Do-notation for chains of transformations

 A particular idiom kept appearing in Egel since I started using `|>` to form chains of transformations, I kept introducing an abstraction to set the chain up with an unknown initial argument.

I pondered on it for a while and introduced `do` syntactic sugar into Egel. The semantics of `(do f |> g |> h) x` is `x |> f |> g |> h` for example. That allows one to abstract from superfluous variables.

It works.  Below, an example taken from Advent of Code '22.

# Advent of Code (AoC) - day 5, task 2

import "prelude.eg"
import "os.ego"
import "regex.ego"

using System
using OS
using List

def input =
    let L = read_line stdin in if eof stdin then {} else {L | input}

val digits = Regex::compile "[0-9]+"

def parse_crates = 
    do map (do unpack |> chunks 4 |> map (nth 1)) 
    |> transpose |> map (filter ((/=) ' '))
def parse_moves = 
    map (do Regex::matches digits |> map to_int 
         |> [{M,F,T} -> (M, F, T)])

def move =
    [(CC,MM) -> foldl 
        [CC (N,F,T) ->
            CC |> insert (T - 1) 
                   (take N (nth (F - 1) CC) ++ nth (T - 1) CC) 
               |> insert (F - 1) 
                   (drop N (nth (F - 1) CC))]
        CC MM ]

def main =
    input |> break ((==) "") 
          |> [(CC,MM) -> (parse_crates (init CC), parse_moves (tail MM))]
          |> move |> map head |> pack

  

I am not sold on the donation, the abstraction also works as a strong visual reminder that a function is being expressed. But maybe it takes some getting used to. Also, it's a nice pun on Haskell monads and a reference to an old thought of mine that all you should need is function composition to chain actions, and that later became applicatives.

That billion dollar mistake. In Haskell...?

This is a short observation on 'the billion-dollar mistake' of Hoare, implementing null pointers in Algol W back in 1965. Dereferencing a null pointer usually causes a runtime error immediately terminating the program, and lots of programs crashed due to that.

This mistake is used ad nauseam to plead for safer languages, which made sense at the time since crashing programs had become the default. What is often not told is that runtime exceptions are standard and must be carefully handled in almost all languages. Let's take Haskell, one of the ostensibly claimed safest languages in the world.

Runtime exceptions can occur due to a variety of reasons, applying a partial function outside its domain is one of them. Let's try 'head []' in Haskell.

λ 
> head []
No instance for (Show a0)
arising from a use of ‘show_M340108553800667339831401’
The type variable ‘a0’ is ambiguous
Note: there are several potential instances:
instance Show a => Show (Const a b)
-- Defined in ‘Control.Applicative’
instance Show a => Show (ZipList a)
-- Defined in ‘Control.Applicative’
instance Show GeneralCategory -- Defined in ‘Data.Char’
...plus 44 others
In the expression:
show_M340108553800667339831401 (let e_1 = head [] in e_1)
In an equation for ‘e_134010855380066733983140134010855380066733983140111’:
e_134010855380066733983140134010855380066733983140111
= show_M340108553800667339831401 (let e_1 = head [] in e_1)
In the expression:
(let
e_134010855380066733983140134010855380066733983140111
= show_M340108553800667339831401 (let ... in e_1)
in e_134010855380066733983140134010855380066733983140111) ::
String_M340108553800667339831401

That didn't go too well, Haskell cannot figure out the particular type instance for an empty list. Okay, let's add an assertion.

λ 
> let x = head ([]::[Int]) in x
*Exception: Prelude.head: empty list

And boom, there you have it. Haskell terminates with a runtime exception. In fact, any Haskell program can have this potential 'bomb' in it. 

What, in the abstract, is the difference between 'nullptr.x' and 'head []'? Both terminate the program due to a runtime exception.

I fully agree that Haskell is a safer language than most imperative ones. But that 'billion dollar mistake'? That is in Haskell too.

Musings on Bell

"Why is a raven like a writing-desk?" So, I've officially joined the ranks of online science cranks with some musings on Bell's inequalities. I am actually pretty much a firm believer in his result, but it was a thought I wanted to expand somewhat further.

I've been right and wrong in the past. I was using a linear transformation from digital circuits to CNF in SAT solving and was pointing out that years before other people noticed that existed, turns out it was a rediscovery of Tseitin mid-sixties; I pointed out that all you need for embedding an impure program into a pure language is a form of composition, so the natural choice for that would be function composition over monads, and Haskell programmers are using applicatives instead. Then a host of small and big views on compiler construction, often as right as they were wrong.

So, the QM thing started off with the notion 'what if superposition is a form of oscillation?' Turns out that doesn't matter much and you need to prove Bell 'wrong' in both cases. A pretty tall order. Especially since this is way out of my field.

But I decided to write it down anyway, maybe it goes somewhere:
https://twitter.com/egel_language/status/1550579321160491013

That QM entanglement thing

While I slowly change a few lines in the Egel interpreter source code from time to time, I am thinking more about QM these days. For whatever reason. So, my braindead musings in all public light for people to laugh at below.

I couldn't help but think: QM is exactly what you get for describing 'spinning' or 'oscillating' phenomena with probability distributions.

The metaphor I have in my mind: Envision you're on a nice tropical island with a lighthouse. The light the lighthouse casts on the island is a spinning phenomenon. 50% of the time it faces you, 50% of the time it doesn't. The 'state', or rather 'behaviour', of that lighthouse can be described with a ket, and letting your hermitian loose on it will confirm that it's a 50/50 chance that you'll 'see' the light passing in front of you.

Now suppose you're on an island with two lighthouses, One lighthouse faces you 70% of the time, another 40% of the time. (The analogy with QM breaks here a bit but fix the behaviour of the lighthouses to fit your fantasy or understanding of QM.)

So when you make measurements of one lighthouse you'll know the probability distribution of the other lighthouse, without any 'spooky action at a distance.' I just don't see it.

ADDENDUM: These are indeed musings on Bell's inequalities.  I agree with all that. But my idea is: Bell showed that there are no hidden variables, there cannot be a definite state satisfying the inequalities. What he didn't show was that there cannot be an 'oscillating' state (resulting in related probability distributions.)

ADDENDUM2: Dumbing it further down. Consider a fair coin, a ket faithfully describes: this is a system that once observed will have a 50/50 chance of returning heads or tails. Bell says there are no hidden variables in there. True, the system's behaviour, not state, is completely and faithfully described. Because there is no definite state until you flip it.

ADDENDUM3: The basic observation is that the difference between a superposition and an 'oscillating' state isn't that big. But where Bell says, reject local+real, I would say, local+real makes more sense so just accept that what you're studying is 'oscillating'. To make that stick is of course another issue.

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) ]