Inductive Reasoning in Algorithms¶

Proving correctness by establishing a base case and showing that if the property holds for smaller inputs it holds for larger ones mirrors the structure of recursive and iterative algorithms themselves.

Tension Addressed¶

Optimality vs. Simplicity (elegant proofs matching algorithm structure)

Recognizable As¶

Recursive correctness arguments, "assume it works for n-1" reasoning, structural induction on data types, convergence proofs

Canonical Sources¶

Peano, Arithmetices Principia (1889); Burstall, Proving Properties of Programs by Structural Induction (1969)

Transfers To¶

Mathematical proofs, type system soundness, protocol verification, scientific reasoning, legal argumentation

Inductive reasoning is the natural companion to recursive algorithm design: the structure of the proof mirrors the structure of the solution.