Design by Provable Contracts

e.g. This is primarily aimed at first- and second-year undergraduates interested in engineering or science, along with high school students and professionals with an interest in programming.Design by Provable Contracts teaches you how to move from "the tests pass" to "the math says it cannot break." Across five modules, you'll climb a five-rung provability ladder — from lint and types, through property-based and bounded-model checking, to dependent-typed proofs in Lean 4 — applied to a single running example: the softmax function used in modern machine learning. By the end, you will be able to: (1) read a peer-reviewed paper and translate its preconditions, postconditions, and invariants into a YAML contract; (2) choose the right verification rung for a given cost-vs-confidence trade-off, using lint, types, proptest, and Kani in Rust; and (3) build a complete pipeline from paper to YAML to Lean theorem, producing a machine-checked guarantee that holds for every input of every length. The course is hands-on and tool-first: Rust for the lower rungs, Lean 4 for the top rung, and YAML as the connective tissue between math and code. You will leave with a reusable mental model and a working capstone you can apply to any safety-critical numerical kernel.