Can we build everything from money (minted tokens)?
Can we build private computing systems, which are ἄπαξ χέων, which means "poured only once"?
As explained first in
Buliga, Marius (2018): Chemlambda strings. figshare. Journal contribution. https://doi.org/10.6084/m9.figshare.5751318.v1
then in
M. Buliga, Artificial life properties of directed interaction combinators vs. chemlambda. https://arxiv.org/abs/2005.06060
it is possible to express a graph rewrite as a chemical reaction of the form
(LEFT PATTERN) + (TOKEN_1) + (ENZYME) = (RIGHT PATTERN) + (TOKEN_2) + (ENZYME)
Here the tokens are small graphs from a pre-defined family. They are used to have a conservative chemical reaction. In the presence of tokens the graph rewrite appears as a permutation of the half-edges of the graph pattern.
As an illustration see this hand made animation of the 9-quine
We can see the tokens as a form of money bricks which are used for universal computation. Verbatim, each program is a graph "made of money" and the (decentralized) execution of the program is a process of money (tokens) exchanges.
As this is one of the chemlambda projects
the relation with chemlambda comes from the problem of naming links in chemlambda graphs (molecules). Minted tokens are a solution for this problem.
We treat in a unitary way a large family of asynchronous graph rewriting automata, by encoding a graph rewrite as a permutation of the ends of the edges of a graph. A local rewrite, i.e. one which involves a small number of nodes and edges, is then encoded as a small permutation.
By varying the permutation we can vary the graph rewrite. As an example, there are 14400 variants of the iconic beta rewrite: https://mbuliga.github.io/hapax/betarand.html
- Chemlambda and hapax: https://mbuliga.github.io/hapax/chemlambda-and-hapax.html
explains the mol notation and the encoding of graph rewrites as permutations; discusses differences from chemlambda
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Ackermann(2,2) with hapax: https://mbuliga.github.io/hapax/hapax-ack.html
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9_quine with hapax: https://mbuliga.github.io/hapax/hapax-9quine.html
two pages which use the js library
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a presentation of the general ideas, towards the end relevant to hapax
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the folder chemlambda: https://github.com/mbuliga/hapax/tree/master/chemlambda
contains the essentials of chemlambda-v2, which is used as an example with hapax