  We define a general class of dependent type theories, encompassing
Martin-L\"of's intuitionistic type theories and variants and extensions. The
primary aim is pragmatic: to unify and organise their study, allowing results
and constructions to be given in reasonable generality, rather than just for
specific theories. Compared to other approaches, our definition stays closer to
the direct or naive reading of syntax, yielding the traditional presentations
of specific theories as closely as possible.
  Specifically, we give three main definitions: raw type theories, a minimal
setup for discussing dependently typed derivability; acceptable type theories,
including extra conditions ensuring well-behavedness; and well-presented type
theories, generalising how in traditional presentations, the well-behavedness
of a type theory is established step by step as the type theory is built up.
Following these, we show that various fundamental fitness-for-purpose
metatheorems hold in this generality.
  Much of the present work has been formalised in the proof assistant Coq.
