Concrete Examples

Concrete Worked Examples & Executable Python Suite

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1. Running the Standalone Python Verifier & Examples

All examples and contract validators live in the standalone normal_forms/ Python package and contracts/ directory:

# 1. Validate all 112 YAML normal form contracts against standard.yaml
python -m normal_forms.catalog

# 2. Run Demo 01: BQNF Incremental Revenue Repair on CDC Events
python -m normal_forms.paid_revenue_example

# 3. Run Demo 02: Unverified Certificate Refusal Gate
python -m normal_forms.unverified_certificate_example

# 4. Run Demo 03: Observer-Relative Freshness SLA Poset Evaluation
python -m normal_forms.observer_freshness_example

# 5. Run Cross-Domain Reconciliation & Loss Ledger Example
python -m normal_forms.reconciliation_example

# 6. Run Demo 05: Multi-Hop Composition (3NF/BCNF -> BQNF Stream -> CODA_MUR Transport)
python -m normal_forms.multi_hop_composition

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2. Example A: Classical 0NF $\to$ 1NF Flattening & 5NF Consulting Witness (NormalFormsEvaluator)

from normal_forms import NormalFormsEvaluator

with NormalFormsEvaluator() as ev:
    # 1. Flatten repeating CSV groups (0NF -> 1NF)
    rows_1nf = ev.normalize_0nf_to_1nf([
        (1, "Alice", "Math,Physics"),
        (2, "Bob", "Chemistry"),
    ])
    print("1NF rows:", rows_1nf)

    # 2. Check 5NF Project-Join witness (Shell2 EXCEPT Fill2)
    witness = ev.evaluate_5nf_project_join_integrity([
        ("Alice", "Acme", "Widget"),
        ("Alice", "Globex", "Gadget"),
        ("Bob", "Acme", "Gadget"),
        ("Alice", "Acme", "Gadget"),  # closes the 3-way cycle
    ])
    print("5NF witness:", witness)

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3. Example B: 3NF Bernstein Synthesis vs BCNF (normal_forms.domain)

Consider the classic Address(street, city, zip) schema (Date & Darwen's street_journal_title isomorphism) with functional dependencies ${(\text{street}, \text{city}) \to \text{zip},; \text{zip} \to \text{city}}:$

• Candidate keys: ${(\text{street}, \text{city}),; (\text{street}, \text{zip})}$.
• Every attribute (street, city, zip) is prime (belongs to at least one candidate key).
• Therefore, Address passes 3NF ($\text{zip} \to \text{city}$ has a prime dependent city), but fails BCNF because determinant zip is not a superkey!
• Decomposing into $R_1(\text{zip}, \text{city})$ and $R_2(\text{street}, \text{zip})$ achieves BCNF losslessly by Heath's Theorem, while illustrating why BCNF does not always preserve all original functional dependencies within single tables.

from normal_forms.domain import (
    street_journal_title,
    street_journal_title_passes_third_and_fails_boyce_codd,
)

print("Passes 3NF and fails BCNF:", street_journal_title_passes_third_and_fails_boyce_codd())

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4. Example C: BQNF Change Data Capture Incremental Repair (nf.change.bqnf)

Given base relation Orders(order_id, customer_id, status, amount, updated_at) and boundary view:

SELECT customer_id, SUM(amount) AS paid_revenue
FROM Orders
WHERE status = 'paid'
GROUP BY customer_id;

Case	CDC Event	Defect Class in $Q^1$	Terminal Route	Output Repair / Reason
1. Pending $\to$ Paid	old: {status: 'pending', amount: 100} $\to$ new: {status: 'paid', amount: 120}	[0] (Exact Coboundary)	Repair	{customer_id: 7, delta_revenue: +120.0}
2. Paid Amount Update	old: {status: 'paid', amount: 100} $\to$ new: {status: 'paid', amount: 120}	[0] (Exact Coboundary)	Repair	{customer_id: 7, delta_revenue: +20.0}
3. Paid $\to$ Pending	old: {status: 'paid', amount: 100} $\to$ new: {status: 'pending', amount: 100}	[0] (Exact Coboundary)	Repair	{customer_id: 7, delta_revenue: -100.0}
4. Timestamp Only	updated_at changed; status, amount, customer_id unchanged	[0] (Zero Defect)	Preserve	No boundary columns modified
5. Missing Evidence	old / new missing status and amount	[NonZero - MissingEvidence]	Invalidate	Fails closed when CDC before/after image is incomplete
6. Unsupported Extremum	MAX(amount) boundary without auxiliary extremum cochain	[NonZero - LimitOfSubstrate]	Unsupported	Requires priority-queue cochain or partition recomputation

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5. Epistemic Claim Hygiene Quadrant

1. What it supports:
   • Demonstrates in this toy setting that the Python evaluators reproduce the declared terminal routes for 0NF–5NF, BQNF, CODA_MUR reconciliation, and observer freshness.
2. What it does not support:
   • Does not substitute for production database concurrency control or physical distributed consensus.
3. The narrowest defensible claim:
   • Each worked example executes deterministically against the fixtures in contracts/data/ with AuthorityEffect: None.
4. The next test needed:
   • Randomized fuzzing of mixed INSERT/UPDATE/DELETE sequences against priority-queue and quantile-sketch cochains.