How FunctionaL City formalized its first narratable union through symbolic inspection and provenance scaffolding
In FunctionaL City, every ordinance begins with legibility. Every civic object—whether a lifted cell or symbolic set—is expected to carry its own signage and provenance. This week, the city ratified its first Civic Union, a narratable merger of two symbolic sets: Nat and Odds. The journey began with the development of the civicSetInspectorReport, a signage overlay designed to inspect and narrate any ICivicSet.
The inspector report is more than a diagnostic—it’s a civic artifact. It narrates the lineage, metadata, and symbolic formula of a declared set. Here’s the output for ℕ, the set of natural numbers:
🧾 CivicSet Inspector Report
────────────────────────────
🆔 Symbol: ℕ
📐 Formula: x ≥ 0
📊 Set-Theoretic Metadata:
• Cardinality: Aleph0
• Countability: Countable
• Order Type: TotalOrder
🔍 Min: 0
🔍 Max: —
🧭 Provenance:
Step 1 from ZFC + Peano Axioms on 1/1/1930 12:00:00 AM — Declared ℕ as the set of natural numbers ≥ 0, formalized in ZFC and derived from Peano axioms.
📝 Civic Note:
ℕ, the set of natural numbers ≥ 0, originates from Giuseppe Peano's 1889 axioms,
which defined arithmetic using successor functions and induction. These axioms laid the
foundation for formal number theory. In the early 20th century, Ernst Zermelo introduced
axioms for set theory (1908), later extended by Abraham Fraenkel and others to form ZFC.
Within this framework, ℕ was reconstructed as a set-theoretic object using the von Neumann
ordinal construction, where each natural number is defined as the set of all smaller
natural numbers. This civic declaration reflects that lineage: ℕ is countable, totally ordered,
and formally grounded in ZFC + Peano arithmetic.
This declaration is civic in nature: it doesn’t just define ℕ—it narrates its ancestry. From Peano’s 1889 successor axioms to the von Neumann ordinal construction within ZFC, the report scaffolds a symbolic lineage that remixers can audit, inherit, and extend.
Once Nat and Odds were inspected and declared as lawful ICivicSets, the next ordinance was clear: Union. But in FunctionaL City, unions aren’t just runtime operations—they’re civic acts. Each union must be:
Lifted: Each constituent set is wrapped with provenance metadata.
Tagged: Each wrapper carries a civic tag (SimpleSet:Nat, SimpleSet:Odds, LiftedUnion).
Timestamped: Every union step is chronologically staged.
Narrated: The union carries a civic note, describing its symbolic intent and derived provenance.
Here’s the union metadata:
Union symbol: Some "Nat ∪ Odds"
Union metadata:
Tag: SimpleSet:Nat
Prov: Nat step=1
Tag: SimpleSet:Odds
Prov: Odds step=1
Tag: LiftedUnion
Prov: Nat ∪ Odds step=2
Each wrapper—A and B—is a narratable civic object:
A -> set Some "Nat" with prov Some { SourceName = "Nat ∪ Odds (A-wrapper)",
Step = 2,
Timestamp = Some 10/14/2025 1:26:31 AM,
Note = "Derived provenance (union/lifted)" }
B -> set Some "Odds" with prov Some { SourceName = "Nat ∪ Odds (B-wrapper)",
Step = 2,
Timestamp = Some 10/14/2025 1:26:31 AM,
Note = "Derived provenance (union/lifted)" }
The union is then flattened and collapsed to concrete members:
Flattened members (Choice): [Choice1Of2 1; Choice1Of2 2; Choice1Of2 3; Choice2Of2 1; Choice2Of2 3; Choice2Of2 5]
Collapsed to Concrete: [1; 2; 3; 5]
This isn’t just a union—it’s a Civic Union. It’s narratable, timestamped, and legacy worthy.
With the inspector report scaffolding symbolic lineage and the union constructor lifting sets into provenance-aware wrappers, FunctionaL City now has the infrastructure to support:
Multi-type Civic Unions: With canonical FOL formulas and monotonic step numbers.
Dispatcher Signage Overlays: So every civic module can narrate its own onboarding.
Provenance Bridges: Linking symbolic declarations (SetProvenance) with runtime traceability (Provenance).
Now that we have proof of concept, it’s time to take the CivicSet from 35% to 65% design completion. To get there will require some work. I will need to go back through the code and refactor and document what is there before moving on to coding the rest of the modules in the CivicSet namespace. Please be aware as Foundations is still a construction zone. You can find the code here
City Limits
Primitives ordinance book.
First Order Logic ordinance book.
Civic Set ordinance book.
Keep an eye out for future editions of Message from the Mayor as the city grows and random musings develop along the way. In the meantime, keep an eye on the BlogDistrict README.md for updates.
Signed,
FrankL
Mayor and City Engineer of FunctionaL City