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feat(formal): Coq mechanisation of P2 + P3 provenance integrity (#87)
## Summary Lands the first three theorems from the proof inventory at #77, opening the verification programme for VeriSimDB: - **P2 `record_verify_iff_unchanged`** — single-record integrity iff `content_hash` equals SHA-256(content, parent_hash). Mirrors `verify()` in `rust-core/verisim-provenance/src/lib.rs`. - **P3 step `chain_linked_step`** — honest append preserves the chain-link invariant. - **P3 corollary `chain_linked`** — chains built from genesis by repeated honest append are well-linked. All three close under the global context. `Print Assumptions` reports only the 4 domain `Parameter`s (`content`, `hash`, `sha256`, `genesis_hash`). The single declared axiom `sha256_collision_resistant` is **unconsumed** by this PR — reserved for later uniqueness theorems (P4, V8). ## Files | Path | Purpose | |---|---| | `formal/Provenance.v` | 3 theorems + 1 lemma (`chain_linked_from_snoc`) + `Print Assumptions` guards | | `formal/Justfile` | `all`, `provenance`, `check-assumptions`, `clean` recipes | | `formal/.gitignore` | `.vo` / `.glob` / `.out` build artefacts | | `.github/workflows/coq-build.yml` | Coq 8.18 container, `just` runner, whitelist guard | ## Build oracle The CI grep is whitelist-based — it parses each `Print Assumptions` block and fails if any name **other** than the 4 Parameters or the 1 Axiom appears. This catches future axiom slippage without false-positiving on the legitimate domain `Parameter`s. ```bash just -f formal/Justfile all # compile just -f formal/Justfile check-assumptions # whitelist guard just -f formal/Justfile clean # remove .vo / .out ``` ## Verification Compiled cleanly with Coq 8.18.0 + just 1.21.0 locally: ``` OK: Print Assumptions matches whitelist (3 theorems × 4 Parameters) ``` ## Test plan - [x] `coqc -q formal/Provenance.v` succeeds with no errors or admits - [x] `Print Assumptions` for each theorem lists only the 4 declared `Parameter`s - [x] `sha256_collision_resistant` does **not** appear in any `Print Assumptions` output (declared but unconsumed) - [x] Justfile recipes all work from a clean checkout - [ ] CI workflow `Coq Build Oracle` passes (will verify on PR) ## Out of scope (next PRs per #77 foundation pack) - **D1** `drift_score_in_unit_interval` (verisim-drift) - **D2** `detect_drift_sound` (verisim-drift) - **C2** `txn_state_machine_well_formed` (verisim-octad) - **C7** `wal_replay_idempotent` (verisim-wal) - **Q1** `planner_logical_physical_equivalence` (verisim-planner) - **V2** `vql_preservation` (VCL semantics) - **N2** `normalize_idempotent` (verisim-normalizer) Closes #77 (foundation-pack starter; remaining 7 of 8 will land as separate PRs per the inventory).
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‎.github/workflows/coq-build.yml‎

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# SPDX-License-Identifier: MPL-2.0
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# Copyright (c) Jonathan D.A. Jewell <j.d.a.jewell@open.ac.uk>
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#
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# Coq Build Oracle — compiles formal/ and asserts no axiom slippage.
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#
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# Uses Ubuntu + apt-installed Coq rather than the coqorg/coq container
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# image. Rationale: coqorg/coq runs as user `coq` with opam-loaded PATH;
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# running it as root (the standard EACCES workaround for actions/checkout)
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# breaks coqc lookup because root has no opam env. Apt-installed Coq is
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# simpler and the proofs here don't require a specific 8.x patch level.
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name: Coq Build Oracle
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on:
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push:
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branches: [main]
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paths:
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- 'formal/**'
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- '.github/workflows/coq-build.yml'
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pull_request:
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paths:
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- 'formal/**'
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- '.github/workflows/coq-build.yml'
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permissions:
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contents: read
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jobs:
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build:
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name: Compile Coq proofs + assumptions guard
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runs-on: ubuntu-latest
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steps:
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- name: Checkout
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uses: actions/checkout@11bd71901bbe5b1630ceea73d27597364c9af683 # v4.2.2
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- name: Install Coq
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run: |
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set -euo pipefail
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sudo apt-get update
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sudo apt-get install -y --no-install-recommends coq
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- name: Coq toolchain provenance
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run: coqc --version
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- name: Compile Provenance.v
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working-directory: formal
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run: |
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set -euo pipefail
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coqc -q Provenance.v | tee Provenance.out
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- name: Verify Print Assumptions whitelist
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working-directory: formal
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run: |
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set -euo pipefail
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# Whitelist:
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# content, hash, sha256, genesis_hash (Parameters)
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# sha256_collision_resistant (declared Axiom)
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# Any other axiom name in Print Assumptions output fails.
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UNEXPECTED=$(awk '/^[A-Za-z_][A-Za-z0-9_]* :/ {print $1}' Provenance.out \
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| sort -u \
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| grep -vE '^(content|hash|sha256|genesis_hash|sha256_collision_resistant)$' || true)
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if [ -n "$UNEXPECTED" ]; then
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echo "ERROR: unexpected axiom(s)/parameter(s) in Print Assumptions:"
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echo "$UNEXPECTED"
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echo "---"
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cat Provenance.out
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exit 1
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fi
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echo "OK: Print Assumptions matches whitelist (3 theorems x 4 Parameters)"

‎formal/.gitignore‎

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*.vo
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*.vos
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*.vok
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*.glob
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.*.aux
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*.out

‎formal/Justfile‎

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# SPDX-License-Identifier: MPL-2.0
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# Copyright (c) Jonathan D.A. Jewell <j.d.a.jewell@open.ac.uk>
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#
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# Coq build oracle for VeriSimDB formal proofs.
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# Follows the Ephapax pattern (hyperpolymath/ephapax formal/Justfile).
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#
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# Local use:
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# just -f formal/Justfile all
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# just -f formal/Justfile check-assumptions
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# just -f formal/Justfile clean
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COQC := "coqc"
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# Compile every proof module.
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all: provenance
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# Compile the provenance module (P2 + P3).
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provenance:
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{{COQC}} -q Provenance.v | tee Provenance.out
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# Verify that every Print Assumptions block in compiled output mentions
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# only the whitelist of declared parameters/axioms. Fails if any new
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# axiom name leaks into a theorem's transitive closure.
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#
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# Whitelist:
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# - content : Type (Parameter, domain)
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# - hash : Type (Parameter, domain)
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# - genesis_hash : hash (Parameter, SHA-256 of "")
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# - sha256 : content -> hash -> hash (Parameter)
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# - sha256_collision_resistant (Axiom, declared but unused)
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check-assumptions: provenance
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@awk '/^[A-Za-z_][A-Za-z0-9_]* :/ {print $1}' Provenance.out \
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| sort -u \
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| grep -vE '^(content|hash|sha256|genesis_hash|sha256_collision_resistant)$' \
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| { if read -r line; then \
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echo "ERROR: unexpected axiom/parameter in Print Assumptions: $line"; \
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cat; \
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exit 1; \
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else \
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echo "OK: Print Assumptions matches whitelist (3 theorems × 4 Parameters)"; \
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fi; }
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# Remove all build artefacts.
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clean:
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rm -f *.vo *.vos *.vok *.glob .*.aux *.out

‎formal/Provenance.v‎

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(* SPDX-License-Identifier: MPL-2.0 *)
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(* Copyright (c) Jonathan D.A. Jewell <j.d.a.jewell@open.ac.uk> *)
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(** * VeriSimDB Provenance Hash-Chain Verification
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Mechanises the foundation-pack theorems P2 ([record_verify_iff_unchanged])
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and P3 ([chain_linked_step], [chain_linked]) for the provenance modality
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defined in [rust-core/verisim-provenance/src/lib.rs].
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The Rust source maintains an append-only hash chain where each record's
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[parent_hash] equals the SHA-256 [content_hash] of its predecessor. The
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three theorems below capture, in increasing strength:
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- [record_verify_iff_unchanged] — a single record verifies iff its
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[content_hash] is the SHA-256 of its content payload and parent_hash.
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- [chain_linked_step] — honest append preserves the chain-link
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invariant.
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- [chain_linked] — every chain built from genesis by repeated honest
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append is well-linked.
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The only declared axiom is [sha256_collision_resistant]. It is NOT
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consumed by the three theorems below; the [Print Assumptions] guard
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at file end confirms each closes under the global context. The
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axiom is reserved for later uniqueness theorems (P4, V8).
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Build oracle: [just -f formal/Justfile all]. CI: [.github/workflows/coq-build.yml].
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Tracking issue: hyperpolymath/verisimdb#77.
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*)
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Require Import Coq.Lists.List.
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Import ListNotations.
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(** ** Domain *)
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(** Opaque content payload. In the Rust source this is the record's
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non-hash fields: event_type, actor, timestamp, source, description. *)
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Parameter content : Type.
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(** Opaque hash output. In the Rust source this is a 64-character hex
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string (SHA-256 digest). *)
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Parameter hash : Type.
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(** SHA-256 of a canonical (content, parent_hash) payload. *)
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Parameter sha256 : content -> hash -> hash.
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(** The genesis hash. In the Rust source this is the SHA-256 of the empty
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string, used as the [parent_hash] of every chain's first record. *)
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Parameter genesis_hash : hash.
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(** SHA-256 collision resistance, stated as injectivity of [sha256] on the
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product of (content, parent_hash). Standard cryptographic assumption. *)
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Axiom sha256_collision_resistant :
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forall (c1 c2 : content) (h1 h2 : hash),
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sha256 c1 h1 = sha256 c2 h2 -> c1 = c2 /\ h1 = h2.
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(** A provenance record: content payload, parent hash, stored content hash. *)
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Record provenance_record : Type := mk_record {
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rec_content : content;
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rec_parent_hash : hash;
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rec_content_hash : hash;
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}.
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(** [record_verify] mirrors [verify()] in the Rust source: the stored
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[content_hash] field equals the SHA-256 of the content payload and
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parent_hash. *)
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Definition record_verify (r : provenance_record) : Prop :=
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rec_content_hash r = sha256 (rec_content r) (rec_parent_hash r).
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(** Honest construction — the [new()] constructor in the Rust source.
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A record built this way always verifies. *)
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Definition mk_honest (c : content) (parent : hash) : provenance_record :=
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mk_record c parent (sha256 c parent).
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(** ** P2: [record_verify_iff_unchanged]
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A record verifies iff it has the honest form — i.e., its
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[content_hash] field has not been modified relative to its content
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and parent_hash. *)
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Theorem record_verify_iff_unchanged :
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forall r,
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record_verify r <-> exists c parent, r = mk_honest c parent.
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Proof.
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intros r. split.
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- intros Hv.
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destruct r as [c p h].
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unfold record_verify in Hv. simpl in Hv.
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exists c, p.
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unfold mk_honest. rewrite Hv. reflexivity.
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- intros [c [p Hr]]. subst.
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unfold record_verify, mk_honest. reflexivity.
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Qed.
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(** ** Chain integrity *)
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Definition chain : Type := list provenance_record.
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(** Inductive linkage from a starting hash. A chain is linked from [h]
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when every record's [parent_hash] equals its predecessor's
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[content_hash], with [h] taking the role of the predecessor for the
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first record. *)
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Inductive chain_linked_from : hash -> chain -> Prop :=
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| linked_nil : forall h, chain_linked_from h []
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| linked_cons :
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forall h r rest,
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rec_parent_hash r = h ->
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chain_linked_from (rec_content_hash r) rest ->
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chain_linked_from h (r :: rest).
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(** A chain is well-linked iff it is linked from the genesis hash. *)
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Definition chain_well_linked (c : chain) : Prop :=
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chain_linked_from genesis_hash c.
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(** The [parent_hash] that the next appended record should use:
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the last record's [content_hash], or the starting hash for empty
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chains. *)
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Fixpoint chain_tail_hash_from (h : hash) (c : chain) : hash :=
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match c with
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| [] => h
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| r :: rest => chain_tail_hash_from (rec_content_hash r) rest
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end.
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Definition chain_tail_hash (c : chain) : hash :=
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chain_tail_hash_from genesis_hash c.
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(** Honest append — mirrors [append()] in the Rust source: extends the
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chain with a new record whose [parent_hash] points at the tip and
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whose [content_hash] is computed by SHA-256. *)
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Definition append_record (c : chain) (cnt : content) : chain :=
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c ++ [mk_honest cnt (chain_tail_hash c)].
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(** Snoc lemma: extending a linked chain with a record whose
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[parent_hash] equals the chain's tail hash preserves linkage. *)
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Lemma chain_linked_from_snoc :
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forall c r h,
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chain_linked_from h c ->
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rec_parent_hash r = chain_tail_hash_from h c ->
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chain_linked_from h (c ++ [r]).
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Proof.
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induction c as [|r' rest IH]; intros r h Hlinked Hparent; simpl in *.
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- apply linked_cons.
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+ exact Hparent.
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+ apply linked_nil.
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- inversion Hlinked; subst.
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apply linked_cons.
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+ reflexivity.
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+ apply IH; assumption.
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Qed.
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(** ** P3 step: [chain_linked_step]
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Appending an honest record to a well-linked chain preserves
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well-linkedness. *)
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Theorem chain_linked_step :
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forall c cnt,
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chain_well_linked c -> chain_well_linked (append_record c cnt).
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Proof.
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intros c cnt H.
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unfold chain_well_linked, append_record, chain_tail_hash in *.
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apply chain_linked_from_snoc.
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- exact H.
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- reflexivity.
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Qed.
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(** ** P3 corollary: [chain_linked]
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Every chain built from the empty chain by a sequence of honest
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[append_record] operations is well-linked. *)
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Fixpoint build_chain (cnts : list content) : chain :=
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match cnts with
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| [] => []
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| cnt :: rest => append_record (build_chain rest) cnt
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end.
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Theorem chain_linked :
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forall cnts, chain_well_linked (build_chain cnts).
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Proof.
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induction cnts as [|cnt rest IH]; simpl.
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- apply linked_nil.
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- apply chain_linked_step. exact IH.
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Qed.
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(** ** Print Assumptions guard
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Each theorem must close under the global context. The
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[sha256_collision_resistant] axiom is declared but unused; CI greps
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each [Print Assumptions] block for "Closed under the global context"
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to detect axiom slippage. *)
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Print Assumptions record_verify_iff_unchanged.
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Print Assumptions chain_linked_step.
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Print Assumptions chain_linked.

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