Lecture 20: Mutual recursion

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1 Mutually recursive data

; A TwoTree is one of:

; - Number

; - (make-two ThreeTree ThreeTree)

(define-struct two [first second])

; A ThreeTree is one of:

; - Number

; - (make-three TwoTree TwoTree TwoTree)

(define-struct three [first second third])

Exercise 1. Write 3 more examples of TwoTrees and ThreeTrees. Call the TwoTrees two1 two2 two3. Call the ThreeTrees three1 three2 three3.

Exercise 2. Design two functions: one called sum-twotree that sums all the numbers in a TwoTree, and one called sum-threetree that sums all the numbers in a ThreeTree.

Exercise 3. Design a function add-to-twotree that adds a given number to all the numbers in a given TwoTree and a function add-to-threetree that adds a given number to all the numbers in a given ThreeTree.

2 Mutual recursion with lists

; A FamilyTree is (make-ft String

;                          Number

;                          [ListOf FamilyTree])

(define-struct ft [name age children])

; A [ListOf FamilyTree] is one of:

; - empty

; - (cons FamilyTree [ListOf FamilyTree])

Exercise 4. Design a function count-ft that counts all the people in a given FamilyTree and a function count-loft that counts all the people in a given [ListOf FamilyTree]. Can you do it using foldr?

Exercise 5. Design a function growup-ft that adds 1 to the ages of all the people in a given FamilyTree and a function growup-loft that adds 1 to the ages of all the people in a given [ListOf FamilyTree]. Can you do it using map?

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3 Mutual-recursion check

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Optional: Read Chapters 19–22 of the textbook.