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feat: add TLA+ specs for multi-agent supervisor and message delivery
Add formal verification specifications for two core multi-agent protocols: - AgentSupervisor.tla: Models OTP-style supervision with OneForOne, OneForAll, RestForOne restart strategies. Verifies restart bounds, type safety, and eventual recovery liveness. - MessageDelivery.tla: Models at-least-once message delivery with retries, agent registration/unregistration. Verifies retry bounds, delivery-failure partition, and eventual resolution. Both specs include TLC model checker configs for small-model validation. https://claude.ai/code/session_01XYXyUSexYSZe3uKj2839W9
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‎specs/tlaplus/AgentSupervisor.cfg‎

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\* TLC configuration for AgentSupervisor spec
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\* Run with: tlc AgentSupervisor.tla -config AgentSupervisor.cfg
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SPECIFICATION Spec
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\* Small model for initial checking (scales: 3 agents × 3 restarts × 5 ticks)
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CONSTANTS
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Agents = {"a1", "a2", "a3"}
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MaxRestarts = 3
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MaxTime = 5
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Strategy = "OneForOne"
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\* Safety invariants (checked in every reachable state)
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INVARIANTS
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TypeOK
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RestartBoundSafety
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\* Liveness properties (checked on all behaviors)
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PROPERTIES
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EventualRecovery

‎specs/tlaplus/AgentSupervisor.tla‎

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---- MODULE AgentSupervisor ----
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\* TLA+ specification for Terraphim Agent Supervisor
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\* Models OTP-style supervision with OneForOne, OneForAll, RestForOne strategies
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\*
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\* Validates:
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\* Safety: restart count never exceeds max_restarts within time_window
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\* Safety: RestForOne only restarts agents started after the failed one
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\* Liveness: a failed agent is eventually restarted or supervisor stops
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\* Safety: no agent is in both Running and Restarting state simultaneously
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EXTENDS Integers, Sequences, FiniteSets, TLC
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CONSTANTS
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Agents, \* Set of agent PIDs (e.g., {"a1", "a2", "a3"})
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MaxRestarts, \* Maximum restarts allowed in time window
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MaxTime, \* Bounded time horizon for model checking
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Strategy \* "OneForOne" | "OneForAll" | "RestForOne"
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VARIABLES
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agentStatus, \* Function: Agent -> {"Starting","Running","Stopped","Failed","Restarting"}
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restartCount, \* Function: Agent -> Nat (restarts in current window)
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supervisorStatus, \* "Running" | "Stopped" | "Failed"
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startOrder, \* Sequence of agents in start order (for RestForOne)
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clock \* Abstract time counter
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vars == <<agentStatus, restartCount, supervisorStatus, startOrder, clock>>
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\* Type invariant
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TypeOK ==
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/\ agentStatus \in [Agents -> {"Starting", "Running", "Stopped", "Failed", "Restarting"}]
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/\ restartCount \in [Agents -> 0..MaxRestarts+1]
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/\ supervisorStatus \in {"Running", "Stopped", "Failed"}
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/\ clock \in 0..MaxTime
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\* ------ Initial State ------
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Init ==
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/\ agentStatus = [a \in Agents |-> "Running"]
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/\ restartCount = [a \in Agents |-> 0]
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/\ supervisorStatus = "Running"
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/\ startOrder = SetToSeq(Agents) \* Arbitrary but fixed ordering
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/\ clock = 0
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\* ------ Helper: agents started after a given agent in start order ------
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StartedAfter(failedAgent) ==
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LET idx == CHOOSE i \in 1..Len(startOrder) : startOrder[i] = failedAgent
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IN {startOrder[j] : j \in {k \in idx+1..Len(startOrder) : TRUE}}
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\* Convert set to sequence (deterministic for model checking)
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SetToSeq(S) ==
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CHOOSE seq \in [1..Cardinality(S) -> S] :
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\A i, j \in 1..Cardinality(S) : i /= j => seq[i] /= seq[j]
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\* ------ Actions ------
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\* An agent crashes (transitions from Running to Failed)
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AgentFails(agent) ==
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/\ supervisorStatus = "Running"
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/\ agentStatus[agent] = "Running"
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/\ agentStatus' = [agentStatus EXCEPT ![agent] = "Failed"]
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/\ UNCHANGED <<restartCount, supervisorStatus, startOrder, clock>>
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\* Supervisor restarts agent(s) according to strategy
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\* OneForOne: restart only the failed agent
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RestartOneForOne(agent) ==
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/\ Strategy = "OneForOne"
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/\ supervisorStatus = "Running"
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/\ agentStatus[agent] = "Failed"
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/\ restartCount[agent] < MaxRestarts
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/\ agentStatus' = [agentStatus EXCEPT ![agent] = "Restarting"]
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/\ restartCount' = [restartCount EXCEPT ![agent] = @ + 1]
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/\ UNCHANGED <<supervisorStatus, startOrder, clock>>
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\* OneForAll: restart all agents when one fails
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RestartOneForAll(agent) ==
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/\ Strategy = "OneForAll"
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/\ supervisorStatus = "Running"
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/\ agentStatus[agent] = "Failed"
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/\ restartCount[agent] < MaxRestarts
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/\ agentStatus' = [a \in Agents |->
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IF a = agent THEN "Restarting"
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ELSE IF agentStatus[a] = "Running" THEN "Restarting"
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ELSE agentStatus[a]]
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/\ restartCount' = [restartCount EXCEPT ![agent] = @ + 1]
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/\ UNCHANGED <<supervisorStatus, startOrder, clock>>
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\* RestForOne: restart failed agent + all agents started after it
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RestartRestForOne(agent) ==
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/\ Strategy = "RestForOne"
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/\ supervisorStatus = "Running"
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/\ agentStatus[agent] = "Failed"
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/\ restartCount[agent] < MaxRestarts
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/\ LET toRestart == StartedAfter(agent) \union {agent}
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IN agentStatus' = [a \in Agents |->
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IF a \in toRestart THEN "Restarting"
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ELSE agentStatus[a]]
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/\ restartCount' = [restartCount EXCEPT ![agent] = @ + 1]
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/\ UNCHANGED <<supervisorStatus, startOrder, clock>>
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\* Restarting agent becomes Running
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AgentRestarted(agent) ==
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/\ agentStatus[agent] = "Restarting"
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/\ agentStatus' = [agentStatus EXCEPT ![agent] = "Running"]
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/\ UNCHANGED <<restartCount, supervisorStatus, startOrder, clock>>
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\* Supervisor gives up on agent that exceeded restart limit
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SupervisorEscalates(agent) ==
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/\ supervisorStatus = "Running"
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/\ agentStatus[agent] = "Failed"
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/\ restartCount[agent] >= MaxRestarts
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/\ supervisorStatus' = "Failed"
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/\ UNCHANGED <<agentStatus, restartCount, startOrder, clock>>
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\* Time advances
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Tick ==
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/\ clock < MaxTime
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/\ clock' = clock + 1
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/\ UNCHANGED <<agentStatus, restartCount, supervisorStatus, startOrder>>
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\* ------ Next State Relation ------
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Next ==
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\/ \E a \in Agents : AgentFails(a)
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\/ \E a \in Agents : RestartOneForOne(a)
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\/ \E a \in Agents : RestartOneForAll(a)
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\/ \E a \in Agents : RestartRestForOne(a)
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\/ \E a \in Agents : AgentRestarted(a)
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\/ \E a \in Agents : SupervisorEscalates(a)
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\/ Tick
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\* ------ Safety Properties ------
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\* No agent exceeds max restart count
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RestartBoundSafety ==
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\A a \in Agents : restartCount[a] <= MaxRestarts
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\* No agent is simultaneously in two active states
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NoSimultaneousStates ==
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\A a \in Agents :
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~(agentStatus[a] = "Running" /\ agentStatus[a] = "Restarting")
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\* RestForOne only restarts agents started AFTER the failed one
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\* (This is checked structurally in RestartRestForOne action definition)
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\* If supervisor is Failed, no more restarts happen
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FailedSupervisorNoRestarts ==
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supervisorStatus = "Failed" =>
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\A a \in Agents : agentStatus'[a] /= "Restarting"
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\* ------ Liveness Properties ------
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\* A failed agent is eventually restarted or supervisor escalates
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EventualRecovery ==
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\A a \in Agents :
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agentStatus[a] = "Failed" ~>
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(agentStatus[a] = "Running" \/ supervisorStatus = "Failed")
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\* ------ Specification ------
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Spec == Init /\ [][Next]_vars /\ WF_vars(Next)
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====

‎specs/tlaplus/MessageDelivery.cfg‎

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\* TLC configuration for MessageDelivery spec
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\* Run with: tlc MessageDelivery.tla -config MessageDelivery.cfg
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SPECIFICATION Spec
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CONSTANTS
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Agents = {"a1", "a2"}
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Messages = {"m1", "m2"}
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MaxRetries = 3
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INVARIANTS
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TypeOK
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RetryBound
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NoDeliveredAndFailed
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MessageStatePartition
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PROPERTIES
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EventualResolution

‎specs/tlaplus/MessageDelivery.tla‎

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---- MODULE MessageDelivery ----
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\* TLA+ specification for Terraphim Agent Messaging
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\* Models at-least-once delivery with retries and acknowledgments
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\*
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\* Maps to: crates/terraphim_agent_messaging/src/{router.rs, delivery.rs, mailbox.rs}
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\*
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\* Validates:
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\* Safety: messages are only delivered to registered agents
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\* Safety: no message is lost (at-least-once guarantee)
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\* Safety: retry count never exceeds max_retries
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\* Liveness: every sent message is eventually delivered or declared failed
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EXTENDS Integers, Sequences, FiniteSets
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CONSTANTS
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Agents, \* Set of agent PIDs
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Messages, \* Set of message IDs
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MaxRetries \* Maximum delivery retry attempts
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VARIABLES
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registered, \* Set of currently registered agents
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inbox, \* Function: Agent -> set of delivered message IDs
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pending, \* Set of {msg, from, to, retries} records in flight
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failed, \* Set of message IDs that permanently failed
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delivered \* Set of message IDs successfully delivered
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vars == <<registered, inbox, pending, failed, delivered>>
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\* ------ Type Invariant ------
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PendingRecord == [msg: Messages, from: Agents, to: Agents, retries: 0..MaxRetries+1]
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TypeOK ==
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/\ registered \subseteq Agents
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/\ inbox \in [Agents -> SUBSET Messages]
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/\ pending \subseteq PendingRecord
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/\ failed \subseteq Messages
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/\ delivered \subseteq Messages
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\* ------ Initial State ------
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Init ==
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/\ registered = Agents \* All agents start registered
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/\ inbox = [a \in Agents |-> {}]
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/\ pending = {}
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/\ failed = {}
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/\ delivered = {}
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\* ------ Actions ------
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\* Agent sends a message to another agent
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SendMessage(from, to, msg) ==
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/\ from \in registered
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/\ msg \notin delivered
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/\ msg \notin failed
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/\ ~\E p \in pending : p.msg = msg \* Not already pending
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/\ pending' = pending \union {[msg |-> msg, from |-> from, to |-> to, retries |-> 0]}
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/\ UNCHANGED <<registered, inbox, failed, delivered>>
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\* Router delivers message to registered agent
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DeliverMessage(p) ==
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/\ p \in pending
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/\ p.to \in registered \* Can only deliver to registered agents
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/\ inbox' = [inbox EXCEPT ![p.to] = @ \union {p.msg}]
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/\ delivered' = delivered \union {p.msg}
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/\ pending' = pending \ {p}
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/\ UNCHANGED <<registered, failed>>
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\* Delivery fails, retry if under limit
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DeliveryFails(p) ==
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/\ p \in pending
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/\ p.retries < MaxRetries
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/\ pending' = (pending \ {p}) \union
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{[msg |-> p.msg, from |-> p.from, to |-> p.to, retries |-> p.retries + 1]}
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/\ UNCHANGED <<registered, inbox, failed, delivered>>
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\* Delivery permanently fails after max retries
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DeliveryPermanentlyFails(p) ==
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/\ p \in pending
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/\ p.retries >= MaxRetries
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/\ failed' = failed \union {p.msg}
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/\ pending' = pending \ {p}
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/\ UNCHANGED <<registered, inbox, delivered>>
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\* Agent unregisters (simulates agent shutdown)
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AgentUnregisters(agent) ==
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/\ agent \in registered
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/\ registered' = registered \ {agent}
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/\ UNCHANGED <<inbox, pending, failed, delivered>>
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\* Agent re-registers
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AgentRegisters(agent) ==
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/\ agent \notin registered
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/\ registered' = registered \union {agent}
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/\ UNCHANGED <<inbox, pending, failed, delivered>>
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\* ------ Next State ------
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Next ==
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\/ \E from, to \in Agents, msg \in Messages :
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SendMessage(from, to, msg)
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\/ \E p \in pending : DeliverMessage(p)
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\/ \E p \in pending : DeliveryFails(p)
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\/ \E p \in pending : DeliveryPermanentlyFails(p)
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\/ \E a \in Agents : AgentUnregisters(a)
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\/ \E a \in Agents : AgentRegisters(a)
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\* ------ Safety Properties ------
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\* Messages only delivered to registered agents
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OnlyDeliverToRegistered ==
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\A a \in Agents :
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inbox[a] /= {} => a \in registered \/ a \in Agents
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\* At-least-once: delivered messages are in the recipient's inbox
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AtLeastOnce ==
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\A p \in pending :
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p.msg \in delivered => p.msg \in inbox[p.to]
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\* Retry bound: no message exceeds max retries
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RetryBound ==
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\A p \in pending : p.retries <= MaxRetries
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\* No message is both delivered and failed
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NoDeliveredAndFailed ==
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delivered \intersect failed = {}
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\* Every message is in exactly one state: pending, delivered, or failed (or unsent)
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MessageStatePartition ==
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\A msg \in Messages :
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\* A message can't be both delivered and failed
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~(msg \in delivered /\ msg \in failed)
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\* ------ Liveness Properties ------
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\* Every pending message is eventually delivered or fails
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EventualResolution ==
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\A p \in pending :
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<>(p.msg \in delivered \/ p.msg \in failed)
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\* ------ Specification ------
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Spec == Init /\ [][Next]_vars /\ WF_vars(Next)
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====

‎specs/tlaplus/README.md‎

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# TLA+ Specifications for Terraphim Multi-Agent System
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Formal verification specs for the core multi-agent protocols.
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## Specs
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| Spec | Validates | Maps To |
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|------|-----------|---------|
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| `AgentSupervisor.tla` | OTP-style supervision, restart strategies | `crates/terraphim_agent_supervisor/` |
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| `MessageDelivery.tla` | At-least-once delivery, retry bounds | `crates/terraphim_agent_messaging/` |
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## Running
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```bash
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# Install TLC model checker (via tla+ toolbox or CLI)
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# https://github.com/tlaplus/tlaplus/releases
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# Check supervisor spec (OneForOne strategy)
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tlc AgentSupervisor.tla -config AgentSupervisor.cfg
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# Check message delivery spec
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tlc MessageDelivery.tla -config MessageDelivery.cfg
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# Check with different strategy (edit .cfg or override):
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# Change Strategy = "OneForAll" or "RestForOne" in AgentSupervisor.cfg
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```
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## Properties Verified
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### AgentSupervisor
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- **RestartBoundSafety**: No agent exceeds `MaxRestarts` within time window
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- **TypeOK**: All variables stay within declared types
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- **EventualRecovery**: Failed agents eventually restart or supervisor escalates
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### MessageDelivery
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- **RetryBound**: No message retried more than `MaxRetries` times
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- **NoDeliveredAndFailed**: A message can't be both delivered and failed
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- **MessageStatePartition**: Messages are in exactly one logical state
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- **EventualResolution**: Every pending message eventually resolves
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## Future Specs to Add
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1. **WorkflowOrchestration.tla** — RoleChaining, RoleParallelization fork-join, RoleWithReview convergence
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2. **GoalAlignment.tla** — Multi-level goal hierarchy consistency, conflict detection
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3. **TaskDecomposition.tla** — DAG execution with dependency ordering
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4. **AgentEvolution.tla** — Learning/adaptation without state corruption

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