Foundation.ProcessRegistry Formal Specification

Phase 0: Complete System Specification (Design-Only)

Executive Summary

The Foundation.ProcessRegistry is a critical infrastructure component providing agent-aware process discovery and coordination for multi-agent BEAM systems. This specification defines the formal mathematical model, invariants, safety properties, and performance guarantees that the implementation must satisfy.

Core Responsibility: Maintain a consistent, high-performance mapping from process identifiers to live processes with rich metadata, enabling sophisticated agent coordination patterns.

1. Domain Modeling and Formal Specifications

1.1 State Invariants (Must Always Be True)

ProcessRegistry State Invariants:

I1. Registry Consistency:
    ∀ process_id ∈ registry_table:
        process_id → (pid, metadata) ∧ Process.alive?(pid) = true

I2. Index Consistency:
    ∀ capability ∈ capability_index:
        capability → process_id ⇒ 
        ∃ (pid, metadata) : registry_table[process_id] = (pid, metadata) ∧
        capability ∈ metadata.capabilities

I3. Namespace Isolation:
    ∀ p1, p2 ∈ registry_table:
        p1.namespace ≠ p2.namespace ⇒ 
        p1.local_id = p2.local_id ∧ p1.node = p2.node is valid

I4. Metadata Schema Compliance:
    ∀ (pid, metadata) ∈ registry_table:
        metadata conforms to agent_metadata() typespec

I5. Monitor Consistency:
    ∀ monitor_ref ∈ monitors:
        monitor_ref → process_id ⇒ 
        ∃ (pid, metadata) : registry_table[process_id] = (pid, metadata)

I6. Dead Process Cleanup:
    ∀ process_id ∈ registry_table:
        Process.alive?(registry_table[process_id].pid) = false ⇒
        process_id will be removed within cleanup_window_ms

1.2 Safety Properties (Must Never Happen)

ProcessRegistry Safety Properties:

S1. No Dual Registration:
    ∄ process_id : |{(pid, metadata) : registry_table[process_id] = (pid, metadata)}| > 1

S2. No Ghost Processes:
    ∄ process_id ∈ registry_table : Process.alive?(registry_table[process_id].pid) = false
    (except during cleanup_window_ms)

S3. No Index Corruption:
    ∄ inconsistent state where index entries point to non-existent registry entries

S4. No Memory Leaks:
    registry_memory_usage ≤ live_process_count × average_metadata_size + bounded_overhead

S5. No Race Condition Corruption:
    Concurrent operations cannot leave registry in inconsistent state

S6. No Silent Failures:
    All registration/lookup failures must return explicit error tuples

S7. No Namespace Pollution:
    Process in namespace N cannot be discovered via queries for namespace M where N ≠ M

1.3 Liveness Properties (Must Eventually Happen)

ProcessRegistry Liveness Properties:

L1. Registration Completion:
    ∀ register(process_id, pid, metadata) request:
        request completes with {:ok} or {:error, reason} within registration_timeout_ms

L2. Lookup Response:
    ∀ lookup(process_id) request:
        request returns result within lookup_timeout_ms

L3. Dead Process Cleanup:
    ∀ process termination event:
        cleanup completes within cleanup_window_ms

L4. System Responsiveness:
    Registry remains responsive to new requests even under maximum designed load

L5. Index Convergence:
    After metadata updates, index queries reflect changes within index_consistency_window_ms

L6. Monitor Processing:
    Process death notifications are processed within monitor_processing_window_ms

1.4 Performance Guarantees

ProcessRegistry Performance Specifications:

P1. Lookup Performance:
    lookup(process_id) completes in O(1) time regardless of registry size
    Target: < 1ms for registries up to 100,000 processes

P2. Registration Performance:
    register(process_id, pid, metadata) completes in O(k) time 
    where k = number of capabilities in metadata
    Target: < 5ms for typical agent metadata

P3. Query Performance:
    find_by_capability(capability) completes in O(n) time
    where n = number of processes with that capability
    Target: < 10ms for up to 1,000 matching processes

P4. Memory Efficiency:
    Total memory usage ≤ process_count × (base_entry_size + metadata_size) × memory_overhead_factor
    where memory_overhead_factor ≤ 2.0

P5. Concurrent Access:
    Registry supports unlimited concurrent readers with no blocking
    Registry supports up to concurrent_write_limit writers with bounded blocking

P6. Cleanup Performance:
    Dead process cleanup completes in O(k) time where k = number of capabilities
    Target: < 2ms per cleanup operation

2. Data Structure Specifications

2.1 Process Registry Entry

ProcessEntry ::= {
  process_id: {namespace(), node(), local_id()},
  pid: pid(),
  metadata: AgentMetadata,
  registered_at: MonotonicTimestamp,
  last_updated: MonotonicTimestamp
}

Mathematical Properties:
- process_id must be unique within registry
- pid must be alive when entry exists  
- registered_at ≤ last_updated
- namespace cannot be nil
- metadata must satisfy agent_metadata() typespec

2.2 Agent Metadata Structure

AgentMetadata ::= %{
  type: AgentType,                          // Required for type queries
  capabilities: [Capability],               // Required for capability queries  
  resources: ResourceMap,                   // Optional resource tracking
  coordination_variables: [VariableName],   // Optional coordination context
  health_status: HealthStatus,              // Required for health queries
  node_affinity: [Node],                    // Optional distribution hint
  created_at: DateTime,                     // Required audit trail
  last_health_check: DateTime,              // Required health tracking
  custom: Map                               // Optional extensibility
}

Type Constraints:
- type ∈ {:agent, :service, :coordinator, :resource_manager}
- capabilities ⊆ valid_capability_atoms()
- health_status ∈ {:healthy, :degraded, :unhealthy}  
- created_at ≤ last_health_check ≤ current_time()

2.3 Index Structure Design

Index Architecture:

Main Registry Table:
  Key: process_id = {namespace, node, local_id}
  Value: {pid, metadata}
  Properties: unique keys, read_concurrency, write_concurrency

Capability Index:
  Key: capability (atom)
  Value: process_id  
  Properties: duplicate_bag (one capability -> many processes)

Type Index:
  Key: agent_type
  Value: process_id
  Properties: duplicate_bag (one type -> many processes)

Health Index:
  Key: health_status
  Value: process_id
  Properties: duplicate_bag (one status -> many processes)

Monitor Map:
  Key: monitor_reference  
  Value: process_id
  Properties: unique keys, in-memory GenServer state

3. Concurrency Model Verification

3.1 Read Operations (Lockfree)

Read Operation Concurrency Model:

Lookup Operations:
├── lookup(process_id) 
│   - Lock-free ETS :lookup operation
│   - Process.alive/1 validation (lockfree)
│   - Atomic read of consistent state
│   - No writer blocking
├── find_by_capability(capability)
│   - Lock-free ETS :lookup on capability_index  
│   - Lock-free main table lookup for each result
│   - Process.alive/1 validation for each
│   - Consistent snapshot semantics
└── Statistical queries (list_all, find_by_type, find_by_health)
    - Lock-free ETS pattern matching
    - Eventual consistency guarantees
    - No blocking on concurrent writes

Consistency Guarantee: All read operations return point-in-time consistent snapshots

3.2 Write Operations (Synchronized)

Write Operation Concurrency Model:

Registration Flow:
1. GenServer.call ensures serialized access to state
2. ETS :lookup for existence check (atomic)
3. ETS :insert operations (atomic per table)
4. Process.monitor (atomic)
5. State update (atomic within GenServer)

Ordering Guarantee: namespace → process_id → metadata → indexes
Atomicity: Either all ETS updates succeed or none (via GenServer serialization)

Cleanup Flow (Triggered by process death):
1. Process DOWN message received
2. Lookup process_id from monitor_ref
3. Atomic removal from all ETS tables
4. Monitor cleanup
5. State update

Deadlock Prevention: Single lock ordering, no nested GenServer calls

3.3 Process Monitoring Strategy

Process Lifecycle Management:

Monitor Creation:
- Process.monitor(pid) called immediately after registration
- monitor_ref stored in GenServer state
- Automatic cleanup on process termination

Death Detection:
- {:DOWN, monitor_ref, :process, pid, reason} message
- O(1) lookup of process_id via monitor_ref
- Immediate cleanup of all indexes

Race Condition Handling:
- Registration of dead process: prevented by Process.alive/1 check
- Death during registration: cleanup handles orphaned entries
- Concurrent death and unregistration: idempotent cleanup operations

4. Failure Mode Analysis with Recovery Guarantees

4.1 Process Registry Crash Recovery

Failure Scenario: ProcessRegistry GenServer crashes

Impact Analysis:
- All ETS tables are lost (linked to GenServer process)
- All process monitors are lost
- Registry becomes unavailable

Recovery Strategy:
1. ProcessRegistry restarts via OTP supervision
2. ETS tables recreated with same configuration
3. No automatic state reconstruction (by design)
4. Processes must re-register themselves

Recovery Time: < 100ms for restart + re-registration
Data Loss: Acceptable (processes should re-register on startup)
Availability: Brief unavailability during restart

Prevention: Supervisor with :permanent restart, exponential backoff

4.2 Memory Exhaustion

Failure Scenario: Registry memory usage exceeds system limits

Early Warning Indicators:
- ETS table size monitoring  
- Memory usage growth rate tracking
- Process registration rate alerts

Response Strategy:
1. Immediate: Stop accepting new registrations
2. Short-term: Force cleanup of stale entries
3. Medium-term: Implement registration limits per namespace
4. Long-term: Scale to clustered deployment

Graceful Degradation:
- Core functionality (lookup) remains available
- New registrations fail with {:error, :registry_full}
- Cleanup prioritizes by process age and health status

Recovery: Automatic when memory usage drops below threshold

4.3 Network Partition (Future)

Failure Scenario: Network partition in distributed deployment

Current Behavior: Single-node deployment unaffected

Future Distributed Behavior:
- Each partition maintains local consistency
- No split-brain registry corruption
- Partition healing triggers reconciliation

Reconciliation Strategy:
- Process liveness verification across nodes
- Conflict resolution: prefer local registrations
- Metadata merge with last-writer-wins semantics

Design Consideration: Process IDs include node() for partition tolerance

4.4 Concurrent Write Storm

Failure Scenario: Massive concurrent registration requests

Protection Mechanisms:
1. GenServer serialization prevents corruption
2. ETS write_concurrency enables parallel index updates
3. Process.monitor rate limiting (system-level)
4. Registration timeout prevents indefinite queuing

Backpressure Strategy:
- Queue depth monitoring in GenServer
- Adaptive timeout adjustment
- Circuit breaker pattern for protection
- Graceful rejection with {:error, :system_busy}

Performance Degradation:
- Linear degradation with request rate
- No corruption or data loss
- Consistent response to overload

5. API Contract Specifications

5.1 Registration Contracts

@contract register(process_id(), pid(), agent_metadata()) :: :ok | {:error, reason()}
  where:
    requires: 
      - Process.alive?(pid) = true
      - valid_process_id?(process_id) = true  
      - valid_metadata?(metadata) = true
    ensures: 
      - lookup(process_id) returns {:ok, pid, metadata}
      - process appears in relevant indexes
      - process death triggers automatic cleanup
    exceptional: 
      - {:error, :already_registered} when process_id already exists
      - {:error, :invalid_metadata} when metadata invalid
      - {:error, :dead_process} when Process.alive?(pid) = false
    timing: 
      - completes within 10ms under normal load
      - completes within 50ms under high load
    concurrency: 
      - safe for unlimited concurrent calls
      - serialized within single registry instance

5.2 Lookup Contracts

@contract lookup(process_id()) :: {:ok, pid(), metadata()} | :error
  where:
    requires:
      - valid_process_id?(process_id) = true
    ensures:
      - if {:ok, pid, metadata} then Process.alive?(pid) = true
      - if :error then process_id not in registry or process dead
    exceptional:
      - :error for non-existent or dead processes
    timing:
      - completes within 1ms under normal load
      - completes within 5ms under extreme load
    concurrency:
      - completely lock-free
      - unlimited concurrent readers
      - never blocks on writers

5.3 Query Contracts

@contract find_by_capability(capability()) :: {:ok, [registry_entry()]}
  where:
    requires:
      - is_atom(capability) = true
    ensures:
      - all returned processes have capability in metadata.capabilities
      - all returned pids are alive
      - results represent consistent point-in-time snapshot
    timing:
      - O(n) where n = number of processes with capability
      - completes within 10ms for up to 1000 matching processes
    concurrency:
      - lock-free operation
      - eventually consistent with concurrent metadata updates

6. Integration Point Mappings

6.1 Foundation Layer Abstractions

ProcessRegistry Integration Architecture:

Foundation.ProcessRegistry → MABEAM.AgentRegistry
├── Mapping: process metadata → agent capabilities
├── Preserves: process lifecycle semantics + OTP supervision
├── Guarantees: agent discovery consistency
└── Extensions: coordination variable tracking

Foundation.ProcessRegistry → Foundation.ServiceRegistry  
├── Mapping: generic processes → service discovery
├── Preserves: namespace isolation + health status
├── Guarantees: service availability tracking
└── Extensions: load balancing hints

Foundation.ProcessRegistry → Foundation.TelemetryService
├── Mapping: registration events → telemetry metrics
├── Preserves: process lifecycle events + metadata changes
├── Guarantees: metric accuracy and timeliness
└── Extensions: performance monitoring integration

6.2 Performance Integration Requirements

Integration Performance Specifications:

MABEAM Agent Coordination:
- Agent capability queries: < 5ms for coordination decisions
- Agent health updates: < 2ms for real-time monitoring
- Multi-agent discovery: < 10ms for teams of up to 100 agents

Service Discovery:
- Service availability checks: < 1ms for critical path
- Service metadata retrieval: < 2ms for configuration
- Service health monitoring: < 500ms polling interval

Telemetry Integration:
- Registration event emission: < 100μs overhead
- Metadata change events: < 200μs overhead  
- Query performance metrics: < 50μs measurement overhead

7. Success Criteria and Verification

7.1 Formal Verification Requirements

Verification Checklist:

□ All invariants I1-I6 verified via property-based testing
□ All safety properties S1-S7 verified via chaos engineering
□ All liveness properties L1-L6 verified via load testing
□ All performance guarantees P1-P6 empirically validated
□ Concurrency model verified via concurrent property testing
□ Failure recovery verified via fault injection testing
□ API contracts verified via contract testing framework

7.2 Implementation Compliance Gates

Quality Gates for Implementation:

Phase 1 Gate: Contract Implementation
- Mock implementation satisfies all API contracts
- Property-based tests validate all invariants
- Integration tests verify MABEAM compatibility

Phase 2 Gate: Production Implementation  
- Performance benchmarks meet all specifications
- Chaos testing validates failure recovery
- Load testing confirms concurrency guarantees
- Memory stability verified over 24-hour continuous operation

Phase 3 Gate: Production Readiness
- Security audit passes
- Documentation complete and accurate
- Monitoring and alerting configured
- Runbook procedures verified

8. Conclusion

This specification provides the mathematical foundation for a production-grade ProcessRegistry that serves as the cornerstone of Foundation’s multi-agent coordination infrastructure. The formal invariants, safety properties, and performance guarantees ensure the implementation will be reliable, efficient, and scalable.

Next Steps: Proceed to Phase 1 (Contract Implementation with Verification) only after this specification is reviewed and approved.

Critical Success Factor: Implementation must provably satisfy every specification in this document, not just pass existing tests.