MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science 6.001 Structure and Interpretation of Computer Programs Spring, 2007 Recitation 16b, April 18 Higher Order Procedures Practice (Mike Leventon) Dr. Kimberle Koile 1. Write a function swap that takes a function f, and returns a function that takes two arguments, and returns f with the variables swapped: (f x y) == ((swap f) y x) For example, ((swap -) 4 5) 1. 2. Composing functions Now try to write the function compose that takes two functions, f and g, and returns a function, that takes one argument, and composes f and g on that argument. Example: composing double and cube means take the double of the cube of x ((compose double cube) 3) => (double (cube 3)) => 54 3. Using compose, define the function f^3/2 which takes a number x and computes x 3/2 . 4. Repeated Composition of Functions We saw how to compose two functions to produce another function. For example, we can define the following: (define fourth-power (compose square square)) (define eight-power (compose square (compose square square))) ... and so on ...Write a recursive procedure called repeat that takes a function f and an integer n, and composes f, n times. For example: (define fourth-power (repeat square 2)) (define eight-power (repeat square 3)) ... and so on ... 5. Iterative Repeat: Write a version that creates the repeat procedure iteratively by calling compose. (Note: The procedure created will run as a recursive procedure.) 6. Iterative Repeated 2: Write a version of repeat that creates a procedure that will run as an iterative procedure. (Hint: Do not use
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