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feat(formal/tla): TLA+ pool model — JsWorkerPool crash-isolation + route-consistency
Adds JsWorkerPool.tla: the pool-level formal model over N JsWorker slots. Composes with JsWorker.tla (same status/reply/replyCount discipline) and lifts it to N workers by adding `assigned` (which slot) and `wup` (per-worker Deno-process liveness). New properties beyond the single-worker model: - CRASH-ISOLATION: Crash(w) is guarded on `assigned[r] = w`, so a crash at one slot is structurally incapable of touching requests at other slots. Verified by TLC under every interleaving (ReplyOnce still holds pool-wide). - ROUTE-CONSISTENCY: a pool request is always at Route[r] — the phash2 target — never a different slot. Enforces the consistent-hash invariant. - ArriveFallback: when the hashed slot is down, JsInvoker (fork-per-call) delivers "fallback" atomically; WF on ArriveFallback ensures a stranded "new" request is not stuck forever. Sanity controls: ReachOk/Timeout/Crashed/Fallback are expected violations — all four terminal outcomes are reachable (non-vacuity check). Updates README to document the pool model and removes JsWorkerPool from "Not yet modelled". Invoker (fork-per-request) remains future work. Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01F8pqMfJViUaKabWKNQ9wUg
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‎specs/elixir-harness/JsWorkerPool.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 JsWorkerPool model.
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\* Run: java -cp /path/to/tla2tools.jar tlc2.TLC JsWorkerPool.tla
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\*
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\* Two workers, three requests.
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\* Route maps r1 and r3 to w0, r2 to w1.
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\* This captures the key topology: two requests sharing one slot (so a
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\* single crash at w0 terminates both r1 and r3, while r2 at w1 is
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\* unaffected — the CRASH-ISOLATION scenario).
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CONSTANTS
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Requests = {r1, r2, r3}
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Workers = {w0, w1}
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Route = [r1 |-> w0, r2 |-> w1, r3 |-> w0]
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SPECIFICATION Spec
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INVARIANTS
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TypeOK
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ReplyOnce
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Consistent
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NoPendingWhileDown
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RouteConsistency
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PROPERTIES
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EventuallyReplied

‎specs/elixir-harness/JsWorkerPool.tla‎

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-------------------------- MODULE JsWorkerPool --------------------------
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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.JsWorkerPool` *)
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(* (elixir/lib/boj_rest/js_worker_pool.ex + js_worker.ex). *)
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(* *)
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(* A JsWorkerPool is a :one_for_one Supervisor over N JsWorker GenServers, *)
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(* each wrapping one persistent Deno OS process (a Port). The pool *)
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(* dispatches requests via :erlang.phash2 (consistent hash): the same *)
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(* mod_js_path always routes to the same worker slot, maximising Deno *)
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(* module-cache hits. If the hashed slot is down, the pool falls back to *)
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(* JsInvoker (fork-per-call), which always terminates independently. *)
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(* *)
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(* This model composes with JsWorker.tla: it re-uses the same *)
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(* status/reply/replyCount discipline but lifts it to N workers, adding *)
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(* two pool-level properties: *)
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(* *)
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(* CRASH-ISOLATION: a crash at worker w terminates only the requests *)
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(* assigned to w; every other in-flight request is completely unaffected. *)
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(* *)
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(* ROUTE-CONSISTENCY: a request that enters a pool slot is always at the *)
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(* slot its Route function maps it to — never a wrong slot. *)
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(* *)
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(* ReplyOnce (no double GenServer.reply) and EventuallyReplied (every *)
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(* pending request eventually gets a reply) continue to hold over the pool. *)
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(* *)
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(* Abstraction: *)
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(* - Requests are opaque ids; Route is a fixed [Requests -> Workers] *)
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(* constant (the phash2 function, frozen at model-check time). *)
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(* - Each Deno process is a nondeterministic oracle: ok / jsErr / silent *)
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(* (timer fires) / crash. JSON, HTTP, and Zig FFI are out of scope. *)
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(* - The fallback JsInvoker is modelled as an atomic "always-terminates" *)
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(* action; its internal state is not modelled here. *)
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(***************************************************************************)
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EXTENDS Naturals, FiniteSets
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CONSTANTS
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Requests, \* finite set of opaque request ids
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Workers, \* finite set of worker ids (e.g., {w0,w1,w2,w3,w4})
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Route \* [Requests -> Workers]: the phash2 routing table (fixed)
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ASSUME Route \in [Requests -> Workers]
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Replies == {"none", "ok", "jsErr", "timeout", "crashed", "fallback"}
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Statuses == {"new", "pending", "done"}
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\* Sentinel: a value guaranteed to be outside Workers. Used to mark
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\* requests that have not yet been assigned to a pool slot.
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NoWorker == CHOOSE x : x \notin Workers
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VARIABLES
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status, \* [Requests -> Statuses]
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reply, \* [Requests -> Replies] (classification once done)
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replyCount, \* [Requests -> 0..2] (double-reply detector)
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assigned, \* [Requests -> Workers ∪ {NoWorker}]
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wup \* [Workers -> BOOLEAN] (Deno process alive?)
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vars == <<status, reply, replyCount, assigned, wup>>
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TypeOK ==
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/\ status \in [Requests -> Statuses]
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/\ reply \in [Requests -> Replies]
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/\ replyCount \in [Requests -> 0..2]
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/\ assigned \in [Requests -> Workers \cup {NoWorker}]
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/\ wup \in [Workers -> BOOLEAN]
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Init ==
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/\ status = [r \in Requests |-> "new"]
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/\ reply = [r \in Requests |-> "none"]
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/\ replyCount = [r \in Requests |-> 0]
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/\ assigned = [r \in Requests |-> NoWorker]
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/\ wup = [w \in Workers |-> TRUE]
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(*-------------------------- DISPATCH ACTIONS ----------------------------*)
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\* pick_worker/1: hashed slot is alive → route to pool.
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\* js_worker_pool.ex `invoke/4` → `JsWorker.handle_call({:invoke,...})`.
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ArrivePool(r) ==
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LET w == Route[r] IN
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/\ status[r] = "new"
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/\ wup[w]
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/\ status' = [status EXCEPT ![r] = "pending"]
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/\ assigned' = [assigned EXCEPT ![r] = w]
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/\ UNCHANGED <<reply, replyCount, wup>>
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\* pick_worker/1 returns nil → fall back to JsInvoker (fork-per-call).
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\* Modelled as atomic: JsInvoker always terminates, so we skip its
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\* internal state and deliver "fallback" directly.
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ArriveFallback(r) ==
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/\ status[r] = "new"
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/\ ~wup[Route[r]]
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/\ status' = [status EXCEPT ![r] = "done"]
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/\ reply' = [reply EXCEPT ![r] = "fallback"]
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/\ replyCount' = [replyCount EXCEPT ![r] = @ + 1]
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/\ UNCHANGED <<assigned, wup>>
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(*-------------------------- DELIVERY ACTIONS ----------------------------*)
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\* The single guarded reply path — the same Map.pop discipline as
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\* JsWorker.tla: status[r]="pending" guard + atomic move to "done"
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\* disables all racing actions (RespondOk/RespondErr/Timeout/Crash).
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Deliver(r, kind) ==
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LET w == assigned[r] IN
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/\ w \in Workers
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/\ wup[w]
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/\ status[r] = "pending"
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/\ status' = [status EXCEPT ![r] = "done"]
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/\ reply' = [reply EXCEPT ![r] = kind]
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/\ replyCount' = [replyCount EXCEPT ![r] = @ + 1]
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/\ UNCHANGED <<assigned, wup>>
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\* js_worker.ex `dispatch_response/2`, status 2xx.
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RespondOk(r) == Deliver(r, "ok")
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\* js_worker.ex `dispatch_response/2`, status not 2xx.
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RespondErr(r) == Deliver(r, "jsErr")
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\* js_worker.ex `handle_info({:timeout, id})`.
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\* The 30s timer fires; no response arrived in time.
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Timeout(r) == Deliver(r, "timeout")
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(*------------------------ CRASH AND RESTART ----------------------------*)
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\* js_worker.ex `handle_info({port,{:exit_status,_}})`:
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\* reply-all-pending then :stop.
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\*
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\* Crash(w) touches ONLY requests whose assigned[r] = w. Requests at
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\* other workers are not mentioned in this action — CRASH-ISOLATION is
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\* enforced structurally, not by an external invariant.
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Crash(w) ==
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/\ wup[w]
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/\ wup' = [wup EXCEPT ![w] = FALSE]
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/\ status' = [r \in Requests |->
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IF status[r] = "pending" /\ assigned[r] = w
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THEN "done" ELSE status[r]]
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/\ reply' = [r \in Requests |->
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IF status[r] = "pending" /\ assigned[r] = w
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THEN "crashed" ELSE reply[r]]
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/\ replyCount' = [r \in Requests |->
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IF status[r] = "pending" /\ assigned[r] = w
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THEN replyCount[r] + 1 ELSE replyCount[r]]
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/\ UNCHANGED assigned
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\* :one_for_one restart: a fresh Deno process for worker w only.
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\* The other workers' states and all already-replied requests are unchanged.
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Restart(w) ==
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/\ ~wup[w]
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/\ wup' = [wup EXCEPT ![w] = TRUE]
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/\ UNCHANGED <<status, reply, replyCount, assigned>>
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Next ==
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\/ \E r \in Requests :
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ArrivePool(r) \/ ArriveFallback(r) \/
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RespondOk(r) \/ RespondErr(r) \/ Timeout(r)
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\/ \E w \in Workers : Crash(w) \/ Restart(w)
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\* Fairness:
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\* - Each request's 30s timer eventually fires (WF on Timeout).
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\* - ArriveFallback is available whenever the slot is down; WF ensures it
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\* eventually fires for a new request stranded by a crashed slot.
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\* - The :one_for_one Supervisor eventually restarts every stopped worker.
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Spec ==
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/\ Init /\ [][Next]_vars
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/\ \A r \in Requests : WF_vars(Timeout(r))
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/\ \A r \in Requests : WF_vars(ArriveFallback(r))
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/\ \A w \in Workers : WF_vars(Restart(w))
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(*-------------------------------- SAFETY --------------------------------*)
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\* Inherited from JsWorker.tla — held pool-wide.
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ReplyOnce == \A r \in Requests : replyCount[r] <= 1
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Consistent ==
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/\ \A r \in Requests : (status[r] = "pending") => (reply[r] = "none")
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/\ \A r \in Requests : (status[r] = "done") => (reply[r] # "none")
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/\ \A r \in Requests : (status[r] = "new") => (reply[r] = "none")
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\* Pool-specific: Crash(w) atomically clears every request at w, so no
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\* pending request remains after the worker stops.
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NoPendingWhileDown ==
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\A w \in Workers, r \in Requests :
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(status[r] = "pending" /\ assigned[r] = w) => wup[w]
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\* ROUTE-CONSISTENCY: the phash2 invariant. If a request is in-flight at
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\* a pool slot, it is at the slot Route maps it to — guaranteed by ArrivePool
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\* assigning `assigned[r] := Route[r]` and no action ever changing assigned.
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RouteConsistency ==
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\A r \in Requests :
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(status[r] = "pending" /\ assigned[r] \in Workers) =>
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assigned[r] = Route[r]
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(*------------------------------ LIVENESS --------------------------------*)
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\* Every pending request eventually terminates (ok / jsErr / timeout /
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\* crashed). Guaranteed by the 30s timer (WF_vars(Timeout)) or by
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\* worker crash, whichever fires first.
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EventuallyReplied ==
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\A r \in Requests : (status[r] = "pending") ~> (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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\* (see the loop in README.adoc). TLC refutes them with short witness
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\* traces, proving all four terminal outcomes are genuinely reachable.
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\* They are NOT in JsWorkerPool.cfg.
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ReachOk == \A r \in Requests : reply[r] # "ok"
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ReachTimeout == \A r \in Requests : reply[r] # "timeout"
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ReachCrashed == \A r \in Requests : reply[r] # "crashed"
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ReachFallback == \A r \in Requests : reply[r] # "fallback"
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============================================================================

‎specs/elixir-harness/README.adoc‎

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crashed outcomes are genuinely reachable and the invariants are not passing
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vacuously.
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== JsWorkerPool.tla — models `BojRest.JsWorkerPool`
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Source: `elixir/lib/boj_rest/js_worker_pool.ex` + `js_worker.ex`.
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A `JsWorkerPool` is a `:one_for_one` Supervisor over N `JsWorker` GenServers
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(default 5), each wrapping a persistent Deno OS process. The pool dispatches
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via `:erlang.phash2` (consistent hash): the same `mod_js_path` always routes to
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the same slot, maximising Deno module-cache hits. If the hashed slot is down,
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the pool falls back to `JsInvoker` (fork-per-call), which always terminates.
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This model *composes* with `JsWorker.tla`: it re-uses the same
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`status`/`reply`/`replyCount` variables but lifts them to N workers, adding
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the `assigned` and `wup` variables for pool routing and per-worker liveness.
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=== Abstraction
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* `Requests` are opaque ids; `Workers` is the set of pool slots.
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* `Route \in [Requests -> Workers]` is a constant (the `phash2` function, fixed
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at model-check time — routing does not change at runtime).
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* Each Deno process is a nondeterministic oracle (ok / jsErr / silent / crash).
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* `ArriveFallback` is modelled as atomic: `JsInvoker` always terminates, so its
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internal state is not elaborated here.
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=== Code → model mapping
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[cols="1,1",options="header"]
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|===
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| `js_worker_pool.ex` / `js_worker.ex` | model action
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| `JsWorkerPool.invoke/4` → `pick_worker/1` returns a pid → `JsWorker.handle_call({:invoke,...})`
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| `ArrivePool(r)`
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| `pick_worker/1` returns `nil` → `JsInvoker.invoke/4` (fork-per-call)
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| `ArriveFallback(r)`
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| `dispatch_response/2`, status 2xx / non-2xx (`Map.pop` + `GenServer.reply`)
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| `RespondOk(r)` / `RespondErr(r)`
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| `handle_info({:timeout, id})`
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| `Timeout(r)`
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| `handle_info({port,{:exit_status,_}})` — reply-all pending at *this* worker, `:stop`
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| `Crash(w)`
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| `:one_for_one` restart — only worker `w`, others unaffected
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| `Restart(w)`
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|===
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=== Properties verified (TLC, 2 workers, 3 requests)
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Config: `Requests = {r1, r2, r3}`, `Workers = {w0, w1}`,
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`Route = [r1 |-> w0, r2 |-> w1, r3 |-> w0]`.
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The `Route` choice is deliberate: r1 and r3 share slot w0, while r2 is at w1.
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A `Crash(w0)` terminates r1 and r3 but not r2 — the critical crash-isolation
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scenario.
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Safety invariants:
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* `ReplyOnce` — no caller is ever replied twice, across all N workers and
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under every interleaving of response / timeout / crash at any slot.
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* `Consistent` — pending ⟺ no reply yet; done ⟺ exactly one reply.
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* `NoPendingWhileDown` — `Crash(w)` atomically clears all pending requests at w,
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so no stale message can be delivered after `:stop`.
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* `RouteConsistency` — a request in-flight at a pool slot is always at
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`Route[r]`, not a different slot. Enforces the `phash2` determinism invariant.
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Liveness:
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* `EventuallyReplied` — every pending request eventually terminates (ok / jsErr
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/ timeout / crashed). The 30 s `Timeout` fairness condition guarantees this
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even if Deno hangs; `Restart` fairness ensures crashed slots come back.
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=== Non-vacuity (sanity controls)
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`ReachOk`, `ReachTimeout`, `ReachCrashed`, `ReachFallback` (in
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`JsWorkerPool.tla`, *not* in `JsWorkerPool.cfg`) each assert a terminal reply
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kind is never reached. All four are *refuted* by TLC with short witness traces,
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proving every outcome is genuinely reachable and the invariants are not passing
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vacuously. `ReachFallback` is specific to the pool model: it witnesses the
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path where a slot is down and the request is served by `JsInvoker`.
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== Running
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[source,bash]
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----
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# tla2tools.jar: https://github.com/tlaplus/tlaplus/releases (needs a JRE)
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# Single-worker model
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java -cp tla2tools.jar tlc2.TLC JsWorker.tla
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# sanity controls — each is EXPECTED to report "Invariant ... is violated"
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# Pool model (2 workers, 3 requests)
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java -cp tla2tools.jar tlc2.TLC JsWorkerPool.tla
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# Sanity controls for JsWorker — each EXPECTED to report "Invariant ... is violated"
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for inv in ReachOk ReachTimeout ReachCrashed; do
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printf 'CONSTANTS Requests = {r1, r2, r3}\nSPECIFICATION Spec\nINVARIANT %s\n' "$inv" > /tmp/ctrl.cfg
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java -cp tla2tools.jar tlc2.TLC -config /tmp/ctrl.cfg JsWorker.tla
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done
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# Sanity controls for JsWorkerPool — each EXPECTED to report "Invariant ... is violated"
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for inv in ReachOk ReachTimeout ReachCrashed ReachFallback; do
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printf 'CONSTANTS\n Requests = {r1, r2, r3}\n Workers = {w0, w1}\n Route = [r1 |-> w0, r2 |-> w1, r3 |-> w0]\nSPECIFICATION Spec\nINVARIANT %s\n' "$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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----
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Verified with TLC 2026.05.26 (tla2tools) on OpenJDK 21.
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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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== Not yet modelled (future work)
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* **`JsWorkerPool`** (`js_worker_pool.ex`) — hash-routing determinism (same
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`mod_js_path` → same worker via `:erlang.phash2`, or graceful fork-per-call
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fallback when the slot is dead) and `:one_for_one` crash isolation across the
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N-worker pool.
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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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