jameshaydon / sixty

Dependent type checker using normalisation by evaluation

sixty

A type checker for a dependent type theory using normalisation by evaluation, with an eye on performance. Might go into Sixten one day.

Roadmap

• Surface syntax
• Core syntax
• Safe and fast phantom typed De Bruijn indices
• Evaluation
  • Inlining of globals
• Readback
• Parsing
  • Indentation-sensitivity
• Pretty printing
  • Scope-aware name printing
• Unification and meta variables
  • Pruning
  • The "same meta variable" intersection rule
  • Solution inlining
  • Elaboration of meta variable solutions to local definitions
  • Case expression inversion
• Basic type checking
• Elaboration postponement ("impredicative polymorphism" inference)
  • Lazily written solutions
• Approximate polymorphic variable inference
• Query architecture
  • Parallel type checking
• Simple modules
  • Top-level definitions
  • Name resolution
  • Imports
• Tests
  • Error tests
  • Multi-module tests
• Position-independent implicit arguments
• Errors
  • Source location tracking
    • Meta variable locations
  • Error recovery during
    • Parsing
    • Elaboration
    • Unification
  • Print the context and let-bound variables (including metas)
• Data
  • Elaboration of data definitions
  • Constructors
    • Type-based overloading
  • ADT-style data definitions
• Pattern matching elaboration
  • Case expressions
  • Exhaustiveness check
  • Redundant pattern check
  • Clause elaboration
  • Pattern lambdas
• Inductive families
• Glued evaluation
• Let definitions by clauses
  • Mutually recursive lets
• Command-line parser
• Language server
  • Diagnostics
  • Hover
    • Print the context and let-bound variables (including metas)
  • Jump to definition
  • Multi file projects
  • Reverse dependency tracking
  • Completion
  • Type-based refinement completion snippets
  • Find references
  • Renaming
  • Code lenses
  • Language server tests
• File watcher
• Cached builds
  • Per-module caches
• Backend
  • Typed lambda lifting
    • Recursive let bindings
  • Typed closure conversion
  • Code generation
    • Basics
    • Closures
  • Garbage collection
  • Extern code
• Prevent CBV-incompatible circular values
• Literals
  • Numbers
  • Strings
• Records
• Binary/mixfix operators
• REPL
• Integrate into Sixten

Inspiration

• András Kovács' smalltt and work on Dhall
• Thierry Coquand's semantic type checking
• Danny Gratzer's nbe-for-mltt