Superfluous Thoughs

While I am still working on Egel, some Facebook thoughts -I now assume known- I threw through Google translate:

"Little big thoughts." Causality is an old discussion in metaphysics. If you have two related events A and B, and they happen one after the other, then we call event A the 'cause' and event B the 'effect'. There is not much to argue with and it is utterly pointless to think deeply about it because we simply cannot see into the future.

So just a few pointless thoughts again because my brain is taking me down strange paths.

The first thought is that we can never prove that the universe is causal. With every two observations that we make, usually the relationship is described mathematically, you end up with a relation R(A,B) and there is simply nothing in that relation R that says that B is physically determined by A or vice versa.

You can make causality very plausible, however, but that gets hairy fast too. One definition I once learned of causality was precisely a mathematical one.

Let's take the Fibonacci numbers, where each number is the sum of the preceding two numbers:

1, 1, 2, 3, 5, 8, 13, 21, ...

A very well-known series, but also one that we call causal because every number depends on its past. And yet you can also turn that definition on its head.

The problem is exactly that when I have the number '13', I know that the two preceding numbers were '5' and '8', given the rules of this small universe. So what tells me that it is not exactly the other way around with this series and that the past depends on the future?

What you really want somewhere is that you have an event of which you can no longer reconstruct the past. There has to be a loss of information for this to happen.

Occam's razor, that again proves nothing because often misunderstood as 'the simplest explanation is true' when scientists mean 'don't make the model more difficult than you need', then gives you an intuitive explanation that events apparently cannot depend on the future because there's not enough information there to construct them.

And that's exactly what physicists don't see, the most fundamental models can be read in two directions. Forward as well as backward, there is no loss of information. (In addition, I can give a trivial intuition that Quantum Mechanics is precisely an indication of retrocausality, the reverse.)

Well, another one in a series of completely superficial thoughts.

Mimalloc Concurrent Reference Counting Back-end

 Right, so I would really want to write a typed Egel.  But I decided I cannot without a better performing back-end, I would just add types to a too slow language. Seems I cannot get rid of rewriting the Egel interpreter for a while yet.

I studied various solutions, hoped for a drop-in concurrent reference counting garbage collector but none exist. So now I am writing an back-end on basis of Daan Leijen's excellent mimalloc which I'll use as the concurrent slab allocator.  The code for the moment does seem to write itself, which is excellent.

I can only hope it'll give me the one order increase in performance I need, otherwise, it'll be all for nought. But I'll do some extensive testing on this (since that needs to be done) and that'll include performance metrics.

Typed Egel

 Below, how Egel could look typed.  But I need something for software engineering in the large too, objects or modules or something. Mulling over that.

def fib: int -> int = [ 0 -> 1 | 1 -> 1 | | N -> N + fib (N - 1) + fib (N - 2) ]

type list[N] = nil | cons N list[N]

def concat: [N] => list[N] -> list[N] -> list[N] = [ nil YY -> YY | (cons X XX) YY -> cons X (concat XX YY) ] class ord N = def compare: N -> N -> int def less: N -> N -> bool instance ord int = def compare: int -> int -> int = int_compare def less: int -> int -> bool = int_less def sort: [ord N] => list[N] -> list[N] = [ nil -> nil | (cons X XX) -> insert X (sort XX) ] where def insert: [ord N] => N -> list[N] = [ X nil -> cons X nil | X (cons Y YY) -> if X < Y then cons X (cons Y YY) else cons Y (insert X YY) ]

Botched Argument, Botched Algorithm

 "Everybody can know but the point is to understand." That's supposedly a quote by Einstein.

I've been discussing the previous post somewhat and been pointed at regular trees and how OCaml does it.

My point is, and I don't know whether it's true either, when you think your type system gives an inductive proof but it is actually giving a botched bisimulation argument, then that leads to botched algorithms and then also to incomprehensible errors. Because you fundamentally misunderstood the solution to the problem, or you didn't even get the problem right.

Indicative of that could be stuff like this: https://github.com/ocaml/ocaml/issues/7726

Then there was a comment on that I didn't propose a solution out of the conundrum. I don't have one but my instinct is to make the bisimulation relation explicit in the typing rules; i.e., the typing rules should include a bisimulation relation Eq: T x T. Because imperative type checkers prove types equal with a proof of existence of a bisimulation relation; I also suspect you cannot do it any other way without getting close but fundamentally getting it wrong.

But I don't know but that's what I want to experiment with. Once I get the egel interpreter sources accepted and compiled again.

Hindley-Milner Inference is Not-That-Good (Kind-Of)

 Egel doesn't have a type checker,  the two major reasons for that was that I a) wanted to explore the operational model and types are overhead on that endeavour, and b) type systems are hard to get right and easy to get wrong. Of course, I am also thinking about what will come after Egel, and that'll be a typed functional language bootstrapped with the interpreter.

But there's a separate reason I didn't want to immediately dive into a typed language, and that is that I find Hindley-Milner based type inferers lacking for programming languages. (If there's such a thing, you can tweak everything into something like a HM-type system description.)

The reason for that is that HM influences towards a particular style of reasoning. Reading T-Lam, from top to bottom, you can see it as an algorithmic description of: when I know this and that entails that then I can conclude that .. That's bottom-up reasoning, often touted as a major accomplishment. Clear, concise, syntax-driven, and all that. Also, good for teaching. In essence, it is the formula for creating an inductive proof.

However, for those who have studied typing of imperative languages ostensibly derived from Algol, you'll notice that that isn't exactly how their type algorithms work. Principally, in an imperative language you usually reason along with what you know: while proving the equivalence of two types you may encounter (other) type equivalences and postulate those as knowns, and -in the end- use those postulates to finish the argument. That's a bisimulation proof.

However, HM-inferencers can be abused to construct bisimulation proofs once you declare the type of a term since it'll happily reason along with user-supplied postulates. But HM style based inferencers often aren't good at creating or deriving bisimilar types per se; which I actually encountered in real-life situations using GHC or Ocaml.

It's awkward to realize that most faculty are teaching students inductive type systems whereas all type algorithms used in industry construct bisimulation proofs. I don't think current HM based inferencers are even that good -though you can tweak everything- for a programming language, and subsequently, I want to implement a functional language with a type system that derives bisimilar types.

Pending Language Changes

 While I am kicking and screaming to get the egel compiler accepted by a c++ compiler that supports modules, I have a number of pending language changes that I want to implement.

1. Import declarations should take qualified identifiers instead of strings.  I've been confronted with modules and been looking at other languages and all of them (Java, Python, Haskell, C++) now default to identifiers instead of strings (file paths) for inclusion of other modules.
   I assume in the end people found out that separating the file system from the module system is the way to go. I'll do that too.
2. Lowercase namespaces.  I once decided on uppercase namespaces since I thought that would distract a bit from the uppercase Prolog-like variables Egel has. But I was wrong, they just look ugly.
   
3. Reintroduce the monadic minus.  The monadic minus was problematic and is problematic. At some point, I decided that if I cannot solve the problem then I won't, and removed all the code regarding it. And then it turned out during Advent of Code that I better not had.
4. Local combinator defintions. I knew it would come to this, but after Advent of Code, I decided that, yes, local combinator definitions introduced with a where are handy and moreover, look pretty.
5. Quotation. I am not too interested in all the dynamic things you can do with quoted combinators but I'll implement these anyway.

That should be about it for all language changes I want for a 0.2 release.

Push C++20 Modules Hard

 A bit of the rationale behind why you really want to push c++20 modules hard, and why I am jumping on the bandwagon early.

In my online discussions, the most notable feature of c++20 modules mentioned is that'll substantially decrease compilation time.  Better performance, that's always nice. But.

Modules allow another, better, way to organize your code.

And despite being a programming language enthusiast which implies that I, like a lot of academics, tend to concentrate on the trivial, that's huge. Software engineering isn't about nullptr, but about developing and maintaining large codebases. Another means to organize code will impact everyone.

And it is no wonder Microsoft is leading this endeavour at the moment. The traditional route is from programming language, to operating system, to application; this will change how OSes are written. Whoever is in front of the curve can gain a potential edge in this manner.

That's why I am early in jumping on the bandwagon in this case. This is actually hard since my M1 makes a substandard development machine. So I'll be buying a windows/Linux machine and returning to whatever environment that can give me modules early.