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 http://www.cs.virginia.edu/evans

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

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

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

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

Environments 26 March 2003 CS 200 Spring 2003

(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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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