Lecture Notes, Week 10

• A Fibonacci structure
  • Goal
  • Resources
  • The structure
  • The standard Fibonacci function over natural numbers
  • Computing Fibonacci numbers by exponentiating a 2x2 matrix of natural numbers
  • Exercise 01
  • A perhaps unexpected property
  • Another instance of a Fibonacci structure
  • Polymorphic 2x2 matrices
  • Revisiting the 2x2 matrices of natural numbers
  • Layering a Fibonacci structure on top of another
  • Structure vs. nature
  • Structure vs. nature: the base case
  • Structure vs. nature: the induction step
  • The stepping stone
  • Resources
  • Version
• The abstraction and instantiation of Eureka lemmas about resetting the accumulator
  • Exercise 02
  • Exercise 03
  • Exercise 04
  • Exercise 05
  • Exercise 06
  • Resources
  • Version
• Exercises for Week 10
  • Exercise 00
  • Mandatory exercises
  • Version
• Index of concepts for Week 10
  • Version