  The exchange part of energy density of the linear Dirac--Hartree--Fock (DHF)
model in symmetric nuclear matter is evaluated in a parameter--free closed form
and expressed as density functional. After the rearranging terms the
relativistic mean-field approach with density-dependent couplings may be
recovered with density dependence coming from the Fock exchange. The formalism
developed, is then extended to the nonlinear DHF approximation with field
self-couplings allowed. The nonlinear self--interactions result in essential
density dependence (medium modification) of effective couplings that are
decoupled from the Fock ones.
