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双轴世界实现状态报告 / Dual-Axis Universe Implementation Status Report

中文 | English

中文

已完成的工作

1. ✅ 核心头文件扩展 (include/kos_core.h)

  • ✅ 添加了Universe轴类型枚举 (universe_axis)
  • ✅ 添加了Universe层级信息结构 (universe_info)
  • ✅ 扩展了term_kind枚举，添加了：
    • KOS_TIME - 时间类型
    • KOS_ID - 标识符类型
    • KOS_U - 计算轴Universe类型
    • KOS_TYPE - 逻辑轴Universe类型
  • ✅ 在kos_term结构中添加了universe字段用于存储Universe信息
  • ✅ 添加了Universe union成员用于Universe类型的数据存储
  • ✅ 添加了Universe层级系统的接口声明

2. ✅ Universe层级系统实现 (src/core/universe.c)

  • ✅ 实现了kos_get_universe_info() - 获取类型的Universe信息
  • ✅ 实现了kos_universe_leq() - 检查Universe层级关系
  • ✅ 实现了kos_universe_lift_to_logic() - Universe Lifting规则：U_i : Type_{i+1}
  • ✅ 实现了kos_prop_embed_to_data() - Proposition Embedding规则：Prop ↪ U_1

3. ✅ 类型构建器更新 (src/core/type_builder.c)

  • ✅ 添加了kos_mk_time() - 创建时间类型
  • ✅ 添加了kos_mk_id() - 创建标识符类型
  • ✅ 添加了kos_mk_universe_computational() - 创建U_i类型
  • ✅ 添加了kos_mk_universe_logical() - 创建Type_i类型
  • ✅ 所有类型构建函数都正确初始化了universe字段
  • ✅ 实现了Σ类型和Π类型的Universe层级计算（max(i,j)规则）
  • ✅ 更新了kos_term_copy()以支持新类型
  • ✅ 更新了kos_term_free()以支持新类型

4. ✅ 存储系统更新 (src/core/storage.c)

  • ✅ 更新了序列化函数以支持新类型（TIME, ID, U, TYPE）
  • ✅ 添加了新类型的JSON序列化支持

5. ✅ 构建系统更新 (CMakeLists.txt)

  • ✅ 添加了src/core/universe.c到构建列表

待完成的工作

1. ⏳ 类型检查器更新 (src/core/type_checker.c)

需要添加：

  • Universe层级验证逻辑
  • Universe Lifting规则的应用
  • 新类型（TIME, ID, U, TYPE）的类型检查
  • 类型构造时的Universe层级约束检查

当前状态： 类型检查器需要扩展以支持Universe层级系统

2. ⏳ 归约和替换系统更新

需要更新：

  • src/core/reduction.c - 添加对新类型的归约支持
  • src/core/substitution.c - 添加对新类型的替换支持

3. ⏳ 其他文件的兼容性更新

可能需要更新：

  • 领域特定代码（manufacturing等）可能需要适配新类型
  • 运行时代码可能需要处理新类型

4. ⏳ 编译和测试

  • 需要修复所有编译错误
  • 需要验证新功能的正确性
  • 需要进行集成测试

实现的核心特性

Universe层级系统

根据Kos.tex文档定义，实现了：

  1. 双轴结构

    • 计算轴 (U_i): UNIVERSE_COMPUTATIONAL
    • 逻辑轴 (Type_i): UNIVERSE_LOGICAL

  2. 层级关系

    • Prop : Type_1
    • Type_i : Type_{i+1}
    • U_i : U_{i+1}
    • U_i : Type_{i+1} (通过Lifting规则)

  3. Universe Lifting规则

    • U_i : Type_{i+1} (计算轴可提升到逻辑轴)
    • Prop ↪ U_1 (命题可嵌入到数据轴)

  4. 类型构造规则

    • Σ类型：U_max(i,j) 规则
    • Π类型：Type_max(i,j) 规则（或Impredicative规则）

代码质量

  • ✅ 所有新代码都遵循了现有代码风格
  • ✅ 添加了适当的注释说明
  • ✅ 保持了与现有代码的兼容性（通过初始化universe字段为默认值）

下一步行动

  1. 立即需要：更新类型检查器以支持Universe层级验证
  2. 重要：更新归约和替换系统
  3. 必要：修复编译错误并进行测试
  4. 建议：添加单元测试验证Universe层级系统的正确性

注意事项

  • 当前实现是基础的，某些高级特性（如完整的依赖类型检查、上下文处理）可能需要进一步细化
  • Universe层级系统的完整集成需要类型检查器的支持
  • 建议在完成类型检查器更新后再进行全面的测试

English

Dual-Axis Universe Implementation Status Report

Completed Work

1. ✅ Core Header File Extensions (include/kos_core.h)

  • ✅ Added Universe axis type enum (universe_axis)
  • ✅ Added Universe level information structure (universe_info)
  • ✅ Extended term_kind enum, added:
    • KOS_TIME - Time type
    • KOS_ID - Identifier type
    • KOS_U - Computational axis Universe type
    • KOS_TYPE - Logical axis Universe type
  • ✅ Added universe field to kos_term structure for storing Universe information
  • ✅ Added Universe union member for Universe type data storage
  • ✅ Added Universe level system interface declarations

2. ✅ Universe Level System Implementation (src/core/universe.c)

  • ✅ Implemented kos_get_universe_info() - Get type's Universe information
  • ✅ Implemented kos_universe_leq() - Check Universe level relationships
  • ✅ Implemented kos_universe_lift_to_logic() - Universe Lifting rule: U_i : Type_{i+1}
  • ✅ Implemented kos_prop_embed_to_data() - Proposition Embedding rule: Prop ↪ U_1

3. ✅ Type Builder Updates (src/core/type_builder.c)

  • ✅ Added kos_mk_time() - Create time type
  • ✅ Added kos_mk_id() - Create identifier type
  • ✅ Added kos_mk_universe_computational() - Create U_i type
  • ✅ Added kos_mk_universe_logical() - Create Type_i type
  • ✅ All type builder functions correctly initialize universe field
  • ✅ Implemented Universe level calculation for Σ and Π types (max(i,j) rule)
  • ✅ Updated kos_term_copy() to support new types
  • ✅ Updated kos_term_free() to support new types

4. ✅ Storage System Updates (src/core/storage.c)

  • ✅ Updated serialization functions to support new types (TIME, ID, U, TYPE)
  • ✅ Added JSON serialization support for new types

5. ✅ Build System Updates (CMakeLists.txt)

  • ✅ Added src/core/universe.c to build list

Pending Work

1. ⏳ Type Checker Updates (src/core/type_checker.c)

Need to add:

  • Universe level verification logic
  • Application of Universe Lifting rules
  • Type checking for new types (TIME, ID, U, TYPE)
  • Universe level constraint checking during type construction

Current status: Type checker needs extension to support Universe level system

2. ⏳ Reduction and Substitution System Updates

Need to update:

  • src/core/reduction.c - Add reduction support for new types
  • src/core/substitution.c - Add substitution support for new types

3. ⏳ Compatibility Updates for Other Files

May need to update:

  • Domain-specific code (manufacturing, etc.) may need to adapt to new types
  • Runtime code may need to handle new types

4. ⏳ Compilation and Testing

  • Need to fix all compilation errors
  • Need to verify correctness of new features
  • Need to perform integration testing

Implemented Core Features

Universe Level System

According to Kos.tex document definition, implemented:

  1. Dual-Axis Structure

    • Computational axis (U_i): UNIVERSE_COMPUTATIONAL
    • Logical axis (Type_i): UNIVERSE_LOGICAL

  2. Level Relationships

    • Prop : Type_1
    • Type_i : Type_{i+1}
    • U_i : U_{i+1}
    • U_i : Type_{i+1} (through Lifting rule)

  3. Universe Lifting Rules

    • U_i : Type_{i+1} (computational axis can be promoted to logical axis)
    • Prop ↪ U_1 (propositions can be embedded into data axis)

  4. Type Construction Rules

    • Σ type: U_max(i,j) rule
    • Π type: Type_max(i,j) rule (or Impredicative rule)

Code Quality

  • ✅ All new code follows existing code style
  • ✅ Added appropriate comments
  • ✅ Maintained compatibility with existing code (by initializing universe field to default values)

Next Steps

  1. Immediate need: Update type checker to support Universe level verification
  2. Important: Update reduction and substitution systems
  3. Necessary: Fix compilation errors and perform testing
  4. Recommended: Add unit tests to verify correctness of Universe level system

Notes

  • Current implementation is basic, some advanced features (such as complete dependent type checking, context handling) may need further refinement
  • Complete integration of Universe level system requires type checker support
  • Recommend comprehensive testing after completing type checker updates