Task Management System - Formally Verified with TLA+

A sample task management system with mathematical correctness guarantees, built using TLA+ formal specifications and implemented in Go with property-based testing.

🌟 Key Features

• Formally Verified: Complete TLA+ specification with proven safety and liveness properties
• Property-Based Testing: Automated verification that implementation matches specification
• Runtime Invariant Checking: Continuous correctness validation
• Dependency Management: Automatic task blocking/unblocking with cycle detection
• Priority Inheritance: Critical tasks escalate their dependencies
• Session Management: Secure multi-user authentication with session handling
• Bulk Operations: Efficient batch status updates
• RESTful API: Clean HTTP interface following REST principles

📚 Table of Contents

• Architecture Overview
• Why Formal Verification?
• Quick Start
• Project Structure
• TLA+ Specification
• Implementation Design
• Property-Based Testing
• API Documentation
• Building & Deployment
• Development
• Contributing
• License

🏗 Architecture Overview

graph TB
    subgraph "Formal Specification Layer"
        TLA[TLA+ Specification]
        INV[Safety Invariants]
        LIVE[Liveness Properties]
        TLA --> INV
        TLA --> LIVE
    end
    
    subgraph "Implementation Layer"
        API[REST API]
        UC[Use Cases]
        DOM[Domain Model]
        REPO[Repository]
        API --> UC
        UC --> DOM
        UC --> REPO
    end
    
    subgraph "Verification Layer"
        RT[Runtime Invariants]
        PBT[Property Tests]
        REF[Refinement Tests]
        RT --> UC
        PBT --> UC
        REF --> UC
    end
    
    TLA -.->|Refines| DOM
    INV -.->|Validates| RT
    LIVE -.->|Ensures| PBT

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🔬 Why Formal Verification?

Traditional testing can only verify a finite number of scenarios. This system uses TLA+ formal specification to mathematically prove correctness across all possible states and transitions.

What We Prove

1. Safety Properties (things that must never happen):

   • No task orphaning
   • No cyclic dependencies
   • No invalid state transitions
   • Consistent timestamps
   • Authentication required for all operations

2. Liveness Properties (things that must eventually happen):

   • All tasks eventually complete or cancel
   • Blocked tasks unblock when dependencies complete
   • Critical tasks get priority
   • No starvation of users or tasks

3. Fairness Guarantees:

   • Every user gets access to the system
   • High-priority tasks progress before low-priority
   • Resources are distributed fairly

🚀 Quick Start

Prerequisites

• Go 1.21+
• Docker 20.10+
• Java 11+ (for TLA+ verification)

Installation

# Clone the repository
git clone https://github.com/bhatti/sample-task-management.git
cd task-management

# Install dependencies and verify specifications
make setup
make deps

# Verify TLA+ specifications
make tla-verify

# Run tests
make test-all

# Start the server
make run

Docker Quick Start

# Build and run with Docker Compose
docker-compose up

# Access the API
curl http://localhost:8080/health

Basic Usage

# Authenticate
curl -X POST http://localhost:8080/auth/login \
  -H "Content-Type: application/json" \
  -d '{"user_id": "alice"}'

# Create a task
curl -X POST http://localhost:8080/tasks \
  -H "Content-Type: application/json" \
  -d '{
    "title": "Implement feature",
    "description": "Add new functionality",
    "priority": "high",
    "assignee": "alice",
    "tags": ["feature"],
    "dependencies": []
  }'

# Update task status
curl -X PUT http://localhost:8080/tasks/1/status \
  -H "Content-Type: application/json" \
  -d '{"status": "in_progress"}'

📁 Project Structure

sample-task-management/
│
├── TLA+ Specifications/
│   ├── TaskManagementImproved.tla    # Main specification
│   ├── DiscoveredProperties.tla      # Additional properties
│   ├── RefinementMapping.tla         # Implementation mapping
│   └── PropertyCounterexamples.tla   # Test scenarios
│
├── task-management/                  # Go Implementation
│   ├── cmd/server/                   # Application entry point
│   ├── internal/
│   │   ├── domain/                   # Core business entities
│   │   │   ├── task.go              # Task entity (maps to TLA+ task record)
│   │   │   ├── user.go              # User and session entities
│   │   │   └── system.go            # System state (maps to TLA+ variables)
│   │   ├── usecase/                  # Business logic
│   │   │   └── task_usecase.go      # TLA+ actions as Go methods
│   │   ├── repository/               # Data access interfaces
│   │   ├── infrastructure/           # Infrastructure implementations
│   │   │   └── memory/               # In-memory storage
│   │   └── api/http/                 # REST API handlers
│   ├── pkg/invariants/               # Runtime invariant checking
│   └── test/
│       ├── property/                 # Property-based tests
│       ├── refinement/               # Refinement verification
│       └── statemachine/             # State machine tests
│
├── Build & Deployment/
│   ├── Makefile                      # Build automation
│   ├── Dockerfile                    # Multi-stage container build
│   ├── docker-compose.yml            # Service orchestration
│   └── .github/workflows/            # CI/CD pipelines
│
└── Documentation/
    ├── README.md                      # This file
    ├── BUILD.md                       # Build instructions
    ├── PropertyAnalysisGuide.md      # Property documentation
    └── BehavioralAnalysis.md         # Refinement analysis

📐 TLA+ Specification

The system is formally specified in TLA+ with comprehensive safety and liveness properties.

Core Specification Components

---------------------------- MODULE TaskManagementImproved ----------------------------
VARIABLES
    tasks,          \* Function from task ID to task record
    userTasks,      \* Function from user ID to set of task IDs
    nextTaskId,     \* Counter for generating unique task IDs
    currentUser,    \* Currently authenticated user
    clock,          \* Global clock for timestamps
    sessions        \* Active user sessions

Key Actions (TLA+ → Go Mapping)

TLA+ Action	Go Implementation	Description
Authenticate(user)	TaskUseCase.Authenticate()	User login
CreateTask(...)	TaskUseCase.CreateTask()	Task creation with validation
UpdateTaskStatus(...)	TaskUseCase.UpdateTaskStatus()	State transitions
CheckDependencies	TaskUseCase.CheckDependencies()	Automatic unblocking
BulkUpdateStatus(...)	TaskUseCase.BulkUpdateStatus()	Batch operations

Safety Invariants

SafetyInvariant ==
    /\ NoOrphanTasks           \* Every task has an owner
    /\ TaskOwnership           \* Tasks are in assignee's list
    /\ ValidTaskIds            \* IDs are sequential
    /\ NoDuplicateTaskIds      \* All IDs unique
    /\ ValidStateTransitions   \* Only legal state changes
    /\ ConsistentTimestamps    \* Time ordering preserved
    /\ NoCyclicDependencies    \* No dependency cycles
    /\ AuthenticationRequired  \* All operations authenticated

🎯 Implementation Design

Clean Architecture Layers

1. Domain Layer (internal/domain/)

   • Pure business entities
   • No external dependencies
   • Maps directly to TLA+ types

2. Use Case Layer (internal/usecase/)

   • Business logic implementation
   • Each method maps to a TLA+ action
   • Validates preconditions and postconditions

3. Repository Layer (internal/repository/)

   • Abstract data access
   • Enables testing without infrastructure
   • Supports different storage backends

4. API Layer (internal/api/)

   • REST endpoints
   • Request/response handling
   • Authentication middleware

State Management

// Domain state maps to TLA+ variables
type SystemState struct {
    Tasks       map[TaskID]*Task      // Maps to TLA+ tasks
    UserTasks   map[UserID][]TaskID   // Maps to TLA+ userTasks
    NextTaskID  TaskID                // Maps to TLA+ nextTaskId
    CurrentUser *UserID               // Maps to TLA+ currentUser
    Clock       time.Time             // Maps to TLA+ clock
    Sessions    map[UserID]*Session   // Maps to TLA+ sessions
}

Invariant Checking

Every operation validates invariants at runtime:

func (uc *TaskUseCase) CreateTask(...) (*Task, error) {
    // Precondition checks (from TLA+)
    if currentUser == nil {
        return nil, fmt.Errorf("authentication required")
    }
    
    // Perform operation
    task := createTask(...)
    
    // Postcondition validation
    if err := uc.invariantChecker.CheckAllInvariants(state); err != nil {
        rollback()
        return nil, fmt.Errorf("invariant violation: %w", err)
    }
    
    return task, nil
}

🧪 Property-Based Testing

Refinement Verification

Tests verify that the Go implementation correctly refines the TLA+ specification:

func TestRefinementMapping(t *testing.T) {
    // Generate random operation sequence
    operations := generateRandomOperations(100)
    
    // Execute in both Go and TLA+ simulator
    for _, op := range operations {
        goResult := executeGoOperation(op)
        tlaResult := simulateTLAOperation(op)
        
        // Verify states remain equivalent
        assert.Equal(t, tlaResult, goResult)
        
        // Check invariants preserved
        assert.NoError(t, checkInvariants(goState))
    }
}

Property Tests

// Property: No orphan tasks after any operation
func TestNoOrphanTasksProperty(t *testing.T) {
    quick.Check(func(ops []Operation) bool {
        state := executeOperations(ops)
        return checkNoOrphanTasks(state) == nil
    }, nil)
}

// Property: Dependency cycles never created
func TestNoCyclicDependencies(t *testing.T) {
    quick.Check(func(deps [][]TaskID) bool {
        state := createTasksWithDependencies(deps)
        return !hasCycles(state.Tasks)
    }, nil)
}

📡 API Documentation

Authentication

POST /auth/login
Content-Type: application/json

{
  "user_id": "alice"
}

Response: 200 OK
{
  "token": "...",
  "user_id": "alice",
  "expires_at": "2024-01-01T00:00:00Z"
}

Task Operations

POST /tasks
Authorization: Bearer {token}
Content-Type: application/json

{
  "title": "Implement feature",
  "description": "Detailed description",
  "priority": "high",
  "assignee": "bob",
  "due_date": "2024-02-01T00:00:00Z",
  "tags": ["feature", "backend"],
  "dependencies": [1, 2]
}

Response: 201 Created
{
  "id": 3,
  "title": "Implement feature",
  "status": "blocked",  // Auto-set based on dependencies
  "created_at": "2024-01-01T00:00:00Z"
}

Bulk Operations

POST /tasks/bulk-update
Authorization: Bearer {token}
Content-Type: application/json

{
  "task_ids": [1, 2, 3],
  "status": "in_progress"
}

Response: 200 OK
{
  "updated": 3,
  "failed": 0
}

🔨 Building & Deployment

Local Development

# Run with hot reload
make serve

# Run tests continuously
make watch

# Check code quality
make check

Build

# Build for all platforms
make build-all

# Build Docker image
make docker-build

# Deploy to Kubernetes
kubectl apply -f k8s/

CI/CD Pipeline

The project uses GitHub Actions for continuous integration and deployment:

1. TLA+ Verification - Verify specifications on every commit
2. Testing - Run all test suites including property-based tests
3. Security Scanning - Check for vulnerabilities
4. Multi-platform Build - Compile for Linux, macOS, Windows
5. Container Build - Create and push Docker images
6. Release - Automated GitHub releases on tags

🧩 Development

Running Tests

# All tests
make test-all

# Specific test types
make test-property      # Property-based tests
make test-refinement    # Refinement verification
make test-concurrent    # Concurrency tests

# Coverage report
make test-coverage
open build/coverage/coverage.html

TLA+ Verification

# Verify specifications
make tla-verify

# Run simulation
make tla-simulate

# Check specific properties
java -cp /usr/local/lib/tla2tools.jar tlc2.TLC \
  -config PropertyVerification.cfg \
  TaskManagementImproved.tla

Debugging

# Run with debug logging
LOG_LEVEL=debug make run

# Connect debugger (port 2345)
docker-compose --profile development up

# Profile performance
make profile
go tool pprof build/profile/cpu.prof

🤝 Contributing

We welcome contributions! Please see our Contributing Guide for details.

Development Process

1. Fork the repository
2. Create a feature branch
3. Write TLA+ specification for new features
4. Implement with corresponding tests
5. Verify all properties still hold
6. Submit a pull request

Code Standards

• All new features must have TLA+ specifications
• Property-based tests required for critical paths
• Runtime invariant checking for new operations
• 80% minimum test coverage
• Pass all linters and security scans

📊 Performance

• Throughput: 10,000+ operations/second
• Latency: < 10ms p99 for single operations
• Scalability: Tested with 1M+ tasks
• Verification: TLA+ checked up to 10^6 states

🔒 Security

• Authentication required for all operations
• Session-based access control
• No SQL injection (type-safe queries)
• Dependency vulnerability scanning
• Runtime invariant enforcement

📚 Documentation

• Build & Deployment Guide
• TLA+ Specification Guide
• API Reference
• Architecture Decision Records

📈 Project Status

• ✅ TLA+ specification complete
• ✅ Core implementation done
• ✅ Property-based testing implemented
• ✅ Docker deployment ready
• 🚧 Kubernetes operators in progress
• 📋 PostgreSQL persistence planned

🙏 Acknowledgments

This project demonstrates the practical application of formal methods in software:

• TLA+ by Leslie Lamport for formal specification
• Go for efficient implementation
• Property-based testing for verification
• Inspired by Amazon's use of TLA+ in systems

📄 License

MIT License - see LICENSE file for details.

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Built with formal methods for reliability, implemented with Go for performance, and tested with property-based verification for correctness.