Algorithmic chemistry and the chemical concrete machine

I just discovered the work of Fontana and Buss on Algorithmic Chemistry. The ideas appear to be very close to what I am trying to do with the chemical concrete machine (independently, because of my relative ignorance of past research in the field, but I’m improving my knowledge day by day).

I shall jump directly to differences. At first sight there are a lot of ideas which look the same, mainly that lambda terms are molecules and chemical reactions are related to reduction in lambda calculus.

The main differences are:

• for the chemical concrete machine, molecules are not just any abstract list, but a particular one, expressed as certain graphs,
• I don’t use lambda calculus, but a more powerful version, graphic lambda calculus, which works directly with such “molecules” (i.e. graphs in $GRAPH$), being free from any linear writing convention or variable names,
• chemical reactions between such molecules do not correspond to lambda abstraction or to the application. Instead, the chemical reactions correspond to reduction moves, mainly to the graphic beta move,
• molecules are not functions, because of the lack of extensionality (eta reduction), which is good, because it makes the calculus much more concrete than with extensionality (but this is an argument which needs more details, that’s for later). For now I shall just mention my belief that extensionality and types are an unnecessary relics of thought (controversial, I know) and one of the main stumbling blocks on the path of reconciling syntactic with semantic is keeping types and extensionality (the short argument against these is that there’s nothing like types or extensionality  in any biological brain, and probably is just another manifestation of the cartesian disease).

But otherwise my proposal of the chemical concrete machine is clearly in the field of algorithmic chemistry!

5 thoughts on “Algorithmic chemistry and the chemical concrete machine”

1. YMorita says:

I always looking forward to seeing your study.

Something may wrong in your paper “Graphic lambda calculus”.
http://arxiv.org/abs/1305.5786

In page 2 Definition 2.1, you mention about ε-gate, but there is no diagram about it.

In page 13, you mention about combinator K, but it is deferent from traditional definition K = “λx.λy.x” .
In a diagram about combinator K, I think a direction of left-side arrow in the λ-gate is reversed.

Thank you.

1. Thank you for the comment. I shall make the corrections. Indeed, the epsilon gate should be in definition 2.1 and there is an extra “y” in the expression of K in page 13, expression of K. I have not yet identified the place where there is an arrow reversed.

2. I remembered now: the article Graphic lambda calculus is concentrated on the lambda calculus and knots parts. There is a section on emergent algebras, but in order to have the whole picture, the other articles have to be read. But this is no excuse for deleting the epsilon gate from definition 2.1, my bad.

2. YMorita says:

OK, Thank you!