cubicaltt VS HVM

- cubicialtt a programming language based on cubical type theory in which univalence from homotopy type theory isn't an axiom but a theorem

If you’re interested in programming languages specifically, the current state of the art is called Cubical Type Theory. CuTT has lots of flavours and the community hasn’t coalesced around a single design. The paper I personally found easiest to digest was the “ABCFHL” paper, but I’d recommend reading it alongside the original CCHM paper. None of the publications made an ounce of sense to me until after I’d digested Favonia’s YouTube channel, Mortberg’s lecture notes and this other series of lectures from Harper (particularly the final one).

I updated the blog post to include some people in academia who contributed. I've been interacting with Kent Palmer and Sylvester James Gates, Jr. The latter held lectures about the philosophy of mathematics. I've been using work inspired by Vladimir Voevodsky, e.g. cubicaltt (https://github.com/mortberg/cubicaltt), which is also performed by academics.

Reminds me of HVM[0]

[0]https://github.com/HigherOrderCO/HVM

Really interesting to see how new lang concepts and refinements keep popping up this last decade, between Vale, Gleam, Hylo, Austral...

Linear types really opened up lots of ways to improve memory management and compilation improvements.

I have a tangential question that is related to this cool new feature.

Warning: the question I ask comes from a part of my brain that is currently melted due to heavy thinking.

Context: I write a fair amount of Clojure, and in Lisps the code itself is a tree. Just like this F# parallel graph type-checker. In Lisps, one would use Macros to perform compile-time computation to accomplish something like this, I think.

More context: Idris2 allows for first class type-driven development, where the types are passed around and used to formally specify program behavior, even down to the value of a particular definition.

Given that this F# feature enables parallel analysis, wouldn't it make sense to do all of our development in a Lisp-like Trie structure where the types are simply part of the program itself, like in Idris2?

Also related, is this similar to how HVM works with their "Interaction nets"?

https://github.com/HigherOrderCO/HVM

https://www.idris-lang.org/

https://clojure.org/

I'm afraid I don't even understand what the difference between code, data, and types are anymore... it used to make sense, but these new languages have dissolved those boundaries in my mind, and I am not sure how to build it back up again.

Impressive presentation but I find two things missing in particular:

* GRIN [1] - arguably a breakthrough in FP compilation; there are several implementation based on this

* HVM [2] - parallel optimal reduction. The results are very impressive.

[1] https://link.springer.com/chapter/10.1007/3-540-63237-9_19

[2] https://github.com/HigherOrderCO/HVM

Purity has nothing to do with memoization. Haskell's semantics never "rewrite under a lambda" (unlike, e.g. HVM). Calling (\_ -> e) () twice will (modulo optimizations) always perform the computation in e twice.

The most recent exploration of this, that I'm aware of is HVM (another intermediate language / runtime), although this one is not actually based on the lambda calculus, but on the interaction calculus.

Then, actually unrelated but worth mentioning: HVM. Finally, something new on the functional front that isn't dependent types!

If you are into functional PL, how about https://github.com/HigherOrderCO/HVM? You could experiment if you could schedule that on a GPU?

In the interest of seeking ways of optimizing my code, I stumbled upon http://www.rntz.net/datafun/ as a means to do incremental computations of fixpoints while avoiding redundant work. And also the idea of automatic parallelism achieved by using Interaction Nets as a model of computation https://github.com/HigherOrderCO/HVM.