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COM1340 - Winter 2003 Higher-order operations on lists February 19, 2003 |
(define (sorter lst cmp)
... )
By varying the cmp argument, we can sort lists containing different kinds of data and the direction of the sort, and so on. Those familiar with C/C++ may recognize a similarity here with the standard library function qsort(), which takes a function pointer argument. In this handout, we'll see other uses for passed-in procedures.
Why do we want to return procedures? Often, we want to create a class of related functions specialized to particular values:
(define (make-adder n)
(lambda (m) (+ n m)))
(define add3 (make-adder 3))
(define add42 (make-adder 42))
When applied to a value, the make-adder procedure returns
a procedure of one argument. Question: what happens when make-adder
is applied to a value other than a number?
of 
arguments
and 
lists, each of length 
. It returns a list of length 
consisting of the result of applying 
to corresponding elements in
the argument lists. Examples:
(map + '(1 2 3) '(4 5 6)) => (5 7 9) (map add3 '(11 22 33)) => (14 25 36)
When map is applied to a single list, we can consider it a
homomorphism (a structure-preserving map in the mathematical
sense) because it preserves the structure of the input list. When
applied to two or more lists, map squeezes the result into a single list.
Class exercise: write map that takes a procedure and just one list as input.