Universalist

Intent

Use Algebra-Driven Design (ADD) to find the smallest algebra that fits the domain, encode it in types, and enforce laws with tests.

Core workflow (ADD)

1. Frame the domain: observations, invariants, operations.
2. Pick the minimal algebra; avoid overfitting.
3. Define types: make illegal states unrepresentable.
4. State laws: identity, associativity, distributivity, absorption, round-trip, homomorphism.
5. Derive operations from the algebra (map/fold/compose) to reduce ad hoc branching.
6. Refactor architecture to match algebra boundaries.
7. Test the laws (property/model/metamorphic checks).
8. Iterate: if laws are hard to state or test, the algebra is likely wrong.

Minimal-algebra decision guide

• Alternatives/variants → coproduct (tagged union)
• Independent fields → product (record/struct)
• Combine + identity → monoid
• Combine, no identity → semigroup
• Ordering/permissions → poset/lattice
• Add+multiply structure → semiring
• Structure-preserving map → functor
• Effectful apply → applicative
• Sequenced effects → monad

Testing expectations

• Include law/property tests for the chosen algebra.
• Prefer property-based checks when the repo already supports them.
• If not, write minimal deterministic law checks in the existing test framework.
• Don’t assume tooling exists; propose new dependencies only with user approval.

References

• references/addd-overview.md
• references/addd-sources.md
• references/structures-and-laws.md
• references/testing-playbook.md
• references/case-studies.md
• references/examples-haskell.md
• references/examples-go.md
• references/examples-typescript.md

Scripts

• scripts/emit_law_test_stub.sh prints illustrative law-test stubs for Haskell, Go, or TypeScript.