Abstraction

1. Abstraction Lab 3 Karl Lieberherr

2. Abstractions in Scheme for traversing and processing data • lists • map: same function applied to all elements • records • explicitly enumerate relevant elements • Example: BusRoute example (Lab 1) • (define (proc-towns towns) (map proc-town towns)) • (define (proc-town town) (proc-busStops(Town-busStops town)))

3. Abstractions in Scheme for traversing and processing data unions: explicitly enumerate relevant alternatives in cond clause. ;; capacity checking example (define (weight-item l) (cond [(Simple? l) (Simple-weight l)] [(Container? l) (weight-container l)]))

4. compacting information: variants of map • (andmap p alox) • determine whether p holds for every item on alox • (ormap p alox) • determine whether p holds for at least one item on alox

5. Compacting information with fold • (foldr + 0 (map weight-item l)) (Capacity checking example) • Two versions: foldr and foldl • Very flexible because compacting function is a parameter (+ above)

6. Container capacity example (define-struct Container (contents capacity)) (define-struct Simple (name weight))

7. A more interesting use of map and fold (define (check ac)   (wv-violations    ((make-Container-Visitor      (lambda (name weight) (make-wv weight 0))      (lambda (wvs capacity)        (let* ((totals                (foldr (lambda (wv1 wv2)                         (make-wv                          (+ (wv-weight wv1) (wv-weight wv2))                          (+ (wv-violations wv1) (wv-violations wv2))))                       (make-wv 0 0)                       wvs))               (total-weight (wv-weight totals))               (total-violations (wv-violations totals)))          (make-wv total-weight                   (if (> total-weight capacity)                       (+ 1 total-violations)                       total-violations)))))     ac)))

8. Functional Visitor: does traversal (define (make-Container-Visitor simple-visitor container-visitor) (define (visitor c) (cond ((Simple? c) (simple-visitor (Simple-name c) (Simple-weight c))) ((Container? c) (container-visitor (map visitor (Container-contents c)) (Container-capacity c))) (else ???))) visitor)

9. filter ;; filter : (X -> boolean) (listof X) -> (listof X) (eliminate-expensive u toys) Question: does it make sense to generalize filter to any kind of Scheme structure? • consider a container c • filter-struct : (X -> boolean) (structure containing X) -> (structure containing X)

10. Exercise: filter • Design a dir structure (HTDP 224 -226) and filter out all files whose size is greater than 100. • Choose a structure that minimizes conditionals.

11. apply: from help desk procedure:  (apply proc arg1 ... args)  proc must be a procedure and args must be a list. Calls proc with the elements of the list (append (list arg1 ...) args) as the actual arguments. (apply + (list 3 4))                      ===>  7 (define compose   (lambda (f g)     (lambda args       (f (apply g args))))) ((compose sqrt *) 12 75)                      ===>  30

12. Exercise: apply and eliminate lambda (define compose (lambda (f g) (lambda args (f (apply g args))))) (define (compose2 f g) (lambda args (f (apply g args)))) (define (compose3 f g) (local (define (myf args) (f (apply g args)))) myf)) ((compose sqrt *) 12 75) ((compose2 sqrt *) 12 75) ((compose3 sqrt *) '(12 75)) How can we write compose3 without requiring the ‘?