David Evanshttp://www.cs.virginia.edu/evans

CS200: Computer ScienceUniversity of VirginiaComputer Science

Lecture 25: The Metacircular Evaluator

EvalEval

ApplyApply

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Menu• Metacircular Evaluator Core Review

• Implementing Environments

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Environmental Model of Evaluation1. To evaluate a combination, evaluate all the

subexpressions and apply the value of the first subexpression to the values of the other subexpressions.

2. 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.

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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))))

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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))))

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Environments

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globalenvironment

(nest 3)

+ : #<primitive:+>

nest: x : 3

parameters: xbody: (lambda (x) (+ x x))

x : 3

(define nest (lambda (x) (lambda (x) (+ x x))))> ((nest 3) 4)

((lambda (x) (+ x x)) 4)x : 4

(+ x x)

From Lecture 19:

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Representing Environments

An environment is a frame and a parent.

x : 4

(define (make-new-environment frame env) (cons frame env))

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Environment Procedures

(define (first-frame env) (car env))

(define (enclosing-environment env) (cdr env))

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Representing Frames

A frame is a list of name-value pairs.

x : 4

(define (make-empty-frame) (list))

y : 3

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Environmental Model of Evaluation1. To evaluate a combination, evaluate all the

subexpressions and apply the value of the first subexpression to the values of the other subexpressions.

2. 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.

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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))))

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extend-environment

(define (extend-environment names values env) (make-new-environment (map (lambda (name value) (cons name value)) names values) env))

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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))))

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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

(first-frame env)) (environment-lookup-name name

(enclosing-environment env)))))

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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)))))

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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))))

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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))))

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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))

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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))))

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self-evaluating?

(define (self-evaluating? expr) (or (number? expr) (string? expr) (primitive-procedure? expr)))

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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))

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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))

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Charge

• This is powerful: once we have an metacircular evaluator, we can easily make changes to the language!

• Friday: practice on problem classification problems