Understanding Scheme Procedures & Environments Efficiently

1. Lecture 18 Continue Evaluator

2. symbolprocedure symbol+ symbolx Representing procedures (eval '(define twice (lambda (x) (+ x x))) GE) symbol primitive schemeprocedure +

3. Representing the Environment Abstractly • (eval ‘(twice 4)) • (extend-environment '(x) '(4) GE) x: 10 +: (primitive ...) twice: (procedure ..) GE x: 4 E1 Concretely GE E1 frame list ofvariables list of values 10 x 4 primitive + x twice

4. Representing the Environment E2 • (eval ‘(twice 5)) • (extend-environment '(x) '(5) GE) x 5 GE E1 frame list ofvariables list of values 10 x 4 primitive + x twice

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

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))

7. 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))

8. 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. primitives and initial env. Initialization (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)) (define the-empty-environment '())

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-PrintLoop (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)) 11

12. 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))))

13. 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

14. 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

15. 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))

16. 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>)

17. 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))))

18. Implementing cond: Syntax procedures (cond ((= x 23) (+ x 1)) (else (- x 1))) (if (= x 23) (+ x 1) (- x 1)) (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))

19. Cond syntax (cond ((= x 23) (+ x 1)) (else (- x 1))) cond else - x 1 x 23 = + x 1

20. 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)) begin * x 2 y car

21. Implementing cond (Cont.) (cond ((= x 23) (+ x 1)) (else (- x 1))) (if (= x 23) (+ x 1) (- x 1))

22. 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))))))

23. Details of cond syntax transformation (cond ((= x 23) (+ x 1)) (else (- x 1))) cond else - x 1 = x 23 + x 1

24. Details of cond syntax transformation (expand-clauses else - x 1 = x 23 ) + x 1

25. Details of cond syntax transformation rest first else - x 1 = x 23 + x 1

26. Details of cond syntax transformation (make-if = x 23 + x 1 )) (expand-clauses else - x 1

27. Details of cond syntax transformation (make-if = x 23 + x 1 - x 1 )

28. Details of cond syntax transformation if = x 23 + x 1 - x 1

29. 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

30. Exam 4 Questions 3 Hours You may bring any written or printed material (no laptops..) You can use every function studied in class \ recitation \ exercise All covered material Good Luck and have a nice vacation!