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.

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