If you think about other procedures you've written or read this semester, you can probably identify a variety of other common patterns. Once you've identified a pattern, you can think about turning that pattern into a higher-order procedure. Here are a few worth thinking about.

In cases like sum and product, we used a binary procedure (+ and *, respectively) to combine all the values in a list. We typically call the generalized version of such a procedure fold. For example, (fold + (list 1 2 3 4)) describes 1+2+3+4. Once we've defined fold, we can more easily define sum as (define sum (lambda (lst) (fold + lst))) or even (define sum (l-s fold +))

We've also made it common practice to count all the values in a list that meet some predicate (all the dark colors, all the odd numbers, etc.). Traditionally, we call such counting tallying and call the generalized pattern (tally pred? lst). For example, > (tally odd? (list 1 2 3 4 5)) 3 > (tally even? (list 1 2 3 4 5)) 2 ; Count dark colors > (tally (lambda (c) (< (rgb-brightness c) 25)) colors-rainbow) 3 ; Count dark, non-dark, and light colors using very concise notation. > (tally (o (r-s < 25) rgb-brightness) colors-rainbow) 3 > (tally (o (r-s > 25) rgb-brightness) colors-rainbow) 4 > (tally (o (r-s > 75) rgb-brightness) colors-rainbow) 1

We also use predicates to iterate through lists when we want to remove all the values in the list that meet some predicate, or to select all the values in a list for which some predicate holds. We typically call those procedures (filter pred? lst) and (select pred? lst). > (filter odd? (list 1 2 3 4 5 6 7)) (2 4 6) > (filter even? (list 1 2 3 4 5 6 7)) (1 3 5 7) ; Remove dark colors from the rainbow > (map rgb->color-name (filter (o (r-s < 25) rgb-brightness) colors-rainbow)) ("red" "orange" "yellow" "green") > (select odd? (list 1 2 3 4 5 6 7)) (1 3 5 7) > (select even? (list 1 2 3 4 5 6 7)) (2 4 6) ; Select the dark colors in the rainbow > (map rgb->color-name (select (o (r-s < 25) rgb-brightness) colors-rainbow)) ("blue" "indigo" "violet")