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Having a Turing complete type system is not what you normally want to have, that (it means to have undecidable type checking) makes tooling (and the compiler) way more complex and difficult.
GitHub issue about the Turing completeness:
https://github.com/microsoft/TypeScript/issues/14833
Proof of Turing completeness:
https://gist.github.com/hediet/63f4844acf5ac330804801084f87a...
Another example, SQL-database-in-the-typescript-typesystem here https://github.com/codemix/ts-sql
This would have been much easier if I'd had ts-regexp at the time :)
Check out Hegel[0], it uses Flow syntax, it's compatible w/ .d.ts type definitions and has a smarter type inference model than both TS and Flow IMHO.
[0] https://hegel.js.org/