Mœbius: metaprogramming using contextual types: the stage where system f can pattern match on itself

This is a 5-min presentation video of my talk at POPL 2022 on the foundation of the metaprogramming language, Mœbius. Mœbius supports the generation of System F style polymorphic code, generation of code depending on code/type templates, and analysis of code/type via pattern matching. Our work extends the contextual modal type theory to type variables and a new dimension, "level", which allows us to distinguish code/type templates from values/types. These extensions provide the power to generate polymorphic code fragments without extra redexes, which programmers do not intend to write. Furthermore, Mœbius supports pattern matching on code with an algorithm for the type variable refinement. Our work is a step towards building a general type-theoretic foundation for multi-staged metaprogramming that enforces strong type guarantees as well as makes it easy to generate and manipulate code fragments as a programmer intends.