Clocks, guns, propagators and distributors

Playing a bit with chemlambda, let’s define:

  • multipliers
  • propagators
  • two types of distributors

described in the first figure.

circle_1

The blue arrows are compositions of moves from chemlambda. For instance, referring to  the picture from above,  a graph (or molecule) A is a multiplier if there is a definite finite sequence of moves in chemlambda which transforms the LHS of the first row into the RHS of the first row, and so on.

For example:

  • any combinator (molecule from chemlambda) is a multiplier; I proved this for the BCKW system in this post,
  • the bit is a propagator
  • the application node is a distributor of the first kind, because of the first DIST move in chemlambda
  • the abstraction node is a distributor of the second kind, because of the second DIST move in chemlambda.

Starting from those, we can build a lot of others.

If A \rightarrow  is  a multiplier and \rightarrow B \rightarrow  is a propagator then A \rightarrow B \rightarrow is a multiplier. That’s easy.

From a multiplier and a distributor of the first kind we can make a propagator, look:

circle_3

From a distributor of the second kind we can make a multiplier.

circle_5

We can make as well guns, which shoot graphs, like the guns from the Game of Life.  Here are two examples:

circle_2

We can make clocks (which are also shooting like guns):

circle_4

Funny! Possibilities are endless.

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