Adjoints of coarguments behave inconsistently

[dham]

Consider the following code (Firedrake syntax, but the issue is UFL):

from firedrake import *
m = UnitIntervalMesh(2)
V = FunctionSpace(m, "CG", 1)
ca = Coargument(V.dual(), 0)

ca is really the identity operator in $V^{\ast}\rightarrow V^{\ast}$ (equivalently it is a form in $V^{*}\times V \rightarrow R$) and it can arise in adjoint calculations when a variational problem has a pre-assembled cofunction in its RHS. The issue arises when taking the adjoint of ca. Note:

In [10]: adjoint(ca)
Out[10]: Argument(WithGeometry(FunctionSpace(<firedrake.mesh.MeshTopology object at 0x106be17f0>, FiniteElement('Lagrange', interval, 1), name=None), Mesh(VectorElement(FiniteElement('Lagrange', interval, 1), dim=1), 0)), 0, None)

In [12]: adjoint(2*ca)
Out[12]: FormSum([2*Argument(WithGeometry(FunctionSpace(<firedrake.mesh.MeshTopology object at 0x106be17f0>, FiniteElement('Lagrange', interval, 1), name=None), Mesh(VectorElement(FiniteElement('Lagrange', interval, 1), dim=1), 0)), 0, None)])

In effect, the adjoint of ca is treated as an unknown Function in V but the adjoint of a scalar multiple of ca is treated as a form in $V^{**}\times V^{*}\rightarrow R$ (equivalently an operator in $V\rightarrow V$). These spaces are mathematically isomorphic, but as a matter of type the former is a UFL expression while the latter is a form. When taking the adjoint of a form we expect to get back another form, so the latter would be preferable. This currently causes some special casing in Firedrake.