Theoria's trusted runtime boundary is the native kernel. Assurance commands compare that kernel with independent reference paths, re-admit checked environments through replay, and check generated artifacts. These checks improve confidence; they are not a formal proof of kernel correctness and do not imply Lean feature parity.

Main command

mix theoria.kernel.check

This runs the curated kernel corpus, generated terms, generated environment corpora, theorem-module replay, artifact replay, trusted-adjacent metadata/reduction replay, and invalid-environment rejection checks.

Useful variants:

mix theoria.kernel.check --verbose
mix theoria.kernel.check --coverage
mix theoria.kernel.check --assurance-summary
mix theoria.kernel.check --assurance-summary --coverage
mix theoria.kernel.check --json

Bounds

Generated assurance is bounded so CI remains fast:

mix theoria.kernel.check --generated-size 1 --generated-max-terms 4
mix theoria.kernel.check --environment-depth 8

Defaults are chosen for regular CI. Increase bounds locally for deeper assurance.

What the counts mean

  • Curated corpus: hand-authored infer/check/normalize/defeq/rejection cases.
  • Generated terms: deterministic typed terms checked against production and reference paths.
  • Environment corpus: generated declaration chains replayed and normalized through production/reference paths.
  • Invalid environments: malformed environments rejected with expected reason classes.
  • Metadata replay: replayed declarations preserve trusted-adjacent environment metadata and reduction data. This is analogous in spirit to checking Lean environment-extension data, but it is Theoria-specific assurance, not Lean compatibility.
  • Artifact replay: generated and indexed equation artifacts replay in checked environments.

Summary output

mix theoria.kernel.check --assurance-summary

prints a concise user-facing coverage summary. With --json, the output is backed by Jason-encoded structs.

Lean oracle

Contributor-only Lean validation remains separate:

mix theoria.lean.check

Lean is an external regression oracle, not part of Theoria's trusted runtime path.