Without assuming arbitrary restrictions on grammar notation at the outset, 'Bare Grammars' aim to provide the most straightforward definitions of the constructions present in human languages, together with a compositional semantics. A simple generative approach is presented which induces a natural algebraic notion of structure, with the surprising result that not only classical syntactic relations (like c-command) but also certain morphological relations concerning identity of particular morphemes (e.g. case markers) are properly structural. Formal models of case marking, verb voice,...