  We develop Lagrangian Floer Theory for exact, graded, immersed Lagrangians
with clean self-intersection using Seidel's setup. A positivity assumption on
the index of the self intersection points is imposed to rule out certain (but
not all) disc bubbles. This allows the Lagrangians to be included in the exact
Fukaya category. We also study quasi-isomorphism of Lagrangians under certain
exact deformations which are not Hamiltonian.
