For example the issues with, implied constraints, infinite types, and parametric methods could be solved by using something more properly founded in type theory. Concepts are effectively refinement types[1] and a properly founded implementation from type theory would mitigate these issues.
Concepts are not "effectively" refinement types.
I mean something properly founded in type theory, like say _refinement types_ as implemented in liquid haskell: https://www.microsoft.com/en-us/research/wp-content/uploads/... . Constraints of course are _not_ refinement types, but very close to a _subset_ of refinement types. Specifically they have deep similarity to Refined Type Classes from the above paper.
Having used Idris, LiquidHaskell, and F* to implement provable algorithms for some distributed systems I _don't_ think Go should go down that route. The techniques are simply not simple or clean enough for more general purpose languages. But having a type system which has a subset of those feature, and which stands on firmer mathematical firmament lets you reason about stuff like "which of these two programs is okay:
``` // OK type List(type T) struct { elem T next List(T) }
// NOT OK - Implies an infinite sequence of types as you follow .next pointers. type Infinite(type T) struct { next Infinite(Infinite(T)) }```
Which the go authors see as problematic:
> "It is unclear what the algorithm is for deciding which programs to accept and which to reject."
Idris certainly has no problem choosing which ones should and should not be used.
A similar issue arises in C++; the C++ standard says that there is an implementation defined limit on the total depth of recursive instantiations. Perhaps Go should do something similar.
Consider this sample. We want to be able to define inductive types such as `List(T)`, but not `InfiniteList(T)` or `BigArray(T)`. While `BigArray(T)` is an interesting construct (it's effectively a dependent type)* it jumps past the "can I keep it in my head" smell test for me. As soon as a I have to reason deeply about what a type constructor does it just doesn't feel like Go to me.
So we want to be able to construct types which are inductive but can only calculate a single type. List{T} calculates one type, BigArray calculates _n_ types, and InfiniteList calculates an infinite number of types.
* In Idris one would write something like:
data BigArray : (n : Nat) -> (l : List m) -> Type where
Z l : Vect Z v
n l : Vect n lGo contracts as-written, or "accept a T that can do a thing and have a default implementation", is orthogonal to refinement types.
N.B. I'd really love to see refinement types break past the acceptable threshold of compilation time, since they're really neat and are easy to explain to people in terms of their usefuless.
> We would like to understand better if it is feasible to allow any valid function body as a contract body.
A generic function to compute a type is _very much_ in the realm of both refinement and dependent types. The BigArray example (as mentioned in a sister thread) is just a dependent type.
> The hard part is defining precisely which generic function bodies are allowed by a given contract body. .. We are most uncertain about exactly what to allow in contract bodies, to make them as easy to read and write for users while still being sure the compiler can enforce them as limits on the implementation. That is, we are unsure about the exact algorithm to deduce the properties required for type-checking a generic function from a corresponding contract.
My proposal/goal here is to define a type system, or set of constructors which has nice, formally provable limits on what can be constructed. Those constructs should be both easy to grasp _and_ computationally simple. As you say _general_ refinement types are not suited for a compiler focused on speed; however, a subset can very well be.
It has the advantage of making typeclasses first-class, and of enabling a lot of additional functionality without additional fundamental constructs. It is however very antithetical to what someone means when they say Go is minimalistic.