feat(frontend): detect uninhabited (uninhabited) required-recursion schemas

[tdakkota]

Summary

Closes #8. Required self-recursion — e.g. {type:object, required:[self], properties:{self:{$ref:"#"}}} — has no finite JSON instance (every value must contain a strictly smaller one of itself), but SCC analysis classifies it Guarded/representable: it only checks termination (a base case could exist in the Go type), not inhabitation (whether any instance reaches it). This adds the missing inhabitation analysis.

Approach

A least-fixed-point pass over the reference graph (internal/frontend/inhabit.go, modeled on refkinds.go's cycle-safe walk): inhabited(n) starts false and is proven true only when a finite witness can be built from already-inhabited parts. A purely-required cycle never produces a witness, so it stays uninhabited at the fixed point.

Sound over-approximation — the analysis never false-positives a satisfiable schema:

• Any construct it does not model (combinators, conditionals, const/enum, arrays) ⇒ assumed inhabited (false negatives only, never false positives).
• required only constrains object instances, so it bites only when the node is object-only (type:object); a permitted non-object kind yields a scalar/null witness that ignores required.
• A $ref is treated as a conjunctive constraint: a provably-uninhabited target makes the referrer uninhabited too.

Only recursive required-object emptiness is reported (the surprising case the SCC pass misses); local emptiness (false schema, disjoint kinds) is already modeled by normalization and intentionally not re-reported.

Surfacing

Schema.Uninhabited []UninhabitedNode (alongside Unresolved), turned into a SeverityWarning by Compile (uninhabitedDiagnostics) — the schema is representable but no value inhabits it, so a generator should warn rather than emit a dead recursive type.

Tests (internal/frontend/inhabit_test.go + one Compile test)

Positive: self-recursion and mutual A↔B recursion flagged. Negative (no false positives): optional-property escape, nullable node (type:["object","null"]), untyped (scalar witness), nullable-branch-via-combinator, and finitely-nested required chains — all correctly not flagged.

Verification

• go build ./..., go test ./... (incl. conformance), golangci-lint run ./... → 0 issues

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Unrelated hygiene note: a graphviz test writes graph.dot to the repo root without cleaning it up (and it isn't gitignored). Not touched here; happy to fix separately.

🤖 Generated with Claude Code

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 75.90%. Comparing base (38e2577) to head (55dff8b).

Additional details and impacted files

@@            Coverage Diff             @@
##             main      #13      +/-   ##
==========================================
+ Coverage   75.43%   75.90%   +0.46%     
==========================================
  Files          42       43       +1     
  Lines        3143     3204      +61     
==========================================
+ Hits         2371     2432      +61     
  Misses        629      629              
  Partials      143      143              

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