  The ``classical BRST construction'' as developed by
Batalin-Fradkin-Vilkovisky is a homological construction for the reduction of
the Poisson algebra $P = C^\infty (W)$ of smooth functions on a Poisson
manifold $W$ by the ideal $I$ of functions which vanish on a constraint locus.
This ideal is called first class if $I$ is closed under the Poisson bracket;
geometers refer to the constraint locus as coisotropic. The physicists' model
is crucially a differential Poisson algebra extension of a Poisson algebra $P$;
its differential contains a piece which reinvented the Koszul complex for the
ideal $I$ and a piece which looks like the Cartan-Chevalley-Eilenberg
differential.
  The present paper is concerned purely with the homological (Poisson)
algebraic structures, using the notion of ``model'' from rational homotopy
theory and the techniques of homological perturbation theory to establish some
of the basic results explaining the mathematical existence of the classical
BRST-BFV construction. Although the usual treatment of BFV is basis dependent
(individual constraints) and nominally finite dimensional, I take care to avoid
assumptions of finite dimensionality and work more invariantly in terms of the
ideal. In particular, the techniques are applied to the `irregular' case (the
ideal is not generated by a regular sequence of constraints), although the
geometric interpretation is less complete.
