# Relations as posts — declared, inherited, and eventually algebraic

## Principle

Everything is a post in one graph: content-posts, type-posts, **relation-posts**, and
(later) **constraint-posts**. Nothing about typing is hardcoded — a type-post *declares*
which relations it anchors, declarations are *inherited* down the type closure, and
every candidate set / validation is a transitive graph query (`lib/relations`). This
closes the meta-circular loop the typing plan gestured at: the type system describes
itself in its own graph.

Supersedes the hardcoded `:candidates "types"/"tags"/"all"` field of `host/blog-rel-kinds`.

## North star — the metamodel as a system-construction kit

The destination this is all heading toward: the host stops being "a blog" and becomes a
**self-describing metamodel**. You *define a domain* — types (with schemas/refinements) and
relations (with role signatures + algebra) — and a working system falls out. The blog content
is one seeded configuration; clear it and define different types and you have a different system
on the same engine. Framework, not application (cf. `[[feedback_runtime_control]]`,
`[[project_zero_dependencies]]`).

Most of the **instance UI is already generic** — the edit page's relation editors are generated
by iterating the relations; each picker's candidates come from the relation's `declares`-anchor /
role type; validation comes from the type's `:schema`. So once Slices 6–7 land, "define the
types" through a UI is mostly two surfaces, plus a reset:

1. **Metamodel editor** — create a type-post (give it a schema/refinement); create a relation-post
   (give it a role signature + algebra). The thing that lets you *construct* a system.
2. **Generic instance form** — create/edit any post of any type, driven entirely by the
   definitions above (the relation editors + pickers + save-time validation we already have).
3. **Clear-and-reseed** — wipe instance data, seed only the metamodel roots (`type`, `relation`,
   the core relations); start from a bare kit and build a domain up from nothing.

Sequence: finish the schema language (Slices 6–7) → the two UI surfaces + reset → clear the demo
data and define a real domain through the UI. The slices below are the schema language; this is
what it's *for*.

## Why (the wrinkle that started this)

Candidates for `is-a`/`subtype-of` were `instances-of("type")` — the *instances* that are
types, but NOT the type-defining posts themselves (`type`, `tag`, `article` are wired with
`subtype-of`, no `is-a` edge, so they're not instances of type). So the picker offered
`tutorial` (is-a tag) but never `tag`/`article`/`type` — the things you most want to say a
post *is-a*. The fix is to ask the right question: a candidate is anything that **inherited
the relation's object-end declaration from the anchor**, which includes the roots.

## Model

- A **declaration** is an edge `T --declares--> R`: type-post `T` anchors relation `R` at
  its **object** end ("you may point *at* `T` with `R`"). Seed: `type declares is-a`,
  `type declares subtype-of`, `tag declares tagged`. `related` has no declaration.
- **Candidate set** for relating under `R` = the **down-closure** of `R`'s anchors through
  `inverse(is-a) ∪ inverse(subtype-of)` (a post is a candidate iff it is, transitively, an
  instance-or-subtype of an anchor — or IS one). No anchors ⇒ every post (`related`).
  - `is-a`/`subtype-of`: anchors `{type}` ⇒ the whole type closure (roots + subtypes +
    instances). **Wrinkle fixed.**
  - `tagged`: anchors `{tag}` ⇒ the tags.
  - `related`: no anchor ⇒ all posts.

## Roadmap

### Slice 1 — declarations + candidate-by-inheritance — DONE
- Seed `declares` edges; add `host/blog--reach-down` (down-closure) and rewire
  `host/blog--candidate-pool` to be declaration-driven. `:candidates` becomes vestigial.
- Wrinkle fixed: the type roots now appear as `is-a` candidates.

### Slice 2 — relations as first-class posts — DONE
- `relation` root + `is-a`/`subtype-of`/`tagged`/`related` seeded as posts (each is-a
  relation) owning their metadata in a `:rel` slot (`:symmetric :label :inverse-label`).
  `host/blog-rel-kinds` / `kind-spec` / `kind-symmetric?` now read it; the static registry
  is gone. `host/blog--rel-slugs` = `host/blog-in "relation" "is-a"` (cheap, flat).
- **Perform budget under http-listen (the hard lesson):** a durable read inside the
  render VM raises `VmSuspended`, and too many per request 500s the page. Two fixes:
  (1) relation metadata is loaded into an in-memory cache at boot (`host/blog-load-rel-kinds!`,
  like `load-edges!`) so `kind-spec` is pure; (2) the initial edit page renders its pickers
  EMPTY (the load trigger fills each) — only the relate/unrelate FRAGMENT server-renders
  candidates (`with-cands` flag), so one page render doesn't do `candidate-get × every
  picker`. Benign single-perform suspend/resume still logs `VmSuspended` but returns 200.
- **Live JIT gotcha (cost real time):** the serving-mode JIT drops all-but-first when
  `map`/`for-each`-ing a *function-produced* list — building `rel-kinds` that way rendered
  only 1 of 4 editors live, while conformance + the ephemeral server passed. So
  `host/blog-rel-kinds` is a VALUE the boot populates and the cache loads are UNROLLED.
  **Conformance green ≠ correct live — verify the rendered edit page.** (Re-fold the
  enumeration once plans/jit-bytecode-correctness.md lands.)
### Slice 2.5 — picker title reads are O(page), not O(pool) — DONE
- `relate-candidates` computes the available candidate SLUGS (slug-sorted, no per-candidate
  read), then reads titles ONLY for the page it returns. On the unfiltered path (q="" — the
  initial picker load AND every editor server-fill, the common case) that's ~`limit` reads
  instead of one-per-post — killing the durable-read churn under http-listen. A filter
  (q≠"") still resolves titles across the pool (it matches on the title), but that's the
  interactive path.
- A boot-time slug→title **cache** would make even the filter O(1)-perform, BUT it's blocked
  for now: there's no bulk KV read, and a per-post `host/blog-get` loop **at boot** hits the
  JIT bug (a durable read inside a boot loop drops all-but-first — `load-edges!` only works
  because its loop body is perform-free). Revisit with a bulk read or once the JIT lands.

**Remaining follow-ups:** subject-end declarations (who may be the *source*); a proper
relation-subtype closure when relations get subtyped; the boot title cache above.

### Slice 3 — typed relations (target-type constraints) — DONE
- The declaration's `declares`-anchor IS the target-type constraint: `is-a`/`subtype-of`
  (anchored by `type`) require a type object; `tagged` (anchored by `tag`) a tag. A new
  `wrote` relation needs only a `Work declares wrote` edge — fully data-driven.
- `host/blog--valid-object?(kind, other)` = `other ∈ candidate-pool(kind)` — the SAME set
  the picker offers, so picker and validation agree by construction. `relate-submit` now
  enforces it (an invalid target is a silent no-op, like the other guards); `related`
  (no anchor) accepts any post. The picker never offers an invalid target, so this guards
  crafted/API requests — the jump from "candidate set" to an enforced relation schema.
- NOTE: `host/blog-relate!` (direct/seed) stays UNVALIDATED — the seed needs to write
  `X is-a relation` where `relation` isn't under `type`. Validation is a *handler* boundary.

### Slice 4 — type algebra — DONE (intersection ∧ union)
- An algebraic type is a post with operand edges: `conj` edges (intersection members),
  `disj` edges (union members). `host/blog-instances-of-expr` computes its EXTENT from the
  operands' extents by set intersection / union, RECURSIVELY — so operands can themselves be
  algebraic (meta-circular; tested with `(tag ∧ article) ∧ tag`). `host/blog-is-a-expr?`
  generalises `is-a?` to type expressions. `host/blog-make-and!` / `make-or!` build them.
- Binary today (`nth 0/1`, no fold over operands — robust on the serving JIT); n-ary fold is
  a follow-up once iteration-with-perform is JIT-reliable.
- **Operand edges are KV-only** (`host/blog--add-edge-kv!`, read via `host/blog-out`), NOT in
  lib/relations — feeding extra kinds into the Datalog graph blows up its per-query
  re-saturation; `load-edges!` skips `conj`/`disj` on replay for the same reason.
- **Refinement** `{x : T | φ(x)}` (a type-post with a `:constraint` predicate) → Slice 5,
  with constraints-as-posts. (Process note: a sibling loop running heavy conformance saturates
  the box; host conformance can EXIT 124 purely from CPU contention — use `timeout 1200`.)

### Slice 5 — refinement types (schemas ON the type-post) — DONE
- A type-post carries its schema in a `:schema` slot (a list of `{:block :msg}` rules —
  a refinement `{x : T | x has these blocks}`). `host/blog-schema-of` reads it off the
  post; the hardcoded `host/blog-type-schemas` table is gone. A NEW refinement type is pure
  data: give a type-post a `:schema` (`host/blog--set-schema!`) and its instances are
  validated on save against it — no code. Tested with a `guide` type requiring a `pre` block.
- Save-time validation (`type-issues`/`type-valid?`, the only callers, in the SAVE request)
  unions the schemas of a post's full transitive type set — unchanged, just sourced from the
  posts. `schema-of` reads the post (a durable read) — fine in the save request, never render.
- `host/blog-put!` now MERGES over the previous record, so editing a post's title/content
  doesn't nuke its `:schema` / `:rel` metadata (also closes the Slice 2 "edit drops :rel" gap).
- `article`'s schema migrated onto the article post (`set-schema!` at boot — a single
  read+write, not a loop, so boot-JIT-safe; idempotent, handles the already-seeded article).
- FUTURE: arbitrary predicate constraints (not just required blocks); constraints as their
  own posts; relation cardinality (`is-a` single-valued?) as a declared constraint.

## Parameterised relations (DESIGN — Slices 6 & 7)

The next axis: `Relation<…>`. The key reframe is that the obvious parameters aren't separate
`<N>`s — they split into **two halves**, and they compose into one coherent thing:

1. **The role SIGNATURE** (the *shape* of a tuple) — Slice 6 (a + b + c).
2. **The relation's ALGEBRA** (how it *behaves*) — Slice 7 (d).

A relation is `Relation<signature>`, where a signature is an ordered list of **roles**, each
role carrying a **type** and a **cardinality**; the signature's length is the **arity**.
Today's binary typed relations are the degenerate 2-role case — backward-compatible, nothing
gets thrown away. Prior art to borrow (and stay decidable within): Codd / ER reified
relationships (signature), OWL property characteristics (algebra), Datalog / relation algebra
(derived relations — the undecidable frontier; fence it). Decidability rule of thumb: concrete
+ algebraic role-types and counts stay decidable; arbitrary predicates / recursive rules don't.

### Slice 6 — the role signature (a + b + c)
Generalise the relation-post's `:rel` slot from `{:symmetric :label}` to a `:roles` list —
`{:roles [{:name :type :card} …]}` — driving picker candidates, validation, and arity per-role:
- **(a) per-role type** — each role's `:type` is a type-expr (so it can be algebraic:
  `Relation<Work ∧ Published>`). The object-role's type IS today's `declares`-anchor — make it
  explicit. `valid-object?` becomes per-role `is-a-expr?` against `:type`.
- **(b) arity** = `(len roles)`. Binary stays the fast `src|kind|dst` edge path; **n-ary needs
  reification**: a relation *instance* becomes its own post with role edges (`subject→X`,
  `object→Y`, `recipient→Z`) — on-brand (we made relation *kinds* posts; now *instances* too),
  but a SECOND representation alongside the binary edges, not a tweak. Qualifiers (Wikidata-
  style) then come free as extra roles.
- **(c) cardinality** — `:card` per role (min/max; functional = max 1, required = min 1),
  enforced on relate by counting. Composes with Slice 5 validation. No model change for binary.
- Siblings: ordered roles (set vs list), keys/identity (which roles identify a tuple).
- **Layering (cheapest → deepest):** (c) cardinality on the binary object-role → (a) explicit
  role-type + the 2-role signature abstraction → (b) reified n-ary (the real lift).
- **Variance: nominal, none initially** — no structural subtyping of `Relation<…>` (covariance
  of parameterised types is a research project). JIT caveat: 2-role signatures are unrollable;
  n-ary role-iteration with per-role reads needs the cache/unroll treatment (Slice 2/5 lesson).

### Slice 7 — relation algebra / characteristics (d)
The behaviour half — and (d) **transitivity** is special because we ALREADY hardcode it
(`is-a`/`subtype-of` closure via lib/relations); declaring it generically *removes* code.
- **Algebraic properties** declared on the relation-post (`:transitive :symmetric :reflexive
  :antisymmetric :irreflexive`), with the closure **derived generically** from them — OWL's
  property characteristics. `subtype-of` becomes "a declared transitive + antisymmetric
  relation" (a partial order), not a special case. `:symmetric` (already stored) folds in here.
- **Inverse relations** — a real `:inverse` (not just the `:inverse-label` display hint):
  relating one auto-derives the converse, the way `:symmetric` writes both directions.
- **Sub-relations** — relations subtyping relations (`wrote subPropertyOf created`): X wrote Y
  ⟹ X created Y. Same `subtype-of` machinery, over the `relation` root — meta-circular.
- **Decidable core stops here.** Beyond-d, FENCED: defined-by-rule relations (composition,
  `grandparent = parent ∘ parent` — straight onto the Datalog substrate, but gate to
  stratified/bounded rules) and cross-role refinement predicates (`start < end`) — both need
  the predicate-language-vs-embedded-code decision first.

## Open design questions (track as we go)
1. **Subject-end declarations** — who may be the *source* of a relation (a root `Thing`?).
2. **Inheritance path** — through `is-a` AND `subtype-of` downward (current choice); revisit
   if instances-of-instances as candidates surprises.
3. **Bootstrap / meta-circularity** — `is-a` needs `is-a`; seed relation-posts + `Type is-a
   Type`(?) idempotently, as the type seed already is.
4. **Cost** — `reach-down` is a BFS of direct-edge scans; fine for a small blog, revisit with
   a `lib/relations` transitive query if the graph grows.