15-212: Principles of Programming

We demonstrate a complicated representation invariant using Red/Black Trees. The main lesson is to understand the subtle interactions of invariants, data structures, and reliable code production. In order to write code satisfying a strong invariant, it is useful to proceed in stages. Each stage satisfies a simple invariant, and is provably correct. Together the stages satisfy the strong invariant.

Key Concepts

• Representation invariants
• Weakening an invariant temporarily

Sample Code

On-line Notes by Robert Harper

• Representation Invariants and Data Abstraction

Suggested Reading in Programming in Standard ML:

• Chapter 20: Signature Ascription
• Chapter 32: Data Abstraction

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Michael Erdmann