M-structure
M-structure was invented as a result of early discussions within ParGram on the best cross linguistically valid treatment of auxiliaries (see that page for more discussion). Within ParGram the use of m-structure was abandoned fairly quickly (but the analysis was still current at the time the Grammar Writer's Cookbook was written, see pages 60-67), but then abandoned it as too unwieldy (debugging becomes very difficult whenever several different projections from c-structure must be kept track of). Instead, the ParGram grammars now store information needed for language particular morphosyntactic wellformedness checking in a CHECK feature at f-strucutre.
Within theoretical LFG, m-structure took on a life of its own and current work continues to explore uses or ramifications of adding in this further projection, starting with Frank and Zaenen (1998). A workshop was organized on this topic at the LFG00 conference at Berkeley (http://www.stanford.edu/group/cslipublications/cslipublications/LFG/5/lfg00morphwrk.html) and a collection of papers on morphological issues can be found in Sadler and Spencer (2004).
References
Butt, Miriam, Tracy Holloway King, Maria-Eugenia Niño and Frédérique Segond. 1999. _A Grammar Writer's Cookbook._ CSLI Publications. Frank, Anette and Annie Zaenen. 1998. Tense in LFG: Syntax and Morphology. Reprinted in L. Sadler and A. Spencer (eds.), _Projecting Morphology_. CSLI Publications, Sadler, Lousa and Andrew Spencer (eds.). 2004. _Projecting Morphology_. CSLI Publications.