Definition talk:Parsing Sequence

Shouldn't a parsing sequence be more accurately a rooted tree (maybe more conveniently thought of as a tree upside down, somewhat like the roots of a tree, culminating in a single WFF) of which each branch is finite (but in general needn't be finitely branching, so not finite; I've read up on theories just today concerning infinitary first-order logic, allowing dis- and conjunctions over any index set)? It seems like this is what's meant. Also, in my digital version of Keisler/Robbin (dated 2006, version from 1987) the term parsing sequence appears in $\S 1.1$; this may be due to version mismatch, though. Same for $\S 2$.

While I noted in reading Keisler/Robbin that the parsing sequence as they define it is sensible, I still put for myself the task of one day covering infinitary logics, for which the "parsing tree" concept is actually necessary (since clearly otherwise one runs into trouble). --Lord_Farin (talk) 18:29, 9 November 2012 (UTC)

The orientation of a tree does not matter IMO so referring to such a tree as "upside down" confuses the issue - as an analogy it's stretching it a little. Definition:Rooted Tree has a definition here, and, yes of course needs a refactoring job.

I agree to the extent that I have an intuitive feel for what you are saying - and suggest the two approaches can be married together by presenting and exploiting the (ultimately fairly trivial) fact that the nodes of a finite tree can be presented in a linear manner and therefore a parsing sequence can be presented linearly. The practical upshot of this is that the order of operations may not be critical - doing the branches in a different order should not matter.

So yes, my intuition agrees with this approach. --prime mover (talk) 22:52, 9 November 2012 (UTC)