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[Anders Logg <logg@xxxxxxxxx>]

If we should add notation for boundary conditions to UFL, then I think
it must also be supported through the UFC interface so that the
assembler may assemble the correct matrix/vector directly (without
zeroing out entries in a separate step).

Regarding the notation, maybe it should be a constraint on the
function spaces. Take for example Poisson with u = g on the boundary:

  Find u in H^1_g : a(v, u) = L(v) for all v in H^1_0

The boundary conditions are part of the test and trial spaces
(subscripts g and 0 on H^1). We could do something like

  V = FunctionSpace("Lagrange", "triangle", 1) # test space
  W = FunctionSpace("Lagrange", "triangle", 1) # trial space
  V.restrict(g)
  W.restrict(0)

  a = dot(grad(v), grad(u))*dx
  L = v*f*dx

-- 
Anders

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