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Environment Model Examples

Environment Model Examples. Prof. Tony White April 2010. Ref: http://www.cs.caltech.edu/courses/cs1/resources/environment-model-tutorial/environments.html. Example 1. 1. (define ( foo x ) (+ x 1)) 2. ( foo 2). f oo ’. Π =1. Π =3. Example 2. (let (( x 1)

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Environment Model Examples

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  1. Environment Model Examples Prof. Tony White April 2010 Ref: http://www.cs.caltech.edu/courses/cs1/resources/environment-model-tutorial/environments.html

  2. Example 1 1. (define (foox) (+ x 1)) 2. (foo 2) foo’ Π=1 Π=3

  3. Example 2 (let ((x 1) (y 2)) (+ xy)) let’ Π=3 Π=4

  4. Example 3 1. (lambda (xy) (+ xy)) 1 2) lambda’ Π=1 Π=2

  5. (define (sqrtff) (lambda (x) (sqrt (fx)))) (define (inc n) (+ n 1)) (define f1 (sqrtf inc)) (f1 3) Example 4-a Π=4

  6. (define (sqrtff) (lambda (x) (sqrt (fx)))) (define (inc n) (+ n 1)) (define f1 (sqrtf inc)) (f1 3) Example 4-b sqrtf’ Π=5

  7. (define (sqrtff) (lambda (x) (sqrt (fx)))) (define (inc n) (+ n 1)) (define f1 (sqrtf inc)) (f1 3) Example 4-c sqrtf’ f1’ Π=2 Π=6

  8. (define (sqrtff) (lambda (x) (sqrt (fx)))) (define (inc n) (+ n 1)) (define f1 (sqrtf inc)) (f1 3) Example 4-d sqrtf’ f’ f1’ Π=3 Π=2 Π=6

  9. (define bar (let ((x 1) (y 2)) (lambda (z) (+ xyz)))) (bar 3) Example 5-a let’ Π=5

  10. (define bar (let ((x 1) (y 2)) (lambda (z) (+ xyz)))) (bar 3) Example 5-b let’ bar’ Π=4 Π=6

  11. Example 6: Code (define (fooz) (let ((xz)) (let ((y (+ xz))) (lambda (sym) (cond ((eq? sym 'x) x) ((eq? sym 'y) y) ((eq? sym 'bump-x) (set! x (+ xz))) ((eq? sym 'bump-y) (set! y (+ yz))) ((eq? sym 'reset-x) (set! x 0)) ((eq? sym 'reset-y) (set! y 0))))))) (define f (foo 10)) (f 'x) (f 'y) (f 'bump-x) ; Rest of code not shown

  12. Example 6-a foo’ Π=12

  13. Example 6-b foo’ Π=5 Π=13

  14. Example 6-c foo’ Π=7 Π=15

  15. Example 6-d • Rest of code associated with example 6 left as an exercise to the reader. It really is a set of variations on 6-b and 6-c.

  16. Example 7: Code (define (new-sqrtx) (define (good-enough? guess) (< (abs (- (square guess) x)) 0.000001)) (define (average xy) (/ (+ xy) 2)) (define (improve guess) (average guess (/ x guess))) (define (sqrt-iter guess) (if (good-enough? guess) guess (sqrt-iter (improve guess)))) (sqrt-iter 1.0)) (new-sqrt 2.0)

  17. Example 7-a Π=13

  18. Example 7-b new-sqrt’ Π=12 Π=14

  19. Example 7-c new-sqrt’ sqrt-iter’ Π=12 Π=14 Π=9

  20. (define (foox) (let ((y (lambda (w) (+ xw))) (z (lambda (w) (* xw)))) (y (zx)))) (foo 10) Example 8-a Π=5

  21. (define (foox) (let ((y (lambda (w) (+ xw))) (z (lambda (w) (* xw)))) (y (zx)))) (foo 10) Example 8-b foo’ Π=2 Π=6

  22. (define (foox) (let ((y (lambda (w) (+ xw))) (z (lambda (w) (* xw)))) (y (zx)))) (foo 10) Example 8-c foo’ let’ Π=6 Π=4 Π=2

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