Type systems as macros

We present Turnstile, a metalanguage for creating typed embedded languages. To implement the type system, programmers write type checking rules resembling traditional judgment syntax. To implement the semantics, they incorporate elaborations into these rules. Turnstile critically depends on the idea of linguistic reuse. It exploits a macro system in a novel way to simultaneously type check and rewrite a surface program into a target language. Reusing a macro system also yields modular implementations whose rules may be mixed and matched to create other languages. Combined with typical compiler and runtime reuse, Turnstile produces performant typed embedded languages with little effort.