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Exploring Recursion with Scheme's letrec

Learn to implement and understand the power of recursive procedures using Scheme's letrec construct. Explore syntax, coding examples, and environment augmentation for recursive functions.

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Exploring Recursion with Scheme's letrec

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  1. 3.6 Interpreter: Recursion • Recall Scheme's letrec (recursive let): • > (letrec ((fact (lambda (x) • (if (zero? x) • 1 • (* x (fact (- x 1))))) • (fact 6)) • 720 • Question: Why letrecand notlet?

  2. 3.6 Recursion • Implement letrec for procedures in our toy language: • --> letrec fact(x)= • if zero?(x) then 1 • else *(x, (fact sub1(x))) • in (fact 6) • 720 • --> • We'll use letrec only for procedures....

  3. 3.6 Recursion • Syntax: • <expression> • ::= letrec • {<identifier>({<identifier>}*(,))= <expression>}* • in <expression> letrec-exp (proc-names idss bodies letrec-body) • Question: Why idssand notids?

  4. 3.6 Recursion • Add some code to eval-expression: • (define eval-expression • (lambda (exp env) • (cases expression exp • ... • (letrec-exp (proc-names idss bodies letrec-body) • (eval-expression letrec-body • (extend-env-recursively • proc-names idss bodies env))) • ...))) • So how to write extend-env-recursively?

  5. 3.6 Recursion First augment environment type to include recursive procs: (define-datatype environment environment? (empty-env-record) (extended-env-record (syms (list-of symbol?)) (vals (list-of scheme-value?)) (env environment?)) (recursively-extended-env-record (proc-names (list-of symbol?)) (idss (list-of (list-of symbol?))) (bodies (list-of expression?)) (env environment?)))

  6. 3.6 Recursion • Now write extend-env-recursively as a constructor: • (define extend-env-recursively • (lambda (proc-names idss bodies env) • (recursively-extended-env-record • proc-names idss bodies env))) • Recall that we look up symbols using apply-env: • (define eval-expression • (lambda (exp env) • (cases expression exp • (var-exp (id) (apply-env env id)

  7. 3.6 Recursion Current version: (define apply-env (lambda (env sym) (cases environment env (empty-env-record () (eopl:error ...)) (extended-env-record (syms vals old-env) (let ((pos (list-find-pos sym syms))) (if (number? pos) ; found (list-ref vals pos) (apply-env old-env sym)))))))

  8. 3.6 Recursion (define apply-env (lambda (env sym) (cases environment env ... (recursively-extended-env-record (proc-names idss bodies old-env) (let ((pos (list-find-pos sym proc-names))) (if (number? pos); found (closure (list-ref idss pos) (list-ref bodies pos) env) ; circular! (apply-env old-env sym)))))));notfound

  9. 3.6 Recursion • For our fact example: • proc-names = '(fact) • idss = '((x)) • bodies = '( <<if zero?(x) then 1 • else *(x, fact sub1(x))>> ) • env = '( (fact) • (<closure: fact, x, <<if...) )

  10. 3.6 Recursion fact closure(x) <<if zero? (x) then 1 else fact sub1(x)>>

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