Abstract List Functions

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Abstract List Functions
2
Outline

• Prerequisites
• Abstraction
• Functions as parameters
• Objectives
• Creating anonymous functions
• Scheme's built-in list processing
• Reference
• HTDP Section 21.2, Intermezzo 4

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Background

• We understand that function names can be passed
  as parameters and used to process data
• We now attack two questions
• Can I create temporary, anonymous functions to
  use and discard?
• What standard things might I want to do to create
  and analyze lists?

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Creating Temporary Functions

• We normally define functions in the following
  style
• (define (add-3-to n)
• ( 3 n))
• However, for test purposes, we have also used
• (define test-data (list 'a 'b 'c 'd))
• Scheme permits the definition of a function in
  manner similar to the second definition
• (define add-3-to (lambda (n)
• ( 3 n)) )

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Creating Temporary Functions

• Here,
• (lambda (n)
• ( 3 n))
• creates the body of a function which returns the
  result of adding three to a single parameter
• Then
• (define add-3-to (lambda ) )
• names this anonymous function "add-3-to."
• We can use this technique to define an anonymous
  function to be passed into a function without
  ever naming it

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Avoiding explicit function definition

• Remember this

(define (traverse lst ck lim function) (if
(empty? lst) 0 (if (ck (first lst) lim)
(function (first lst) (traverse (rest
lst) ck lim)) (traverse (rest lst) ck lim))))
(define (older-than st lim) (gt (student-age st)
lim))
(define (count st num) ( 1 num))
(define (total-grade st num) ( (student-grade
st) num))

• (/ (traverse students older-than 21 total-grade)
• (traverse students older-than 21 count))

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Avoiding explicit function definition

• Could be replaced by

• (/ (traverse students older-than 21 (lambda (st
  num)
• ( (student-grade
  st) num)) )
• (traverse students older-than 21 (lambda
  (st num)
• (
  1 num)) ))

• Or even by

• (/ (traverse students (lambda (st lim)
• (gt (student-age st)
  lim))
• 21 (lambda (st num)
• ( (student-grade
  st) num)) )
• (traverse students (lambda (st lim)
• (gt (student-age st)
  lim))
• 21 (lambda (st num)
• ( 1 num)) )))

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Students-4.scm
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Built-in Abstract List Functions

• Most useful examples

• build-list N (N-gtX) -gt (listof X)
• applies the function to the values 0 .. (N-1)
• filter (X -gt boolean) (listof X) -gt (listof
  X)
• chooses items from the first list satisfying
  the
• function
• map (X -gt Y) (listof X) -gt (listof Y)
• applies the function to each item in the old
  list to
• make a new list of the results

• See HTDP page 313 Figure 57 for the complete set
  of functions

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Code Used

• (number-gtstring 123)
• "123"
• (build-list 8 number-gtstring)
• (list "0" "1" "2" "3" "4" "5" "6" "7" )
• (filter (lambda (n) (gt n 3))
• (list 1 2 3 4 5 6 7 8))
• (list 4 5 6 7 8)
• (map number-gtstring (list 12 14 16 18 24))
• (list "12" "14" "16" "18" "24")
• (map (lambda (n) ( 2 n))
• (list 12 14 16 32))
• (list 24 28 32 64)

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Questions?
13
Summary

• You should now know
• Creating anonymous functions
• Scheme's built-in list processing

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