# Chemical actors

UPDATE: Clearly needed a mix of the ActorScript of Carl Hewitt with GLC and chemlambda. Will follow in the months to come!

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Thinking out loud about a variant of the actor model (chapter 3 here), which uses graphic lambda calculus or the chemical concrete machine. The goal is to arrive to a good definition of an Artificial Chemical Connectome.

Have remarks? Happy to read them!

A chemical actor is the following structure:

• a graph $A \in GRAPH$  (or a molecule $A \in MOLECULES$)
• with a unique ID name $ID$
• with a numbering (tagging)  of a (possibly empty) part of it’s free arrows
• with a behaviour, to be specified further.

A communication is:

• a graph  $B \in GRAPH$  (or a molecule)
• with a source ID and a target ID
• with a part of free arrows tagged with tags compatible (i.e. the same) with the ones from the graph from the source ID
• with another part of free arrows tags with tags compatible with the ones from the graph from the target ID

The actor target ID receives a communication from the actor source ID and it becomes:

At this point the actor which has target ID exhibit the following behaviour:

• performs one, several, or in a given order, etc of graph rewrites (only the + unidirectional moves)  which involve at least an arrow between A and B
• following a given algorithm, splits into a new actor and a communication B’ which has as target arrows the one from the lower part of the previous figure (but with another target ID)
• or creates a new actor by using only (-) moves

Remark: the numbers $n, m$ could be uniformly bounded to 2, or 4, or 6, according to user’s wishes. Take a look at the Ackermann machine, for inspiration.