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Understanding Inductive Types: Lists and Family Trees in Functional Programming

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This lecture covers the concept of inductive types in functional programming, focusing on lists and tree structures. Learn how to implement "insert.sort" by following a structured recipe that includes base and recursive cases. We explore shorthand notations for lists and how to represent family trees, defining a family tree node and its properties. Additionally, we introduce a function to check for blue-eyed ancestors within a family tree structure. This knowledge is essential for working on current homework and understanding recursive data structures.

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Understanding Inductive Types: Lists and Family Trees in Functional Programming

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Presentation Transcript

  1. More Inductive Types

  2. Last Lecture • You can figure out "insert sort" yourself • If you follow the recipe, carefully • Recipe tells you: • Think about base case • Think about recursive case (and what to do with result of recursive call) • Make a wish-list (e.g. "insert"), and repeat! • Remember this for current homework

  3. Today's Lecture • A short-hand for lists • Another inductive type: trees!

  4. List Shorthands • (cons 1 (cons 2 (cons 3 empty))) • = (list 123) • (cons (cons 1 (cons 2 (cons 3 empty))) empty) • = (list (list 1 2 3)) • (cons (list 1 2) (list 3 4)) • = (list (list 1 2) 3 4)

  5. A Type for Family Trees ; A family-tree-node (short: ftn) is either ; - empty; or ; - (make-child f m na da ec) ; where f and m are ftns, na ; and ec are symbols, and da is a ; number.

  6. Blue-eyed Ancestor ; blue-eyed-ancestor? : ftn  ->  boolean ; to determine whether ; a-ftree contains a child ; structure with 'blue in the ; eyes field

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