continue evaluator

1

Continue Evaluator

2

z 9

true #t

+

twice

Representing procedures

(eval '(define twice (lambda (x) (+ x x))) GE)

symbolprimitive

schemeprocedure +

symbolprocedure

symbol+

symbolx

3

Representing the Environment

• (eval ‘(twice 4))• (extend-environment '(x) '(4) GE) GE x: 10

+: (primitive ...)twice: (procedure ..)

E1 x: 4

Abstractly

Concretely

GE

list ofvalues

list ofvariables

frame

x 4

E1

x

10

+ twice primitive

4

Representing the Environment

• (eval ‘(twice 5))• (extend-environment '(x) '(5) GE)

GE

list ofvalues

list ofvariables

frame

x 4

E1

x

10

+ twice primitive

x 5

E2

5

(define (lookup-variable-value var env) (define (env-loop env) (define (scan vars vals) (cond ((null? vars) (env-loop (enclosing-environment env))) ((eq? var (car vars)) (car vals)) (else (scan (cdr vars) (cdr vals))))) (if (eq? env the-empty-environment) (error "Unbound variable" var) (let ((frame (first-frame env))) (scan (frame-variables frame) (frame-values frame))))) (env-loop env))

(define (frame-variables frame) (car frame))(define (frame-values frame) (cdr frame))

(define (enclosing-environment env) (cdr env))(define (first-frame env) (car env))

6

(define (define-variable! var val env) (let ((frame (first-frame env))) (define (scan vars vals) (cond ((null? vars) (add-binding-to-frame! var val frame)) ((eq? var (car vars)) (set-car! vals val)) (else (scan (cdr vars) (cdr vals))))) (scan (frame-variables frame) (frame-values frame))))

(define (eval-definition exp env) (let ((name (cadr exp)) (defined-to-be (eval (caddr exp) env))) (define-variable! name defined-to-be env) ‘undefined))

Assignments

(define (eval-assignment exp env) (set-variable-value! (assignment-variable exp) (eval (assignment-value exp) env) env) 'ok)

(define (assignment? exp) (tagged-list? exp 'set!))

(define (assignment-variable exp) (cadr exp))

(define (assignment-value exp) (caddr exp))

set-variable-value!

(define (set-variable-value! var val env) (define (env-loop env) (define (scan vars vals) (cond ((null? vars) (env-loop (enclosing-environment env))) ((eq? var (car vars)) (set-car! vals val)) (else (scan (cdr vars) (cdr vals)))))

(if (eq? env the-empty-environment) (error "Unbound variable -- SET!" var) (let ((frame (first-frame env))) (scan (frame-variables frame) (frame-values frame))))( (env-loop env))

9

Initialization primitives andinitial env.

(define the-empty-environment '())

(define the-global-environment (setup-environment))

(define (setup-environment) (let ((initial-env (extend-environment (primitive-procedure-names) (primitive-procedure-objects) the-empty-environment))) (define-variable! 'true #t initial-env) (define-variable! 'false #f initial-env) initial-env))

10

(define primitive-procedure (list (list 'car car) (list 'cdr cdr) (list 'cons cons) (list 'null? null?) (list '+ +);; more primitives ))

(define (primitive-procedure-names) (map car primitive-procedures))

(define (primitive-procedure-objects) (map (lambda (proc) (list 'primitive (cadr proc))) primitive-procedures))

11

Read-Eval-Print Loop

(define input-prompt ";;; M-Eval input:")(define output-prompt ";;; M-Eval value:")

(define (prompt-for-input string) (newline) (newline) (display string) (newline))

(define (announce-output string) (newline) (display string) (newline))

(define (driver-loop) (prompt-for-input input-prompt) (let ((input (read))) (let ((output (eval input the-global-env))) (announce-output output-prompt) (user-print output))) (driver-loop))

Apply (reminder)

(define (apply procedure arguments) (cond ((primitive-procedure? procedure) (apply-primitive-procedure procedure arguments)) ((compound-procedure? procedure) (eval-sequence (procedure-body procedure) (extend-environment (procedure-parameters procedure) arguments (procedure-env procedure)))) (else (error "Unknown procedure type -- APPLY" procedure))))

15

Execution Examples

• An iterative algorithm in scheme

(eval '(define odd (lambda (n) (odd (- n 2)))) GE)

• A recursive algorithm in scheme

(eval '(define sum (lambda (n) (+ n (sum (- n 1))))) GE)

• Base case and if check omitted from both algorithmsto simplify the example

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(eval '(define odd (lambda (n) (odd (- n 2)))) GE)

(eval '(odd 4) GE)

[call apply, which creates E1: n = 4, then eval body of odd]

(eval '(odd (- n 2)) E1)

(apply (eval 'odd E1) (list (eval '(- n 2) E1)))

[skip some steps in which (- n 2) ==> 2](apply (list ’procedure '(n) '(odd (- n 2)) GE) '(2))

[apply creates E2: n = 2, then eval body of odd]

(eval '(odd (- n 2)) E2))• No pending operations on the recursive call to eval

17

(eval '(define sum (lambda (n) (+ n (sum (- n 1))))) GE)

(eval '(sum 4) GE)

[call apply, which creates E1: n = 4, then eval body of sum]

(eval '(+ n (sum (- n 1))) E1)

(apply '(primitive #[add]) (list (eval 'n E1) (eval '(sum (- n 1)) E1)))

[skip some steps in which (- n 1) ==> 3]

(apply '(primitive #[add]) (list 4 (apply (eval 'sum E1) '(3))))

[apply creates E2: n = 3, then eval body of sum]

(apply '(primitive #[add])(list 4 (eval '(+ n (sum (- n 1))) E2))

• There are pending operations on the recursive call to eval

18

Summary

• Cycle between eval and apply is the core of the evaluator• eval calls apply with operator and argument values• apply calls eval with expression and environment

• What is still missing from scheme ?• Some special forms• data types other than numbers and booleans

19

Note: Syntactic Abstraction

• Semantics• What the language means• Model of computation

• Syntax• Particulars of writing expressions• E.g. how to signal different expressions

• Separation of syntax and semantics: allows one to easily alter syntax

eval/applysyntax

procedures

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Basic Syntax

• Routines to detect expressions(define (if? exp) (tagged-list? exp 'if))(define (lambda? exp) (tagged-list? exp 'lambda))(define (application? exp) (pair? exp))

• Routines to get information out of expressions(define (operator app) (car app))(define (operands app) (cdr app))(define (first-operand args) (car args))(define (rest-operands args) (cdr args))

• Routines to build expressions(define (make-if predicate consequent alternative) (list 'if predicate consequent alternative))

21

Example – Changing Syntax

• Suppose you wanted a "verbose" application syntax:

(CALL <proc> ARGS <arg1> <arg2> ...)

• Changes – only in the syntax routines!

(define (application? exp) (tagged-list? 'CALL))

(define (operator app) (cadr app))

(define (operands app) (cdddr app))

22

Implementing "Syntactic Sugar"

• Idea:• Implement a simple fundamental "core" in the evaluator• Easy way to add alternative/convenient syntax?

• "let" as sugared procedure application:

(let ((<name1> <val1>) (<name2> <val2>)) <body>)

((lambda (<name1> <name2>) <body>) <val1> <val2>)

23

Detect and Transform the Alternative Syntax

(define (eval exp env) (cond ((self-evaluating? exp) exp) ((variable? exp) (lookup-variable-value exp env)) ((quoted? exp) (text-of-quotation exp)) . . . ((cond? exp) (eval (cond->if exp) env)) ((let? exp) (eval (let->combination exp) env)) ((application? exp) (apply (eval (operator exp) env)

(list-of-values (operands exp) env))) (else (error "Unknown expression" exp))))

24

Implementing cond: Syntax procedures

(define (cond-clauses exp) (cdr exp))

(define (cond-else-clause? clause) (eq? (cond-predicate clause) 'else))

(define (cond-predicate clause) (car clause))

(define (cond-actions clause) (cdr clause))

(cond ((= x 23) (+ x 1))

(else (- x 1)))

(if (= x 23) (+ x 1) (- x 1))

25

Cond syntax

(cond ((= x 23) (+ x 1))

(else (- x 1)))

cond

else

23x=

1x+

1x-

26

Transforming sequence of expression toan expression

(define (sequence->exp seq) (cond ((null? seq) seq) ((last-exp? seq) (first-exp seq)) (else (make-begin seq))))

(define (make-begin seq) (cons 'begin seq))

2x*

car y

begin

27

Implementing cond (Cont.)

(cond ((= x 23) (+ x 1))

(else (- x 1)))

(if (= x 23) (+ x 1) (- x 1))

28

Implementing cond

(define (cond->if exp) (expand-clauses (cond-clauses exp)))

(define (expand-clauses clauses) (if (null? clauses) 'false ; no else clause (let ((first (car clauses)) (rest (cdr clauses))) (if (cond-else-clause? first) (if (null? rest) (sequence->exp (cond-actions first)) (error "ELSE clause isn't last -- COND->IF" clauses)) (make-if (cond-predicate first) (sequence->exp (cond-actions first)) (expand-clauses rest))))))

29

Details of cond syntax transformation

(cond ((= x 23) (+ x 1))

(else (- x 1)))

cond

else

23x=

1x+

1x-

30


(expand-clauses

else

23x=

1x+

1x-

)

31


first

else

23x=

1x+

1x-

rest

32


23x=

1x+

else

1x-

(make-if

(expand-clauses ))

33


23x=

1x+

1x-

(make-if

)

34


23x=

1x+

1x-

if

35

Named Procedures

Support (define (foo <parm>) <body>)

(define (eval-definition exp env) (define-variable! (definition-variable exp) (eval (definition-value exp) env) env))

(define (definition-variable exp) (if (symbol? (cadr exp)) (cadr exp) (caadr exp)))

(define (definition-value exp) (if (symbol? (cadr exp)) (caddr exp) (make-lambda (cdadr exp) ;formal params

(cddr exp)))) ;body

Different frame implementation

(define make-frame

(lambda (variables values)

(lambda (var)

(cond ((empty? variables) empty)

((eq? var (car variables))

(make-binding (car variables) (car values)))

(else

(apply (make-frame (cdr variables) (cdr values))

(list var))))

))

New ADT: Box (whose implementation is a black box) for mutable objects!

Details omitted

36

Substitution Model Instead of the Env. Model

• What changes to the evaluator are required?

37

Substitution Model Instead of the Env. Model

• Main changes:• No generation (and passing as parameters) of

environments (only global environment is generated)– Scoping is handled differently (see next)

• No support of assignment– Assignment does not fit well in the functional

programming framework• Besides application, support of other operations stays

almost intact– Omit the environment parameter, and use global

env. Instead• Application requires some work

38

(define applicative-eval

(lambda (exp)

(cond ((atomic? exp) (eval-atomic exp))

…

((application? exp)

(let ((renamed-exp (rename exp)))

(apply-procedure

(applicative-eval (operator renamed-exp))

(list-of-values (operands renamed-exp)))))

(else

(error "Unknown expression type -- EVAL" exp)))))

39

(define apply-procedure

(lambda (procedure arguments)

(cond ((primitive-procedure? procedure)

(apply-primitive-procedure procedure arguments))

((compound-procedure? procedure)

(eval-sequence

(substitute (procedure-body procedure)

(procedure-parameters procedure)

arguments)))

(else

(error "Unknown procedure type -- APPLY" procedure)))))

40

substitute

(define substitute

(letrec ((substitute-var-val

(lambda (exp var val)

(cond ((variable? exp)

(if (eq? exp var) val exp))

((or (number? exp)

(boolean? exp) (quoted? exp) ) exp)

((value? exp)

(substitute-var-val-in-value exp var val))

(else

(map (lambda(e) (substitute-var-val e var val)) exp)))) )

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rename

42

• Implementation can be found in lecture notes• Idea: rename the formal arguments of the closure as well

as all occurrences of them in the body• To distinguish from other variables with the same name

that are e.g. in the global scope

Auxiliary function

(define (make-new-names old-names)

(if (null? old-names) ‘()

(cons (gensym)

(make-new-names (cdr old-names)))))))

This should be inside the code of rename, put as external for clarification!

43

One more auxiliary function

• (define (replace val-exp)

(cond ((or (evaluator-symbol? val-exp)

(primitive-procedure? val-exp)) val-exp)

((evaluator-list? val-exp)

(make-list (map rename (list-content val-exp))))

((compound-procedure? val-exp)

(let* ((params (procedure-parameters val-exp))

(new-params (make-new-names params))

(renamed-subs-body (map rename

(procedure-body val-exp)))

(renamed-body (substitute renamed-subs-body params new-params)))

(make-procedure new-params renamed-body))))

44

Finally- rename

(define (rename exp)

(cond ((atomic? exp) exp)

((lambda? exp)

(let* ((params (lambda-parameters exp))

(new-params (make-new-names params))

(renamed-subs (map rename exp)))

(substitute renamed-subs params new-params)) )

((evaluator-value? exp) (replace exp))

(else (map rename exp))

45

Lists

• (define (evaluator-value? val)

(or (evaluator-symbol? val) (evaluator-list? val)

(primitive-procedure? val)

(compound-procedure? val))))• (define (list-form? exp)

(or (tagged-list? exp ’cons) (tagged-list? exp ’list)

(tagged-list? exp ’append))))• (define (eval-list lst) (make-list (apply-primitive-procedure

(eval (operator lst))

(list-of-values (operands lst))))))

46

The Analyzer

• Main idea: separate the syntactic analysis from evaluation

• Main observation: this corresponds to separating the management of expressions from those of the enviornments

• Simplest analysis:

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

48

The Analyzer (cont.)

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

(define (analyze-definition exp)

(let ((var (definition-variable exp))

(val (analyze (definition-value exp))))

(lambda (env)

(if (not (eq? env the-global-environment))

(error ’eval "non global definition: ~s" exp)

(begin

(add-binding! (make-binding var

(val the-global-environment)))

’ok))))))

49

The Analyzer (cont.)

• (define (analyze-if exp)

(let ((pred (analyze (if-predicate exp)))

(consequent (analyze (if-consequent exp)))

(alternative (analyze (if-alternative exp))))

(lambda (env)

(if (true? (pred env))

(consequent env)

(alternative env))))))

And so on…

50

continue evaluator

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