Name not found:" name)
(if (eq? (car (car frame)) name)
(cdr (car frame))
(frame-lookup-name name (cdr frame)))))
26 March 2003
CS 200 Spring 2003

17. meval (define (meval expr env) (cond ((self-evaluating? expr) expr)
((variable? expr) (environment-lookup-name expr env))
((lambda? expr)
(make-procedure (lambda-parameters expr)
(lambda-body expr) env))
((application? expr)
(mapply (meval (application-operator expr) env)
(map (lambda (subexpr) (meval subexpr env))
(application-operands expr))))
(else (error "Unknown expression: " exp))))
26 March 2003
CS 200 Spring 2003

18. mapply (define (mapply procedure operands) (cond
((primitive-procedure? procedure)
(apply-primitive procedure operands))
((compound-procedure? procedure)
(meval-sequence
(procedure-body procedure)
(extend-environment
(procedure-parameters procedure)
operands
(procedure-environment procedure))))
(else (error “Can’t apply: " procedure))))
26 March 2003
CS 200 Spring 2003

19. procedure procedures
(define (make-procedure parameters body environment)
(list 'procedure parameters body environment))
(define (compound-procedure? expr)
(tagged-list? expr 'procedure))
(define (procedure-parameters procedure)
(cadr procedure))
(define (procedure-body procedure)
(caddr procedure))
(define (procedure-environment procedure)
(cadddr procedure))
(define (tagged-list? expr tag)
(if (pair? expr) (eq? (car expr) tag) #f))
26 March 2003
CS 200 Spring 2003

20. meval (define (meval expr env) (cond ((self-evaluating? expr) expr)
((variable? expr) (environment-lookup-name expr env))
((lambda? expr)
(make-procedure (lambda-parameters expr)
(lambda-body expr) env))
((application? expr)
(mapply (meval (application-operator expr) env)
(map (lambda (subexpr) (meval subexpr env))
(application-operands expr))))
(else (error "Unknown expression: " exp))))
26 March 2003
CS 200 Spring 2003

21. self-evaluating? (define (self-evaluating? expr)
(or (number? expr) (string? expr)
(primitive-procedure? expr)))
26 March 2003
CS 200 Spring 2003

22. Primitive Procedures (define (primitive-procedure? expr)
(tagged-list? expr 'primitive-procedure))
(define (make-primitive-procedure expr)
(list 'primitive-procedure expr))
(define (primitive-procedure-procedure procedure)
(cadr procedure))
26 March 2003
CS 200 Spring 2003

23. the-global-environment
(define the-empty-environment '())
(define the-global-environment
(make-new-environment
(list
(cons '+ (make-primitive-procedure +))
(cons '* (make-primitive-procedure *))
(cons '- (make-primitive-procedure -)) )
the-empty-environment))
26 March 2003
CS 200 Spring 2003

24. Charge
This is powerful: once we have an metacircular evaluator, we can easily make changes to the language!
Friday: practice on problem classification problems
26 March 2003
CS 200 Spring 2003