An interesting discussion (?) started in the comments of this John Baez G+ post concerns differences between “model of computation” and “programming language” denominations (in that post, in particular, for Petri nets).
I reproduce here what I think that are relevant bits for this discussion and later, after possibly several updates, I shall try to write something useful by using these bits.
1. Turing machine and lambda calculus are both models of computation, but lambda calculus is also a programming language and Turing machine is not.
2. Zachariah Hargis makes the point of comparing this model of computation vs programming language distinction as related to the one made by Leibniz between calculus ratiocinator and lingua characteristica. (Among other references, note to self to explore further.)
3. Chemical reaction networks (CRNs) is one fundamental ingredient of molecular computing, no matter what formalization of CRNs is used. Don’t believe that all “computational part” of a CRN is a Petri net (because it is often very important which are concretely the molecules and reactions involved in the CRN, not only the abstract number of species and reaction rates between those).
4. Petri nets, as used in chemistry, are a tool for getting quantitative information from CRNs, once the CRNs are designed by other means. Petri nets might be useful for thinking about CRNs, but not necessary for designing CRNs.
5. CRNs which are designed by using, or embody in some sense lambda calculus is a much more interesting path towards a “programming language”, and a classical one (Fontana and Buss Algorithmic chemistry), than the more studied engineering style implementation of imperative programming and by force copy-paste of TM thinking into bio computing.
6. Among the specifications for a “programming language for chemistry” are the following:
- (a) geometrical (in particular no use of currying, along more obvious features as being parallel, asynchronous, the latter being achievable already by many well known, non exotic programming languages),
- (b) purely syntactic (in particular no names management, nor input-output signalling),
- (c) (maybe an aspect of (b), but not sure) no use of evaluation in computation (strategy).
(The chemical concrete machine satisfies these requirements and moreover it contains lambda calculus, thus showing that such a “language” is possible. However, the chemical concrete machine is based on a made-up, artificial chemistry, thus it provides only a proof of principle for the existence of such a “language”. Or is it? Biochemists help is needed to identify, or search for real chemical reactions which could be used for implementing the chemical concrete machine in reality.)
7. The problem of tacit axioms in history of the Church-Turing thesis might be especially relevant for biochemists, and it could also be mentioned as an argument in favour of making a distinction between “model of computation” and “programming language”: any model of computation uses some tacit axioms, while a programming language does not (only at the semantic level concerning making (human) sense about the results and ways of functioning of the programming language such tacit axioms are used in this case). For biochemists, to not use such tacit axioms is a must when they try to find scientifically valid explanations. CS does well when ignoring these, in most of the cases.