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
  (gt 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 -gt boolean) (listof X) -gt (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 -gt boolean) (structure
  containing X) -gt (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))                      gt  7
• (define compose
•   (lambda (f g)
•     (lambda args
•       (f (apply g args)))))
• ((compose sqrt ) 12 75)                      gt
    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 ?