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Backend-Assurance Harness

External evidence for the class-(J) believe_me axioms in src/abi/Boj/SafetyLemmas.idr. None of these documents or tests change the in-language proof — the believe_me sites stay in source. The harness shrinks the trusted base by replacing "we trust the backend" with "we have read the backend lowering and randomly tested the operation against the claimed property".

Per PROOF-NEEDS.md (Axiom Audit 2026-05-18):

The 5 string/char-primitive axioms are irreducible within Idris2 (opaque primitive types). They cannot be "proved away" in-language; the only reduction path is to shrink the trusted base by validating prim__eqChar / prim__strToCharList / prim__strAppend / prim__strSubstr against the chosen backend (Chez/BEAM) via an external trusted-extraction or property-test harness, then citing that evidence here.

This directory is where the trusted-extraction validation lives. The companion property-test harness lives under elixir/test/backend_assurance/ (BEAM half) and is wired into CI via .github/workflows/backend-assurance.yml.

Coverage

Primitive Axioms covered Trusted-extraction Property test
prim__eqChar charEqSound, charEqSym prim__eqChar.md elixir/test/backend_assurance/prim_eq_char_test.exs
prim__strToCharList unpackLength prim__strToCharList.md elixir/test/backend_assurance/prim_str_to_char_list_test.exs
prim__strAppend appendLengthSum prim__strAppend.md elixir/test/backend_assurance/prim_str_append_test.exs
prim__strSubstr substrLengthBound prim__strSubstr.md elixir/test/backend_assurance/prim_str_substr_test.exs

Each row is delivered as one PR per primitive.

Constraints

  • No new believe_me. External evidence only. The 5 axioms stay.
  • No in-language discharge. Already ruled out by the 2026-05-18 audit.
  • Two backends, not one. The trusted-extraction doc must cite both Chez Scheme (idris2's default codegen) and BEAM (Erlang/Elixir, where BoJ's REST surface runs). Property tests cover BEAM; Chez is argued prose-side from R6RS semantics.
  • Honest framing. If a primitive turns out to not satisfy its axiom under some input class, document the failure and adjust the axiom — do not paper over it.

Running locally

cd elixir
mix deps.get
mix test --only backend_assurance

The harness has no Idris2 dependency; it validates the backend operations the Idris2 axioms ultimately depend on.

References

  • PROOF-NEEDS.md — axiom audit and class-(J) framing.
  • src/abi/Boj/SafetyLemmas.idr — the believe_me declarations.
  • epic #87 Tier C — campaign tracking.