Algebraic law
An algebraic law is a general equation or behavioral property that an operation or implementation is expected to satisfy for applicable values.
Functional Programming in Scala, Second Edition
A law is a general equation or behavioral property that operations or their implementations are expected to satisfy.
- How it is used
- Constrain API operations and supply properties for reasoning, algebraic design, and property-based testing.
- How deep it goes
- Develops concrete mapping and flatMap equations, derives identity, and proves associativity for Option through case expansion.
- Examples
- Uses Par mapping, ExecutorService result comparison, Option cases, parser identities, and generated Order values.
- What you can do after
- Evaluate/understand whether alternative implementations preserve stated API behavior and derive reusable operations from lawful primitives.
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Learn Haskell by Example
Property is the QuickCheck type representing a testable property, including properties augmented with conditions or classifications.
- How it is used
- Expresses implementation invariants as generated tests that search for counterexamples.
- How deep it goes
- Defines Bool and Property forms, demonstrates modifiers and shrinking, and defers custom Testable instances.
- Examples
- Uses sorted lists, rot13 symmetry, alphabet closure, and arithmetic properties in test suites.
- What you can do after
- Apply it via QuickCheck to run generated invariant checks and organize prop_-named tests into Stack suites.
Related concepts
- flatmapused by · FlatMap is an operation that applies a function producing nested collections or computational contexts to each element and combines the resulting contexts into one flattened result.
- monadpart of · A monad is a functional abstraction that encapsulates computational context and provides operations for composing computations while preserving that context.
- QuickCheckused by · QuickCheck is a property-based testing library that generates test inputs from specifications, checks their properties, and may minimize failing counterexamples.
- property-based testingused by · Property-based testing is a software-testing technique that generates varied inputs and checks whether specified general properties of the software’s behavior hold across them.
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