It’s been a little while since I gave an update about Dana, so here it is.

There has been very little code progress in the last week. Instead, because of the self-embedding issues I talked about last time, I have been exploring the use of a combinator calculus as an intermediate stage for typechecking. I’m on to something, though nothing is terribly concrete yet. The combinator basis I’m using is:

Sxyz = xz(yz) Ktxy = x -- with the constraint (y:t) Bxyz = x(yz) Cxyz = xzy Itx = x -- with the constraint (x:t)

Along with primitives for Pi, Arrow (which is always expressible as Pi, but this keeps term size down), and Type.

The point of the constraints is to provide type annotations. I added a type annotation to every combinator which “erases” a lambda (rather than just pushing it downward) during factorization, because when a lambda is erased so is its annotation, so this puts it back.

My goal is for the typechecker not to use any supply of unique names.

Checking is not totally straightforward. Notice how terms like S have no unique most general type; they would have to take some type arguments to do that. So my current lead is that the type of a combinator term t is either a “real” type, or it’s a function which takes a term x and returns the type of t x (or another such function, etc.). This algorithm will be partial; i.e. there will be cases where I require an argument to have an actual type rather than a function. This is because attempting the “total” algorithm is undecidable, so it’s partial anyway.

The other thing I’ve been thinking about is a simple, composable “RTS language”, which does explicit memory management in some form, in which I could implement a garbage collector, etc. This has not been as fruitful as my combinator explorations. I’ve been looking at various forms of linear lambda calculus, which has been neat and enlightening — for example, there is a sense in which all computable functions are differentiable using LLC, which I might blog about soon — but unfortunately it does not look very promising as an RTS language. Any suggestions?

And today I started thinking about what I will need to write my higher-level languages, in particular PureHaskell (Haskell98 sans IO and FFI). It’s pretty annoying that I can’t use any Haskell libraries which use tricky GHC extensions, because those kill my bootstrap (i.e., my PureHaskell compiler needs to be in PureHaskell). There are a lot of libraries that use extensions. For once I wish the flagship compiler weren’t so capable!