15-212: Principles of Programming

We discuss the method of structural induction on recursively defined types. This technique parallels standard induction on predicates, but has a unique character of its own, and arises often in programming.

We also discuss tail recursion, a form of recursion that is somewhat like the use of loops in imperative programming. This form of recursion is often especially efficient and easy to analyze. Accumulator arguments play an important role in tail recursion.

As examples we consider recursively defined lists and trees.

Key Concepts

• Induction on lists and other data structures
• Tail recursion and iteration

Sample Code

Sample Evaluations

Handouts

• Some notes on structural induction

On-line Notes by Robert Harper

• Recursive Functions
• Structural Induction

Suggested Reading in Programming in Standard ML:

• Chapter 26: Structural Induction

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Michael Erdmann