A few years ago, I wrote a compiler for FRACTRAN written in Haskell[0] (translated from Common Lisp) with an associated blog post[1]. Using the tagless-final style you can write a simple program like this:

  sumTo :: FracComp repr => Integer -> [repr [Rational]]
  sumTo n = [addi "c" 0, addi "n" n, while (jge "n" 0) [adds "c" "n", subi "n" 1]]

And the compiler would output this:

  λ> runAssembler (sumTo 10)                      -- Program length: 31
  Right [847425747 % 2,13 % 3,19 % 13,11 % 3,11 % 29,31 % 11,41 % 31,23
  % 11,23 % 47,2279 % 23,59 % 301,59 % 41,67 % 413,329 % 67,61 % 59,73 %
  61,83 % 73,71 % 61,71 % 97,445 % 71,707 % 89,103 % 5353,103 % 83,109 %
  5459,5141 % 109,107 % 103,113 % 749,113 % 19,131 % 113,29 % 131,127 %
  113]
  λ> runAsm (sumTo 10)
  [(Prime 97,55),(Prime 107,1)]

[0] https://github.com/siraben/hasktran

[1] https://siraben.dev/2020/02/26/translating_cl.html

See also: "Building Fizzbuzz in Fractran from the Bottom Up (2016)" [0]

I'll repost my comment from that thread:

>For some reason this makes me imagine an alternate history sci-fi universe where Pythagoras (famous for his love of fractions) invents FRACTRAN. Then Archimedes builds a mechanical computer to execute those programs, and one of the successors of Alexander The Great puts the computer to use in warfare and conquers the world. Science is accelerated so that nuclear physics are invented by the time Jesus is born...

[0] https://news.ycombinator.com/item?id=28448283

I played a lot of the original civ as a kid. I'd be super disappointed if I didn't get railroads before 0. rush pyramids, democracy, tons of tiny self supporting towns. That game didn't really offer a way to convert other cities and towns sort of invasion. so I'd inevitably turn evil and conquer the world. Good times.

In principle Minsky Machines are very similar to abacus algorithms. They do seem in the reach of ancient mathematics.

Reducing them to FRACTRAN requires dealing with some VERY big numbers for not a lot of benefit. You’re probably dealing with those on an abacus anyway…

Who really knows what was in the Library of Alexandria before it was burned for the 6th or 7th time.

Probably a bunch of recipes

But you could only read them after you unscrolled 50 feet of story about how much they enjoyed the buffet platters at Bel's temple as a kid before watching the sacrifices

A FRACTRAN interpreter in FRACTRAN, in 24 fractions:

https://codegolf.stackexchange.com/a/246682/15469

Thanks, the fact that FRACTRAN didnt bootstrap its own interpreter was the reason I didnt use the language seriously for programming!

related: FRACTRAN to brainfuck translator

https://codegolf.stackexchange.com/questions/5210/convert-fr...

I think the world has yet to feel the weight of this great man's contributions. the monstrous moonshines and the freewill theorem seem mind blowing and not very well known at all.

Project Euler challenge involving Fractran: https://projecteuler.net/problem=308

Related:

Building Fizzbuzz in Fractran from the Bottom Up (2016) - https://news.ycombinator.com/item?id=28448283 - Sept 2021 (5 comments)

Open Problems in Communication and Computation (1987) [pdf] - https://news.ycombinator.com/item?id=26074413 - Feb 2021 (2 comments)

Remembering John Conway's FRACTRAN - https://news.ycombinator.com/item?id=23142232 - May 2020 (14 comments)

Building FizzBuzz in Fractran from the Bottom Up - https://news.ycombinator.com/item?id=22866303 - April 2020 (1 comment)

FRACTRAN - https://news.ycombinator.com/item?id=14202367 - April 2017 (8 comments)

Building Fizzbuzz in Fractran from the bottom up - https://news.ycombinator.com/item?id=11894141 - June 2016 (3 comments)

In FRACTRAN, every program is a list of functions - https://news.ycombinator.com/item?id=10091053 - Aug 2015 (1 comment)

FRACTRAN - the esoteric programming language invented by John H Conway - https://news.ycombinator.com/item?id=3119937 - Oct 2011 (1 comment)

TIL John Conway died during the COVID pandemic. I'm as shocked as someone who just discovered John Lennon was killed. :(

Probably the biggest celebrity death of the pandemic, IMO. I believe it was on the nyt front page.

I miss raganwald, I loved it when their posts and comments were blowing up HN.

I only discovered the site recently, but it seems he still posts: raganwald.com

He mentions a CD-ROM version of Society of Mind (https://web.media.mit.edu/~minsky/Voyager.html). I had never heard of it. Does anyone know if the video content from that CD-ROM is available online?

There is a link what appears to be part one in the article.

  https://www.youtube.com/watch?v=-Hx8RixhoOM

Oh I missed that. Thank you so much!

Has anyone made attempts at writing FRACTRAN programs which would calculate `78 * 5^(x - 1)` and `2^x`?

Why?

Those are the necessary pre and post processing steps that you need to compute outside of the FRACTRAN system for the fibonacci example from the article.

If you could do those steps the entire process would be self contained, which you should be able to if the claim of yielding all possible computations is correct.

(actually, it is log2(x) that would need to be implemented and not 2^x, but my point remains).

One reasonable design equivalent to FRACTRAN is to do away with the divisibility checks and store an array of counts of prime factors. Then you could put the input in the 5s slot and read the output from the 2s slot without computing the values of these expressions.

Very long article, and IMO it doesn't justify the "surprisingly deep" claim. Disappointing. Can I have my time back?

tl;dr: a 'usage' of fractran is that fratcran programs are collatz-like sequences, thus, the behaviour of collatz-like sequences is undecidable.