15-150: Principles of Functional Programming

Lecture 3: Recursion and Induction

Key Concepts

• Recursive functions
• Proofs of correctness
• Standard (mathematical) induction --- Mathematical induction can be useful when an integer variable is reduced by 1 in the recursive part of a function.
• Strong induction --- Strong induction can be useful when an integer variable is reduced by more than 1.
• Structural induction --- Structural induction can be useful for recursion over datatypes more general than integers.
• Correspondence between recursive function clauses and proof by induction.

Sample Code

Some Notes on Induction

Here is an introduction to lists.
(There will be additional notes about structural induction over lists and trees next time.)

Slides from Lecture