More about chemical transactions

There is much more about these chemical transactions and their proofs. First is that transactions are partially independent on the molecules. The blockchain may be useful only for having a distributed database of transactions and proofs, available for further use. But there’s more.

Think about this database as one of valid computations, which can then be reused in any combination or degree of parallelism. Then, that’s the field of several competitions.

The same transaction can have several proofs, shorter or longer. It can have big left pattern therefore costly to use it in another computation. Maybe a transaction goes too long and therefore it is not useful to use in combination with others.

When there is a molecule to reduce, the application of a transaction means:
– identify a subgraph isomorphic with the left pattern and pick one such subgraph
– apply the transaction to this particular subgraph (which is equivalent with: reduce only that subgraph of the molecule, and freeze the rest of the molecule, but do it in one step because the sequence of reductions is already pre-computed)

Now, which is more convenient, to reduce the molecule by using the random algorithm and the available graph rewrites, or to use some transactions which fit, which is fast (as concerns step 2) but costly (as concerns step 1), moreover it may be that there is a transaction with shorter proof for that particular molecule, which mixes parts of several available precomputed transactions.

Therefore the addition of transactions and their proofs (needed to be able to validate them) into the database should be made in such a way which profit from this competition.

If I see the reduction of a molecule (which may be itself distributed) as a service then besides the competition for making available the most useful transactions with the shortest proofs, there is another competition between brute force reducing it and using the available transactions, with all the time costs they need.

If well designed, these competitions should lead to the emergence of clusters of useful transactions (call such a cluster a “chemlisp”) and also to the emergence of better strategies for reducing molecules.

This will lead to more and more complex computations which are feasible with this system and probably fast enough they will become very hard to understand by a human mind, or even by using IT tools on a limited part of the users of the system.

Chemical transactions and their proofs

By definition a transaction is either a rewrite from the list of
accepted rewrites (say of chemlambda) or a composition of two
transaction which match. A transaction has a left and a right pattern
and a proof (which is the transaction expressed as a cascade of
accepted rewrites).

When you reduce a molecule, the output is a proof of a transaction.
The transaction proof itself is more important than the molecule from
the start. Indeed, if you think that the transaction proof looks like
a list

rm leftpattern1
add rightpattern1

where leftpattern1 is a list of lines of a mol file, same for the rightpattern1,

then you can deduce from the transaction proof only the following:
– the minimal initial molecule needed to apply this transaction, call
it the left pattern of the transaction
– the minimal final molecule appearing after the transaction, call it
the right pattern of the transaction

and therefore any transaction has:
– a left pattern
– a right pattern
– a proof made of a chain of other transaction which match (the right
pattern of transaction N contains the left pattern of transaction N+1)

It would be useful to think in term of transactions and their proofs
as the basic objects, not molecules.