Phase 3: Property-Based Testing for AI Code · 55 min · Python · Hypothesis · pytest

Deriving Properties from Code

Read the code. Find the invariants. Write the properties.

Hiring signal: Engineers who can derive properties (roundtrip, monotonicity, bounded output, commutativity, identity) from code demonstrate the analytical skills needed to specify invariants for AI-generated functions.

What you will learn

Derive roundtrip properties from serialization/deserialization functions
Derive monotonicity properties from sorting and comparison functions
Derive bounded output properties from mathematical functions
Derive commutativity and identity properties from binary operations
Use the Roundtrip/Model-oracle/Invariant property taxonomy

The Problem

You know how to write property tests with Hypothesis (Lesson 2). But what properties should you test? This is the hardest part of PBT: looking at a function and identifying the invariants it should satisfy. This lesson provides a taxonomy of property types and a systematic process for deriving them from any function.

The Property Taxonomy

Property Type	What it checks	Example
Roundtrip	`decode(encode(x)) == x`	`json.loads(json.dumps(d)) == d`
Monotonicity	`x <= y implies f(x) <= f(y)`	`sort` preserves order
Bounded output	`f(x) in [min, max]` for all x	`clamp(x, 0, 100) in [0, 100]`
Commutativity	`f(a, b) == f(b, a)`	`add(a, b) == add(b, a)`
Identity	`f(x, identity) == x`	`add(x, 0) == x`
Model/Oracle	`f(x) == reference_implementation(x)`	Compare AI sort to `sorted()`
Idempotence	`f(f(x)) == f(x)`	`deduplicate(deduplicate(x)) == deduplicate(x)`
Associativity	`f(f(a, b), c) == f(a, f(b, c))`	`add(add(a, b), c) == add(a, add(b, c))`

The 3-step property derivation process
Read the function signature and docstring -- what does it claim to do? 2. Identify the output domain -- what values can the output take? 3. Ask: what must be true for ALL valid inputs? Write each as a property. Start with roundtrip (if serialization), then model/oracle (if a reference exists), then invariants (bounded output, monotonicity, etc.).

Unlock the full lesson

You've read the first 2 sections. The rest of this lesson covers Roundtrip Properties, Monotonicity Properties, Bounded Output Properties, Model/Oracle Properties, Build It — plus a hands-on lab, quiz, and project artifact.

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