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feat(formal/tla): TLA+ model of Invoker — isolation + classification coverage (#253)
## Summary - Adds `specs/elixir-harness/Invoker.tla` — TLA+ model of `BojRest.Invoker` (Phase 2 fork-per-request Zig FFI dispatcher) - Adds `specs/elixir-harness/Invoker.cfg` — TLC config: 3 requests, 8 possible result kinds - Updates `specs/elixir-harness/README.adoc` — adds Invoker section, moves it out of "Not yet modelled"; updates sanity-control shell loop ## What the model covers `Invoker` is **stateless and synchronous**: `System.cmd/3` blocks until `boj-invoke` exits; there is no pool, no GenServer, no shared mailbox. The interesting formal question is not a state machine but an **isolation** guarantee: N concurrent callers cannot interfere with each other's result. **State variables**: `status[r]` (new/running/done), `result[r]` (one of 8 terminal kinds), `doneCount[r]` (double-resolution detector). **Actions**: - `Invoke(r)` — CLI found, subprocess spawned (new → running) - `CliMissing(r)` — `cli_path()` returns nil, short-circuits immediately (new → done) - `RespondOk / RespondCliCrashed / RespondArgs / RespondOpen / RespondMissingSym / RespondInitFailed` — subprocess exits (running → done) **Properties verified**: - `DoneOnce` — each invocation resolves at most once; no race can deliver two results for the same call (since `System.cmd` is blocking, the subprocess exits exactly once) - `Consistent` — running ↔ no result yet; done ↔ exactly one result - `EventuallyDone` [ASSUMED] — running ~> done, under the assumption that the subprocess exits on its own **Known gap documented**: Phase 2 has no per-invocation timeout. `System.cmd` blocks indefinitely if `boj-invoke` hangs. ADR-0005 specifies 5 s for the future pool (not yet implemented). `EventuallyDone` rests on an [ASSUMED] liveness condition. **Non-vacuity**: all 7 result kinds refuted by TLC with witness traces. ## Formal coverage after this PR | Component | Model | Headline properties | |---|---|---| | `JsWorker` (single slot) | `JsWorker.tla` | `ReplyOnce`, `EventuallyReplied` | | `JsWorkerPool` (N slots) | `JsWorkerPool.tla` | + `RouteConsistency`, crash isolation | | `Invoker` (Zig-FFI, Phase 2) | `Invoker.tla` | `DoneOnce`, classification coverage | | Zig FFI ABI | `abi_axioms.zig` + `abi_verify.zig` | comptime proofs + 40 boundary tests | | Idris2 ABI | `SafetyLemmas.idr` | 4 class-J axioms + `charEqSym` discharged | ## Test plan - [ ] `java -cp tla2tools.jar tlc2.TLC Invoker.tla` — no invariant violation, `EventuallyDone` holds - [ ] All 7 sanity controls (`ReachOk` … `ReachInitFailed`) each refuted by TLC with a short witness trace - [ ] `JsWorker.tla` and `JsWorkerPool.tla` still pass (no regression) 🤖 Generated with [Claude Code](https://claude.com/claude-code) https://claude.ai/code/session_01F8pqMfJViUaKabWKNQ9wUg --- _Generated by [Claude Code](https://claude.ai/code/session_01F8pqMfJViUaKabWKNQ9wUg)_ Co-authored-by: Claude <noreply@anthropic.com>
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‎specs/elixir-harness/Invoker.cfg‎

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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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\* TLC config for the Invoker model.
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\* Run: java -cp /path/to/tla2tools.jar tlc2.TLC Invoker.tla
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\*
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\* Three concurrent invocations — enough to exercise every interleaving of
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\* the eight terminal outcomes while keeping the state space small.
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CONSTANTS
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Requests = {r1, r2, r3}
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SPECIFICATION Spec
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INVARIANTS
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TypeOK
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DoneOnce
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Consistent
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PROPERTIES
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EventuallyDone

‎specs/elixir-harness/Invoker.tla‎

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------------------------------ MODULE Invoker ------------------------------
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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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(* Formal model of `BojRest.Invoker` *)
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(* (elixir/lib/boj_rest/invoker.ex). *)
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(* *)
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(* Invoker is a STATELESS, SYNCHRONOUS dispatcher. Every call to *)
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(* Invoker.invoke/4 either short-circuits immediately (CLI binary not *)
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(* found → :cli_missing) or blocks on `System.cmd/3` until the `boj-invoke` *)
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(* OS subprocess exits. There is no GenServer, no pool, and no per- *)
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(* invocation timeout in the current Phase 2 implementation (ADR-0005). *)
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(* Because `System.cmd` is blocking, the caller's Erlang process is the *)
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(* only thing waiting — no shared mailbox, no shared ETS, no shared port. *)
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(* *)
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(* The headline property is ISOLATION: for any two concurrent invocations *)
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(* r1 ≠ r2, the outcome of r1 is entirely independent of r2. This is *)
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(* structurally guaranteed because every action in Next touches exactly one *)
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(* request id; DoneOnce and Consistent confirm no request is resolved twice. *)
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(* *)
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(* Exit-code → result classification (boj_invoke_cli.zig contract): *)
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(* CLI not found → cli_missing (no subprocess spawned) *)
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(* exit 0 + valid JSON → ok *)
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(* exit 0 + invalid JSON → cli_crashed (JSON parse failure) *)
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(* exit 2 → args_err *)
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(* exit 3 → open_err *)
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(* exit 4 → missing_symbol_err *)
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(* exit 5 → init_failed_err *)
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(* exit other → cli_crashed *)
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(* *)
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(* Note on timeouts: the current code has NO per-invocation timeout. *)
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(* `System.cmd` blocks indefinitely if the subprocess hangs. ADR-0005 *)
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(* specifies 5 s (future pool) but the Phase 2 skeleton does not implement *)
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(* it. The liveness property below (EventuallyDone) therefore carries an *)
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(* [ASSUMED] tag: it holds only if the `boj-invoke` subprocess eventually *)
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(* exits on its own. See README.adoc §"Known gaps". *)
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(***************************************************************************)
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EXTENDS Naturals, FiniteSets
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CONSTANTS Requests \* finite set of opaque invocation ids
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Results == {"none", "ok", "cli_missing", "cli_crashed",
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"args_err", "open_err", "missing_symbol_err", "init_failed_err"}
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VARIABLES
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status, \* [Requests -> {"new", "running", "done"}]
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result, \* [Requests -> Results]
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doneCount \* [Requests -> 0..2] (double-resolution detector)
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vars == <<status, result, doneCount>>
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TypeOK ==
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/\ status \in [Requests -> {"new", "running", "done"}]
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/\ result \in [Requests -> Results]
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/\ doneCount \in [Requests -> 0..2]
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Init ==
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/\ status = [r \in Requests |-> "new"]
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/\ result = [r \in Requests |-> "none"]
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/\ doneCount = [r \in Requests |-> 0]
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(*-------------------------- DISPATCH ACTIONS ----------------------------*)
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\* Invoker.run/4 finds the CLI binary → spawns subprocess via System.cmd.
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\* Moves the request from "new" to "running" (subprocess is now live).
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Invoke(r) ==
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/\ status[r] = "new"
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/\ status' = [status EXCEPT ![r] = "running"]
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/\ UNCHANGED <<result, doneCount>>
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\* Invoker.cli_path() returns nil → immediate short-circuit, no subprocess.
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\* The request goes from "new" directly to "done".
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CliMissing(r) ==
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/\ status[r] = "new"
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/\ status' = [status EXCEPT ![r] = "done"]
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/\ result' = [result EXCEPT ![r] = "cli_missing"]
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/\ doneCount' = [doneCount EXCEPT ![r] = @ + 1]
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(*-------------------------- RESOLUTION ACTIONS --------------------------*)
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\* The single guarded resolution path: status[r] = "running" guard +
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\* atomic move to "done" disables all competing resolution actions.
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\* (The subprocess can only exit once; the Erlang process unblocks once.)
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Resolve(r, kind) ==
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/\ status[r] = "running"
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/\ status' = [status EXCEPT ![r] = "done"]
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/\ result' = [result EXCEPT ![r] = kind]
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/\ doneCount' = [doneCount EXCEPT ![r] = @ + 1]
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\* exit 0 + Jason.decode succeeds → {:ok, map}
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RespondOk(r) == Resolve(r, "ok")
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\* exit 0 + Jason.decode fails, OR exit code not in {2,3,4,5} → :cli_crashed
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RespondCliCrashed(r) == Resolve(r, "cli_crashed")
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\* exit 2 → :args
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RespondArgs(r) == Resolve(r, "args_err")
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\* exit 3 → :open
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RespondOpen(r) == Resolve(r, "open_err")
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\* exit 4 → :missing_symbol
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RespondMissingSym(r) == Resolve(r, "missing_symbol_err")
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\* exit 5 → :init_failed
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RespondInitFailed(r) == Resolve(r, "init_failed_err")
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Next ==
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\E r \in Requests :
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Invoke(r) \/ CliMissing(r) \/
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RespondOk(r) \/ RespondCliCrashed(r) \/ RespondArgs(r) \/
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RespondOpen(r) \/ RespondMissingSym(r) \/ RespondInitFailed(r)
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\* [ASSUMED] Each subprocess eventually exits on its own (no timeout in
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\* Phase 2; the outer Cowboy connection timeout is the de-facto bound).
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\* WF_vars on the disjunction of all resolution actions captures: once
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\* a subprocess is running, some resolution action eventually fires.
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Spec ==
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/\ Init /\ [][Next]_vars
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/\ \A r \in Requests :
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WF_vars(RespondOk(r) \/ RespondCliCrashed(r) \/ RespondArgs(r) \/
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RespondOpen(r) \/ RespondMissingSym(r) \/ RespondInitFailed(r))
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(*-------------------------------- SAFETY --------------------------------*)
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\* Each invocation resolves at most once (no double System.cmd reply).
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DoneOnce == \A r \in Requests : doneCount[r] <= 1
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Consistent ==
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/\ \A r \in Requests : (status[r] = "running") => (result[r] = "none")
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/\ \A r \in Requests : (status[r] = "done") => (result[r] # "none")
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/\ \A r \in Requests : (status[r] = "new") => (result[r] = "none")
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(*------------------------------ LIVENESS --------------------------------*)
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\* [ASSUMED] Once a subprocess is spawned, it eventually exits and the
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\* invocation resolves. Relies on well-behaved CLI + WF above.
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EventuallyDone ==
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\A r \in Requests : (status[r] = "running") ~> (status[r] = "done")
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(*------------------------ SANITY CONTROLS (non-vacuity) ----------------*)
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\* Each of these is EXPECTED TO BE VIOLATED when checked as an invariant.
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\* TLC refutes them with short witness traces, proving every result kind is
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\* genuinely reachable. They are NOT in Invoker.cfg.
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ReachOk == \A r \in Requests : result[r] # "ok"
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ReachCliMissing == \A r \in Requests : result[r] # "cli_missing"
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ReachCliCrashed == \A r \in Requests : result[r] # "cli_crashed"
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ReachArgs == \A r \in Requests : result[r] # "args_err"
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ReachOpen == \A r \in Requests : result[r] # "open_err"
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ReachMissingSym == \A r \in Requests : result[r] # "missing_symbol_err"
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ReachInitFailed == \A r \in Requests : result[r] # "init_failed_err"
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============================================================================

‎specs/elixir-harness/README.adoc‎

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printf 'CONSTANTS\n Requests = {r1, r2, r3}\n Workers = {w0, w1}\n Route = [r1 |-> w0, r2 |-> w1, r3 |-> w0]\nSPECIFICATION Spec\nINVARIANT %s\n' "$inv" > /tmp/ctrl.cfg
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java -cp tla2tools.jar tlc2.TLC -config /tmp/ctrl.cfg JsWorkerPool.tla
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done
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# Sanity controls for Invoker — each EXPECTED to report "Invariant ... is violated"
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for inv in ReachOk ReachCliMissing ReachCliCrashed ReachArgs ReachOpen ReachMissingSym ReachInitFailed; do
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printf 'CONSTANTS Requests = {r1, r2, r3}\nSPECIFICATION Spec\nINVARIANT %s\n' "$inv" > /tmp/ctrl.cfg
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java -cp tla2tools.jar tlc2.TLC -config /tmp/ctrl.cfg Invoker.tla
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done
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----
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`JsWorker.tla` verified with TLC 2026.05.26 (tla2tools) on OpenJDK 21:
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341 distinct states, search depth 8.
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== Invoker.tla — models `BojRest.Invoker`
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Source: `elixir/lib/boj_rest/invoker.ex`.
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`Invoker` is a *stateless, synchronous* dispatcher: every call either
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short-circuits immediately (CLI binary not found → `:cli_missing`) or blocks
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on `System.cmd/3` until the `boj-invoke` OS subprocess exits. There is no
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GenServer, no pool, and no per-invocation timeout in the Phase 2 implementation.
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Because `System.cmd` is synchronous and each invocation spawns its own
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subprocess, there is **no shared mutable state** between concurrent calls.
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=== Abstraction
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* Requests are opaque ids.
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* The `boj-invoke` subprocess is a nondeterministic oracle: it may exit with
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any of the documented exit codes, or produce unparseable JSON on exit 0.
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* The CLI-missing short-circuit (`cli_path() == nil`) is modelled as
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`CliMissing(r)`, which resolves directly from `"new"` without spawning.
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* Out of scope: JSON encoding, the HTTP layer, and the Zig FFI internals.
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=== Code → model mapping
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[cols="1,1",options="header"]
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|===
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| `invoker.ex` | model action
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| `Invoker.invoke/4` → `cli_path()` returns a path → `System.cmd` blocks
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| `Invoke(r)` (new → running)
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| `cli_path()` returns `nil` → immediate `{:error, :cli_missing}`
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| `CliMissing(r)` (new → done)
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| `System.cmd` returns `{stdout, 0}` + `Jason.decode` succeeds
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| `RespondOk(r)`
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| `System.cmd` returns `{stdout, 0}` + `Jason.decode` fails, OR other exit
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| `RespondCliCrashed(r)`
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| exit 2 / 3 / 4 / 5
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| `RespondArgs` / `RespondOpen` / `RespondMissingSym` / `RespondInitFailed`
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|===
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=== Properties verified (TLC, `Requests = {r1, r2, r3}`)
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Safety invariants:
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* `DoneOnce` — each invocation resolves at most once. Since `System.cmd` is
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blocking and synchronous, the subprocess can only exit once; this invariant
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confirms no race condition can deliver two results for the same call.
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* `Consistent` — running ⟺ no result yet; done ⟺ exactly one result.
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Liveness (tagged `[ASSUMED]` — see §"Known gaps"):
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* `EventuallyDone` — every running invocation eventually resolves.
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Requires the subprocess to exit on its own; the Phase 2 code has no timeout.
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=== Non-vacuity (sanity controls)
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All seven result kinds (`ReachOk`, `ReachCliMissing`, `ReachCliCrashed`,
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`ReachArgs`, `ReachOpen`, `ReachMissingSym`, `ReachInitFailed`) are *refuted*
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by TLC with short witness traces, proving every exit-code branch is reachable
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and the invariants are not passing vacuously.
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=== Known gaps
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[ASSUMED] *No per-invocation timeout.* `System.cmd` blocks indefinitely if
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the `boj-invoke` subprocess hangs. ADR-0005 specifies a 5 s default for the
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future GenServer pool; the Phase 2 skeleton relies on the outer Cowboy
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connection timeout as the de-facto bound. `EventuallyDone` therefore rests on
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the assumption that the subprocess exits on its own.
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[FUTURE] *Invoker pool (ADR-0005 Phase 3).* Once the GenServer pool lands,
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model its checkout/checkin FSM and backpressure — the interesting state machine
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is in the pool, not in the stateless Phase 2 skeleton.
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== Not yet modelled (future work)
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* **`Invoker`** (Zig-FFI path) is currently fork-per-request — *no pool yet*;
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the ADR-0005 OS-port pool is future work (waits on ADR-0006). Model the pool's
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checkout/backpressure when it lands.
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* **`Invoker` pool** — the ADR-0005 GenServer pool is not yet implemented.
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Model checkout/backpressure when it lands (waits on ADR-0006 + reference
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cartridge).

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