Kairos Specification Document

Project Overview

Kairos is an AI-first implementation of Homotopy Type Theory (HoTT) using RedPRL/RedTT as its foundation and Anthropic's Model Context Protocol (MCP) for AI integration. The system enables pattern recognition, verification, and transformation in code analysis and proof construction.

Core Components

1. Pattern System

• Implements HoTT patterns using RedPRL's type system
• Supports pattern matching, composition, and transformation
• Maintains evidence tracking for pattern verification
• Enables pattern evolution and learning

Required features:

• Pattern representation using HoTT types
• Pattern composition operations
• Pattern equivalence checking
• Evidence generation and tracking
• Pattern transformation rules

2. MCP Integration

• Implements Anthropic's Model Context Protocol
• Manages AI state and context
• Handles message routing and actions
• Maintains conversation history

Required features:

• Full MCP protocol implementation
• State management system
• Context routing
• Action handling
• Conversation history tracking

3. RedPRL Integration

• Interfaces with RedPRL/RedTT
• Handles type checking and verification
• Manages proof construction
• Converts between RedPRL and Kairos types

Required features:

• RedPRL communication layer
• Type conversion system
• Proof management
• Verification handling

Development Phases

Phase 1: Core Infrastructure (2-3 weeks)

1. Set up project structure
2. Implement basic RedPRL interface
3. Create MCP foundation
4. Develop core type system

Phase 2: Pattern System (3-4 weeks)

1. Implement pattern representation
2. Add pattern matching
3. Create composition operations
4. Build evidence tracking

Phase 3: AI Integration (3-4 weeks)

1. Complete MCP implementation
2. Add state management
3. Implement context handling
4. Create action system

Phase 4: Proof System (4-5 weeks)

1. Implement proof construction
2. Add verification system
3. Create proof composition
4. Build proof transformation

Technical Requirements

Language and Tools

• Primary implementation in Haskell
• RedPRL/RedTT for HoTT foundation
• MCP for AI integration
• Property-based testing with QuickCheck
• Documentation with Haddock

Core Features

1. Pattern Recognition

   • Type-safe pattern representation
   • Pattern matching algorithms
   • Composition operations
   • Transformation rules

2. Proof Construction

   • HoTT-based proof representation
   • Proof verification
   • Proof composition
   • Evidence tracking

3. AI Integration

   • Full MCP support
   • State management
   • Context handling
   • Action processing

4. Type System

   • HoTT types
   • Pattern types
   • Proof types
   • Evidence types

Implementation Guidelines

Code Structure

• Modular design
• Clear separation of concerns
• Type-safe interfaces
• Comprehensive testing
• Detailed documentation

Pattern System Implementation

1. Define core pattern types
2. Implement pattern matching
3. Add composition operations
4. Create transformation system

MCP Integration Steps

1. Implement protocol handlers
2. Add state management
3. Create context system
4. Build action handlers

RedPRL Integration Steps

1. Create communication layer
2. Implement type conversion
3. Add proof management
4. Build verification system

Development Tools and Planning

Project Management

GitHub Project Board

Our development is tracked using a GitHub Project Board that provides:

• Sprint planning and tracking
• Task prioritization
• Progress visualization
• Team coordination

Issue Management

Issues are organized using a comprehensive labeling system:

• Type Labels:

  • epic: High-level tracking issues
  • type-feature: New feature implementation
  • type-bug: Bug fixes
  • type-docs: Documentation updates
  • type-test: Test implementation

• Priority Labels:

  • priority-high: Immediate attention required
  • priority-medium: Standard priority
  • priority-low: Can be addressed later

• Phase Labels:

  • phase-1: Core Infrastructure
  • phase-2: Pattern System
  • phase-3: AI Integration
  • phase-4: Proof System

• Status Labels:

  • status-blocked: Blocked by dependencies

Development Resources

Documentation

• Development Guide: Comprehensive guide for developers
• Contributing Guidelines: How to contribute to the project
• Pull Request Template: Template for creating PRs

CI/CD Pipeline

Our GitHub Actions workflow provides:

• Automated builds
• Test execution
• Code quality checks (HLint)
• Documentation generation (Haddock)

Getting Started with Development

1. Project Setup

   git clone https://github.com/mprestonsparks/kairos.git
   cd kairos
   cabal update
   cabal build

2. Development Workflow

   • Create a new branch for your feature/fix
   • Implement changes following CONTRIBUTING.md
   • Submit PR using the template
   • Await review and CI checks

3. Issue Creation

   • Use appropriate labels
   • Reference related issues/PRs
   • Follow issue templates
   • Include acceptance criteria

4. Code Review Process

   • Ensure CI passes
   • Follow framework guidelines
   • Update documentation
   • Address review comments

Project Structure

kairos/
├── .github/                # GitHub configuration
│   ├── workflows/         # CI/CD workflows
│   └── ISSUE_TEMPLATE/    # Issue templates
├── docs/                  # Project documentation
├── src/                   # Source code
├── test/                  # Test suite
└── scripts/              # Development scripts

Testing Requirements

Unit Testing

• All core functions
• Pattern operations
• MCP functionality
• RedPRL interface

Integration Testing

• Pattern system with MCP
• RedPRL integration
• Proof construction
• Full system tests

Property Testing

• Pattern operations
• Type conversions
• Proof transformations
• State management

Documentation Requirements

Code Documentation

• Full Haddock documentation
• Clear function signatures
• Usage examples
• Implementation notes

User Documentation

• Installation guide
• Usage manual
• API documentation
• Example patterns

Theory Documentation

• HoTT foundations
• Pattern theory
• Proof system
• AI integration

Performance Requirements

Response Time

• Pattern matching: < 100ms
• Proof verification: < 500ms
• AI integration: < 1s
• Type checking: < 200ms

Memory Usage

• Core system: < 500MB
• With AI: < 2GB
• Pattern storage: O(n) where n is pattern size

Error Handling

Required Error Cases

• Invalid patterns
• Failed proofs
• MCP protocol errors
• Type mismatches

Error Reporting

• Detailed error messages
• Error categorization
• Recovery suggestions
• Debug information

Security Requirements

Data Protection

• Secure AI communication
• Safe pattern storage
• Protected proof data
• Encrypted connections

Input Validation

• Pattern validation
• Proof checking
• Type verification
• Protocol validation