alt Hacker News> using dependent type system to have "proofs" be equivalent to "types"
Do you mean proposition as types? And proof has a program?
Or do you see it at somewhat a higher order, since values are proof for a type, and types can perhaps be proof at a higher level if they are first class citizen in the language?
(Which makes me think that dependent types is really a stairway between two type systems?)
Just wondering, since I had never personally seen it described in that fashion.
Other question: What is the function and runtime treatment of dependent types? Can they be instantiated on the spot by runtime values? A bit like defining/declaring functions that return arrays of runtime-known length? Does it involve two aspects of type checking? compile and runtime? Implementation-wise, doesn't it require too many indirections?
Yeah, I just meant proposition-as-types. Sloppy terminology by me. I meant to complain about the general conflation of the "proving system" and the "typechecking system".
Generally in dependent type systems you are limited in some way in what sort of values a type can refer to. The fancy type checking happens at compile time, and then at run time some or most of the type information is erased. The implementation is tricky but the more difficult problem IMO is the developer experience; it involves a lot of extra work to express dependent types and help the compiler verify them.