Foundations of Inductive Types

The complete source of examples from this chapter click here

Exercises


Exercise 14.1 page 392 A direct definition of addition
Exercise 14.4 page 394 Using maximal induction principles (le)
Exercise 14.5 page 396 About Left Factors
Exercise 14.6 page 398 eq_rec as an identity function
Exercise 14.7 page 405 A correct induction principle for lists of trees
Exercise 14.8 page 405 A counting function for trees and lists of trees
Exercise 14.9 page 406 A counting function for trees and lists of trees (cont.)
This (difficult) exercise shows how triangular arrays can be represented through an inductive type family.

Errata

  1. Page 398, (3rd paragraph of 14.2.3),
    Read "R ai+1 ai" instead of "R ai ai+1"
  2. Id:
    The correct definition is:
    forall x, (forall y, R y x -> Phi y) <-> Phi x