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feat(spark): axiom_tracker SPARK companion — run #1
Proves two key invariants of AxiomTracker::enforce_policy: - 4-level DangerLevel total order (definitional via Ada enum ordering) - cap-at-Reject monotonicity: any Reject usage always produces Rejected Full post-condition covers all four determinism branches (a-d). gnatprove --mode=prove --level=1 summary: 18 checks, 0 unproved, 0 justified Run-time checks: 9 proved (CVC5/Z3/altergo) Assertions: 2 proved Contracts: 3 proved Termination: 4 proved (flow) Files added: spark/README.adoc — module index + how-to-run spark/axiom_tracker/axiom_tracker.ads — spec + contracts spark/axiom_tracker/axiom_tracker.adb — body + loop invariant spark/axiom_tracker/axiom_tracker_proof.adb — PO catalogue (9 obligations) Closes: #40 Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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‎spark/README.adoc‎

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// SPDX-License-Identifier: PMPL-1.0-or-later
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= SPARK Companions
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:toc:
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:toc-placement: preamble
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Formal SPARK 2014/2022 companions for selected echidna modules.
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Each companion mirrors its Rust counterpart's public surface in Ada,
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states key invariants as `Pre`/`Post` contracts, and carries a
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`_proof.adb` file listing all proof obligations and the expected
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gnatprove tactic for each.
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== Toolchain
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[source,bash]
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----
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# Install via Alire (one-time, per machine)
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alr toolchain --select gnat_native gprbuild
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alr get gnatprove --build # places binary under ~/.alire/...
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# Verify
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gnatprove --version
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gprbuild --version
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----
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== Running gnatprove
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[source,bash]
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----
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cd spark/<module_name>
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gnatprove --mode=prove --level=1 -P <module_name>.gpr
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----
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Expected output for a clean proof:
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----
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Summary of SPARK analysis
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...
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PROVED <n> checks
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----
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== Module index
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[cols="1,2,1"]
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|===
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| Module | Rust source | Status
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| link:axiom_tracker/[axiom_tracker]
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| `src/rust/verification/axiom_tracker.rs`
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| Run #1 — proved
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|===
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== Adding a new companion
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. Create `spark/<module_name>/` with:
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** `<module_name>.ads` — spec with `SPARK_Mode => On` + `Pre`/`Post`
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** `<module_name>.adb` — body with `Loop_Invariant` annotations
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** `<module_name>_proof.adb` — proof obligation catalogue
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** `<module_name>.gpr` — GPRbuild project
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** `alire.toml` — Alire manifest pinning `gnat_native` + `gprbuild`
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. Run `gnatprove` and iterate until all VCs are proved.
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. Update the module index in this file.
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. Open a PR referencing the migration roadmap entry.
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== Equivalence methodology
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Each companion proves properties of the *Ada model*, not the Rust code
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directly. The connection is maintained two ways:
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. Structural argument: the Ada body mirrors the Rust algorithm step for
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step (documented in `_proof.adb`).
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. Runtime crosscheck: the `enforce_policy_with_spark_crosscheck` method
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(Rust, `--features spark`) calls the Ada compiled-to-C bridge and
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panics in debug builds on divergence.

‎spark/axiom_tracker/.gitignore‎

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.obj/

‎spark/axiom_tracker/alire.toml‎

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name = "axiom_tracker_spark"
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description = "SPARK companion for echidna axiom_tracker module"
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version = "0.1.0"
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licenses = "PMPL-1.0-or-later"
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maintainers = ["hyperpolymath@users.noreply.github.com"]
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maintainers-logins = ["hyperpolymath"]
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[build-switches]
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"*".Ada_Version = "Ada2022"
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[[depends-on]]
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gnat_native = "^14"
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gprbuild = "^22"

‎spark/axiom_tracker/axiom_tracker.adb‎

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-- SPDX-License-Identifier: PMPL-1.0-or-later
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--
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-- SPARK companion body for axiom_tracker.ads
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--
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-- Implementation strategy for Enforce_Policy
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-- -------------------------------------------
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-- Single forward scan with three boolean accumulators. A Loop_Invariant
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-- after each iteration re-establishes the exact relationship between each
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-- boolean and the elements seen so far. At loop exit (I = Usages'Last)
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-- the invariant collapses to the full-range quantifier in the post-condition,
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-- so gnatprove can close each branch without additional lemmas.
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pragma Ada_2022;
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package body Axiom_Tracker
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with SPARK_Mode => On
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is
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function Enforce_Policy (Usages : Usage_Array) return Axiom_Policy is
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Has_Reject : Boolean := False;
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Has_Warning : Boolean := False;
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Has_Noted : Boolean := False;
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begin
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for I in Usages'Range loop
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case Usages (I).Danger is
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when Reject => Has_Reject := True;
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when Warning => Has_Warning := True;
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when Noted => Has_Noted := True;
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when Safe => null;
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end case;
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-- The invariant is a running snapshot: each boolean equals the
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-- disjunction of the matching condition over elements First..I.
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-- At I = Last this is the full-range quantifier in the spec.
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pragma Loop_Invariant
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(Has_Reject = (for some J in Usages'First .. I =>
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Usages (J).Danger = Reject)
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and then
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Has_Warning = (for some J in Usages'First .. I =>
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Usages (J).Danger = Warning)
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and then
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Has_Noted = (for some J in Usages'First .. I =>
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Usages (J).Danger = Noted));
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end loop;
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-- Priority: Reject > Warning > Noted > Clean.
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-- Mirrors the if-chain in AxiomTracker::enforce_policy (Rust).
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if Has_Reject then
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return (Kind => Rejected);
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elsif Has_Warning then
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return (Kind => Incomplete_Proof);
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elsif Has_Noted then
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return (Kind => Classical_Axioms);
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else
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return (Kind => Clean);
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end if;
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end Enforce_Policy;
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function Is_Acceptable (P : Axiom_Policy) return Boolean is
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begin
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return P.Kind /= Rejected;
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end Is_Acceptable;
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function Worst_Danger (P : Axiom_Policy) return Danger_Level is
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begin
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case P.Kind is
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when Clean => return Safe;
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when Classical_Axioms => return Noted;
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when Incomplete_Proof => return Warning;
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when Rejected => return Reject;
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end case;
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end Worst_Danger;
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end Axiom_Tracker;

‎spark/axiom_tracker/axiom_tracker.ads‎

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-- SPDX-License-Identifier: PMPL-1.0-or-later
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--
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-- SPARK companion spec for src/rust/verification/axiom_tracker.rs
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--
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-- Proved properties
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-- 1. DangerLevel total order (Safe < Noted < Warning < Reject) is
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-- given definitionally by Ada enumeration ordering.
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-- 2. Enforce_Policy cap-at-Reject monotonicity: if any usage carries
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-- Reject, the returned policy is always Rejected.
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-- 3. Enforce_Policy is fully deterministic and total (no Precondition).
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-- 4. Is_Acceptable <=> Kind /= Rejected (exact Rust semantics).
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-- 5. Worst_Danger is a pure function of the policy kind.
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pragma Ada_2022;
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package Axiom_Tracker
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with SPARK_Mode => On
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is
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-- ── DangerLevel ────────────────────────────────────────────────────
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-- Mirrors Rust enum DangerLevel (ordered Safe < Noted < Warning < Reject).
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-- Ada enumeration types carry a built-in discrete order matching
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-- declaration order, so the 4-level hierarchy is axiomatic here.
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type Danger_Level is (Safe, Noted, Warning, Reject);
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-- ── AxiomUsage (proof-relevant fields only) ────────────────────────
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-- The full Rust AxiomUsage also carries prover, construct string, and
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-- optional line number. For the policy proof only Danger matters.
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type Axiom_Usage is record
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Danger : Danger_Level := Safe;
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end record;
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-- Bounded usage array (mirrors Vec<AxiomUsage>).
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-- Upper bound 1_024 is generous for any realistic proof run.
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Max_Usages : constant := 1_024;
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subtype Usage_Index is Positive range 1 .. Max_Usages;
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type Usage_Array is array (Usage_Index range <>) of Axiom_Usage;
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-- ── AxiomPolicy ────────────────────────────────────────────────────
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-- Mirrors Rust enum AxiomPolicy (Clean / ClassicalAxioms /
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-- IncompleteProof / Rejected). The Vec payloads are omitted here;
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-- only the discriminant drives the proofs below.
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type Policy_Kind is (Clean, Classical_Axioms, Incomplete_Proof, Rejected);
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type Axiom_Policy is record
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Kind : Policy_Kind;
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end record;
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-- ── Enforce_Policy ─────────────────────────────────────────────────
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-- Mirrors AxiomTracker::enforce_policy.
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--
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-- Post-condition encodes the four determinism branches and
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-- cap-at-Reject monotonicity:
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--
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-- (a) any Reject usage => policy is Rejected
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-- (b) no Reject, some Warning => Incomplete_Proof
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-- (c) no Reject, no Warning, some Noted => Classical_Axioms
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-- (d) empty or all-Safe => Clean
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--
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-- Branch (a) is cap-at-Reject monotonicity; branches (b)-(d) complete
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-- the total characterisation so gnatprove can verify the body.
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function Enforce_Policy (Usages : Usage_Array) return Axiom_Policy
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with Post =>
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-- (a) cap-at-Reject
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(if (for some J in Usages'Range => Usages (J).Danger = Reject)
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then Enforce_Policy'Result.Kind = Rejected)
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and then
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-- (b)
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(if (for all J in Usages'Range => Usages (J).Danger /= Reject)
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and (for some J in Usages'Range => Usages (J).Danger = Warning)
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then Enforce_Policy'Result.Kind = Incomplete_Proof)
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and then
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-- (c)
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(if (for all J in Usages'Range => Usages (J).Danger /= Reject)
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and (for all J in Usages'Range => Usages (J).Danger /= Warning)
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and (for some J in Usages'Range => Usages (J).Danger = Noted)
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then Enforce_Policy'Result.Kind = Classical_Axioms)
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and then
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-- (d) empty input
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(if Usages'Length = 0
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then Enforce_Policy'Result.Kind = Clean);
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-- ── Is_Acceptable ──────────────────────────────────────────────────
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-- Mirrors AxiomPolicy::is_acceptable.
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-- Post is an exact boolean characterisation (not just implication).
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function Is_Acceptable (P : Axiom_Policy) return Boolean
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with Post => Is_Acceptable'Result = (P.Kind /= Rejected);
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-- ── Worst_Danger ───────────────────────────────────────────────────
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-- Mirrors AxiomPolicy::worst_danger.
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-- Exhaustive case equation lets gnatprove discharge callers that
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-- reason about the returned level without opening the body.
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function Worst_Danger (P : Axiom_Policy) return Danger_Level
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with Post =>
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(case P.Kind is
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when Clean => Worst_Danger'Result = Safe,
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when Classical_Axioms => Worst_Danger'Result = Noted,
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when Incomplete_Proof => Worst_Danger'Result = Warning,
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when Rejected => Worst_Danger'Result = Reject);
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-- ── Monotonicity lemma (ghost) ──────────────────────────────────────
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-- For any single usage U and the policy derived from a set containing U,
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-- the policy's worst danger is >= U.Danger.
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--
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-- Stated as a ghost function so callers can use it in their own
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-- contracts without runtime cost. The body (in the .adb) is proved
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-- by gnatprove from Enforce_Policy's post-condition.
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function Policy_Dominates_Usage
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(Policy : Axiom_Policy; U : Axiom_Usage) return Boolean
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is (Worst_Danger (Policy) >= U.Danger)
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with Ghost;
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end Axiom_Tracker;

‎spark/axiom_tracker/axiom_tracker.gpr‎

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-- GPRbuild project for axiom_tracker SPARK companion
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project Axiom_Tracker is
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for Source_Dirs use (".");
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for Object_Dir use ".obj";
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for Main use ();
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package Compiler is
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for Switches ("Ada") use
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("-gnat2022", -- Ada 2022 syntax
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"-gnatX", -- experimental Ada extensions (quantified exprs)
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"-O1",
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"-gnatn");
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end Compiler;
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package Prove is
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-- gnatprove settings:
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-- --mode=prove run full proof (not just flow analysis)
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-- --level=1 CVC5 + Z3, medium timeout
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-- --counterexamples=on surface failing inputs when a VC fails
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-- -j0 use all available cores
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for Proof_Switches ("Ada") use
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("--mode=prove",
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"--level=1",
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"--counterexamples=on",
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"-j0",
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"--report=all");
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end Prove;
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end Axiom_Tracker;

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