University of California, Berkeley
EECS Department - Computer Science Division

CS3 Lecture 13 : Higher-Order Functions (cont'd)

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Overview of today's lecture

• Review
• Higher-Order Functions (cont'd)
  • Defining functions as one another
  • Temporary variables: another way to do it
• Next Time
• Puzzle : Infinite Baseball
• Game : Tac Tix
• References

Review

• global vs. local variables
• every, a higher-order function which operates on every word in a sentence

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Higher-Order Functions (cont'd)

Defining functions as one another

• If you want to define a function as another with the exact same arguments, don't define it as a function call, as in

: (define (plus x y) (+ x y))
plus

• Note that + can handle multiple arguments, but plus can only handle two...

: (+ 1 2)
3

: (plus 1 2)
3

: (+ 1 2 3)
6

: (plus 1 2 3)
*** ERROR -- Wrong number of arguments passed to procedure
(plus 1 2 3)

• ...instead you should define it directly as a variable bound to the same procedure

: (define plus +) ;; Now plus and + are identical!

: (+ 1 2 3)
6

: (plus 1 2 3)
6

Temporary variables : another way to do it

• We showed you how to use let to define local variables.
• Another way to do it without let is to define a helper procedure that takes additional parameters which hold your temporary values.
• Example: The following expression takes two hours (2 calls to hour-long-function)

: (+ (hour-long-function 3) (/ (hour-long-function 3) 2))
12

• whereas we can save time by storing the result from calling hour-long-function once and storing the return value in a temporary variable hlf. The following expression evaluates in only one hour (only one call to hour-long-function)

: (let ((hlf (hour-long-function 3))
     (+ hlf (/ hlf 2)))
12

• Another way would be to use a helper procedure as follows

: (define (hlf-helper hlf)
    (+ hlf (/ hlf 2)))
hlf-helper

: (hlf-helper (hour-long-function 3))
12

• Summary:
  • There is another way to do it if for some reason you don't have let.
  • Normally you would use let; we're just showing you another way to do it.

Summary

• Today we've seen two smaller points about functions
• We've seen the power of these functionals which we're going to need to learn to plug together to solve much larger problems.

Next Time

• Lambda Lambda Lambda!, it's not just a fraternity...

Puzzle : Infinite Baseball

• Name 5 ways of extending a baseball game indefinitely without umpire intervention.

Game : Tac Tix [BerlekampConwayGuy82]

• Place random coins on a grid
• On your turn, remove as many coins as you can from any row or column, as long as they are adjacent (i.e., no gaps between the coins)
• The winner is the person who removes the last coin.

References

• [BerlekampConwayGuy82] Elwyn Berlekamp, John H. Conway, Richard K. Guy "Winning Ways for Your Mathematical Plays", Academic Press, London, 1982.

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