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project_plan.md

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Axiomadic Detailed Project Plan

graph LR
    A[1.1 Core Calculus Implementation] --> B[1.2 Type System Development]
    A --> C[2.1 Parallel Computation Model]
    B --> D[1.3 Effect System and Linear Types]
    B --> E[3.1 Tactic Language Development]
    C --> F[2.2 Automatic Parallelization]
    E --> G[3.2 Theorem Proving Capabilities]
    G --> H[3.3 Integration of Proofs and Code]
    B --> I[4.1 Metaprogramming System]
    A --> J[4.2 Standard Library Development]
    B --> J
    C --> J
    A --> K[5.1 Compiler Development]
    B --> K
    C --> K
    D --> K
    K --> L[5.2 Development Environment]
    J --> M[5.3 Package Management and Build System]
    K --> M
    A --> N[6.1 Language Documentation]
    B --> N
    C --> N
    D --> N
    E --> N
    F --> N
    G --> N
    H --> N
    I --> N
    J --> N
    K --> N
    L --> N
    M --> N
    N --> O[6.2 Community Building]
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Initiative 1: Core Language Development

Project 1.1: Core Calculus Implementation

  • Task 1.1.1: Define core calculus based on interaction combinators
    • Subtask 1.1.1.1: Formalize syntax
    • Subtask 1.1.1.2: Define reduction rules
    • Subtask 1.1.1.3: Prove basic properties (confluence, strong normalization)
  • Task 1.1.2: Implement core calculus in Rust
    • Subtask 1.1.2.1: Develop AST representation
    • Subtask 1.1.2.2: Implement reduction engine
    • Subtask 1.1.2.3: Write unit tests for core operations

Project 1.2: Type System Development

  • Task 1.2.1: Design dependent type system
    • Subtask 1.2.1.1: Define universe hierarchy
    • Subtask 1.2.1.2: Implement Pi types
    • Subtask 1.2.1.3: Design inductive types
  • Task 1.2.2: Incorporate Cubical Type Theory features
    • Subtask 1.2.2.1: Implement path types
    • Subtask 1.2.2.2: Add composition operations
    • Subtask 1.2.2.3: Implement univalence axiom
  • Task 1.2.3: Develop type checker
    • Subtask 1.2.3.1: Implement core type checking algorithm
    • Subtask 1.2.3.2: Add support for subtyping
    • Subtask 1.2.3.3: Optimize type checker for performance

Project 1.3: Effect System and Linear Types

  • Task 1.3.1: Design effect system
    • Subtask 1.3.1.1: Define effect syntax
    • Subtask 1.3.1.2: Implement effect inference
    • Subtask 1.3.1.3: Create effect handlers
  • Task 1.3.2: Implement linear types
    • Subtask 1.3.2.1: Define linear type syntax
    • Subtask 1.3.2.2: Implement usage checking
    • Subtask 1.3.2.3: Integrate with effect system

Initiative 2: Parallelism and Concurrency

Project 2.1: Parallel Computation Model

  • Task 2.1.1: Design parallel primitives
    • Subtask 2.1.1.1: Define spawn and sync operations
    • Subtask 2.1.1.2: Implement futures and promises
    • Subtask 2.1.1.3: Design parallel data structures
  • Task 2.1.2: Implement runtime system
    • Subtask 2.1.2.1: Develop work-stealing scheduler
    • Subtask 2.1.2.2: Implement load balancing
    • Subtask 2.1.2.3: Optimize for different hardware architectures

Project 2.2: Automatic Parallelization

  • Task 2.2.1: Develop parallelization analysis
    • Subtask 2.2.1.1: Implement dependency analysis
    • Subtask 2.2.1.2: Design cost model for parallelization
    • Subtask 2.2.1.3: Create heuristics for parallelization decisions
  • Task 2.2.2: Implement code transformation for parallelism
    • Subtask 2.2.2.1: Develop AST transformation rules
    • Subtask 2.2.2.2: Implement safety checks for parallel execution
    • Subtask 2.2.2.3: Optimize generated parallel code

Initiative 3: Proof Assistant Features

Project 3.1: Tactic Language Development

  • Task 3.1.1: Design tactic language syntax
    • Subtask 3.1.1.1: Define core tactics (intros, apply, rewrite, etc.)
    • Subtask 3.1.1.2: Implement tactic combinators
    • Subtask 3.1.1.3: Design custom tactic definition syntax
  • Task 3.1.2: Implement tactic execution engine
    • Subtask 3.1.2.1: Develop proof state representation
    • Subtask 3.1.2.2: Implement tactic interpreter
    • Subtask 3.1.2.3: Add error handling and reporting for tactics

Project 3.2: Theorem Proving Capabilities

  • Task 3.2.1: Implement proof checking
    • Subtask 3.2.1.1: Develop core proof checker
    • Subtask 3.2.1.2: Implement proof term generation from tactics
    • Subtask 3.2.1.3: Optimize proof checker for large proofs
  • Task 3.2.2: Develop automated proof search
    • Subtask 3.2.2.1: Implement basic proof search strategies
    • Subtask 3.2.2.2: Integrate external automated theorem provers
    • Subtask 3.2.2.3: Develop parallel proof search algorithms

Project 3.3: Integration of Proofs and Code

  • Task 3.3.1: Design proof-carrying code system
    • Subtask 3.3.1.1: Develop syntax for inline proofs
    • Subtask 3.3.1.2: Implement verification condition generation
    • Subtask 3.3.1.3: Create system for managing proof obligations
  • Task 3.3.2: Implement extraction of verified programs
    • Subtask 3.3.2.1: Develop program extraction algorithm
    • Subtask 3.3.2.2: Implement optimization of extracted programs
    • Subtask 3.3.2.3: Ensure correctness preservation in extraction

Initiative 4: Language Features and Standard Library

Project 4.1: Metaprogramming System

  • Task 4.1.1: Design macro system
    • Subtask 4.1.1.1: Develop syntax for macro definitions
    • Subtask 4.1.1.2: Implement hygienic macro expansion
    • Subtask 4.1.1.3: Create debugging tools for macros
  • Task 4.1.2: Implement reflection capabilities
    • Subtask 4.1.2.1: Design reflection API
    • Subtask 4.1.2.2: Implement runtime type information
    • Subtask 4.1.2.3: Develop meta-circular evaluator

Project 4.2: Standard Library Development

  • Task 4.2.1: Implement core data structures
    • Subtask 4.2.1.1: Develop verified list, vector, and map implementations
    • Subtask 4.2.1.2: Implement efficient string handling
    • Subtask 4.2.1.3: Create parallel versions of core data structures
  • Task 4.2.2: Develop mathematical libraries
    • Subtask 4.2.2.1: Implement basic arithmetic and algebra
    • Subtask 4.2.2.2: Develop libraries for advanced mathematics (category theory, topology, etc.)
    • Subtask 4.2.2.3: Create computer algebra system integration

Initiative 5: Tooling and Environment

Project 5.1: Compiler Development

  • Task 5.1.1: Implement frontend
    • Subtask 5.1.1.1: Develop lexer and parser
    • Subtask 5.1.1.2: Implement name resolution and type inference
    • Subtask 5.1.1.3: Create intermediate representation
  • Task 5.1.2: Develop backend
    • Subtask 5.1.2.1: Implement code generation (targeting LLVM)
    • Subtask 5.1.2.2: Develop optimization passes
    • Subtask 5.1.2.3: Implement parallel code generation

Project 5.2: Development Environment

  • Task 5.2.1: Create language server
    • Subtask 5.2.1.1: Implement code completion
    • Subtask 5.2.1.2: Develop real-time type checking and error reporting
    • Subtask 5.2.1.3: Implement refactoring tools
  • Task 5.2.2: Develop integrated debugger
    • Subtask 5.2.2.1: Implement breakpoint system
    • Subtask 5.2.2.2: Develop variable inspection and modification
    • Subtask 5.2.2.3: Create visualization tools for parallel execution

Project 5.3: Package Management and Build System

  • Task 5.3.1: Design package format and repository system
    • Subtask 5.3.1.1: Define package manifest format
    • Subtask 5.3.1.2: Implement version resolution algorithm
    • Subtask 5.3.1.3: Develop central package repository
  • Task 5.3.2: Implement build system
    • Subtask 5.3.2.1: Create build configuration language
    • Subtask 5.3.2.2: Implement incremental compilation
    • Subtask 5.3.2.3: Develop parallel build capabilities

Initiative 6: Documentation and Community

Project 6.1: Language Documentation

  • Task 6.1.1: Write language specification
    • Subtask 6.1.1.1: Document core calculus and type system
    • Subtask 6.1.1.2: Specify standard library interfaces
    • Subtask 6.1.1.3: Create formal semantics
  • Task 6.1.2: Develop user guides and tutorials
    • Subtask 6.1.2.1: Write beginner's guide
    • Subtask 6.1.2.2: Create advanced topics documentation
    • Subtask 6.1.2.3: Develop interactive tutorials

Project 6.2: Community Building

  • Task 6.2.1: Set up community infrastructure
    • Subtask 6.2.1.1: Create project website
    • Subtask 6.2.1.2: Set up forums and chat platforms
    • Subtask 6.2.1.3: Establish code of conduct
  • Task 6.2.2: Organize community events
    • Subtask 6.2.2.1: Plan regular online meetups
    • Subtask 6.2.2.2: Organize annual conference
    • Subtask 6.2.2.3: Facilitate contribution to the project