HVM rediscovers Kauffman’ Arrow and GLC actors

To me it looks like this, see page 6 of this pdf.

Back in 2013, Louis Kauffman invented the Arrow node in the Graphic Lambda Calculus formalism, exactly for such a need. He used Mathematica for the first attempts to automatically reduce GLC.

Here are the extended slides of the ALIFE talk, and you see at page 44 this: ” represents an edge from node a to node b. This means that we can translate our rule driven formalism to graphical representation by just stripping the from each edge rep.”.

At page 46:

See History of Chemlambda for details.

In the first article about molecular computers you see the COMB rewrites. They are part of any chemlambda or chemSKI chemistries.

Moreover, in arXiv:1312.4333, joint with Kauffman we proposed GLC actors, where we describe actors as colors and discuss about what is now called locked or lock free… Of course that this is an obvious problem which has many possible solutions. This has to be a solved problem from the start (not in the middle, wtf??) of any project which claims it does local graphical reductions.

In the old, awk based chemlambda-gui, I implemented these actors as colors and performed simulations to see how the things behave. Colored mol files appear as “mola”.

For example two Ackermann functions sharing a part of their input look like this.

Conclusion: I understood recently that things (some) mathematicians find trivial and obvious to consider are SF for (some) programmers (sorry about that but I’m full of it!). Chemlambda probably contains ideas so advanced just because we mathematicians we think you programmers already and since a long time solved these obvious problems.

I wrote about this project previously. While initially I appreciated it, now…