I saw Joe's strange loop talk [1] a while ago and I get the same vibe reading his post as I did when watching the video. It sounds very cool, but I can't shake the feeling that it only works for 85% of the code. That is to say if you program in exactly the right way, you will be able to do everything you want and it will work with this system, but there are ways of programming that won't work with this system.
More specifically I feel like there are two problems. 1) It feels suspiciously like there's a combination of halting problem and diagonalisation that shows there are an uncountably infinite number of functions that we want to write that can't be named (although I would want to have a better idea of how this is supposed to work before I try to hammer out a proof). 2) I don't understand how it's possible for any hashing scheme to encode necessary properties of a function such that the function with necessary properties has a different hash than an otherwise identical function without these properties. For example can we hash these functions such that stable sort looks different than unstable sort? Wouldn't we need dependent typing to encode all required properties? And if that's the case couldn't I pull a Gödel and show that there's always one more property not encodable in your system?
There are countably infinite number of functions. A simple proof is that each function can be represented as a string, and there are countably infinite number of strings for a finite alphabet. You could also argue that functions are equivalent to Turing machines, and there are a finite number of Turing machines.
More specifically I feel like there are two problems. 1) It feels suspiciously like there's a combination of halting problem and diagonalisation that shows there are an uncountably infinite number of functions that we want to write that can't be named (although I would want to have a better idea of how this is supposed to work before I try to hammer out a proof). 2) I don't understand how it's possible for any hashing scheme to encode necessary properties of a function such that the function with necessary properties has a different hash than an otherwise identical function without these properties. For example can we hash these functions such that stable sort looks different than unstable sort? Wouldn't we need dependent typing to encode all required properties? And if that's the case couldn't I pull a Gödel and show that there's always one more property not encodable in your system?
[1] - https://www.youtube.com/watch?v=lKXe3HUG2l4 [2]
[2] - https://news.ycombinator.com/item?id=8572920 (thanks for the link)