Pronominal argument hypothesis
What she and Ken Hale termed "non-configurational" languages are those which have a number of features that set them apart from the more typical "configurational" languages. In particular, non-configurational languages have free phrase order (inaccurately called "free word order"), where the various phrases in a sentence can come in any order rather than simple SOV, SVO, VSO, or the like. Supporting this free phrase order is the extensive use of what appear to be agreement affixes on the verb, indexing at least the S and O arguments if not others like instrumentals, locatives, etc. There are a couple of other things but I'm going to ignore them for the moment.
The Pronominal Argument Hypothesis (PAH) says that instead of having independent NPs which are the arguments of the verb, the agreement affixes in the verb are actually the real arguments. These are thus not agreement affixes, but actual pronouns. Furthermore, the sentence can consist of just a verb and no other words, and there are no invisible constituents like pro which take the place of arguments.
The PAH has profound implications for languages like Tlingit, and for theoretical linguistics as well. What it means for Tlingit is that the verb is no longer a thing formed by morphological rules and processes, but is instead constructed by syntax. That is, in Tlingit the verb morphology is the syntax, aside from the other stuff that floats around the core of a sentence.
I'm only in the early phases of exploring how the PAH can be applied to Tlingit, so I don't have anything interesting to report yet. But I'll put up some examples in the near future, after I've finished with my literature survey.
Cable, Seth. "Covert A-scrambling in Tlingit". In Lyon, John (ed.) Papers for the 43rd International Conference on Salish and Neighboring Languages. UBC Working Papers in Linguistics. Vancouver: University of British Columbia.
Carnie, Andrew; Harley, Heidi; & Willie, MaryAnn. 2003. Formal approaches to function in grammar: In honor of Eloise Jelinek. Vol. 62 in Linguistik Aktuell/Linguistics Today. Amsterdam: John Benjamins. ISBN 1-58811-348-5.
Jelinek, Eloise. 1984. "Empty categories, case, and configurationality". Natural Language and Linguistic Theory 2.1:39-76.
Jelinek, Eloise; & Demers, Richard. 1994. "Predicates and pronominal arguments in Straits Salish". Language 70.4:697-736.
LeSourd, Philip. "Problems for the pronominal argument hypothesis in Maliseet-Passamaquoddy". Language 82.3:486-514.