ConstantValue and Parameter

[mscroggs]

As discussed at SysGenX meeting, we should:

• Rename ConstantValue to AbstractParameter. This is the base class for parameters (previously constants) without a domain
• Add Parameter class that inherits from AbstractParameter to represent a parameter with an unknown value
• Leave Constant as it is: representing a constant over a domain

[jorgensd]

Is Firedrake (or FEniCSx for that matter) using ConstantValue?
As discussed earlier, Constant with an associated domain is motivated by differentiation (i.e. the derivative of a Constant-value maps to the real-element).

[dham]

Yes, we are using ConstantValue. As soon as you start doing multiple domain calculations, having to associate a domain with a constant is a pain. We concede the differentiation point. For the moment, differentiation WRT to a Parameter won't be possible. In theory in the future it could be made so but that is a much bigger change.

[jorgensd]

I think AbstractParameter should have a dtype as input, as it could be:
Float32,float64,complex64, complex128 etc, which should change the representation of it.

[dham]

Note that enabling differentiation with respect to a Parameter implies having arguments (or equivalent) which are parameters, and those somehow have to have correct parallel semantics. This requires some serious design work.