[WIP] Implement styles in a top-to-bottom approach

[AFeuerpfeil]

I am currently working on getting the algorithms to run for user-defined AbstractMPS types.
To this end, I will go through the algorithms (currently focussing on IDMRG and VUMPS) and implement the Style interface for the highest-level functions, which are called in these algorithms.

Examples for these are calc_galerkin, expectation_value, environments, recalculate!, (A)C(2)_hamiltonian, transfer_leftenv!, transfer_rightenv!.

[github-actions]

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[codecov]

Codecov Report

❌ Patch coverage is 83.33333% with 1 line in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/operators/lazysum.jl	50.00%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/algorithms/groundstate/find_groundstate.jl	76.92% <100.00%> (ø)
src/algorithms/groundstate/idmrg.jl	100.00% <100.00%> (ø)
src/algorithms/groundstate/vumps.jl	85.91% <100.00%> (+0.20%)	⬆️
src/operators/lazysum.jl	70.37% <50.00%> (-1.63%)	⬇️

... and 1 file with indirect coverage changes

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[lkdvos]

This looks great, I really like that we can relax the input types.

[AFeuerpfeil]

It definitely feels like it is going in the right direction.
In my current fork, it is not reducing the size of the code but is also not adding too much boilerplate.
One question I came up with is the following:
Do we at all want to restrict input types to AbstractMPS, AbstractMPO, AbstractMPSEnvironments or just leave that completely open to the user?
And if we want to restrict it, then at which level, only at the topmost function, which dispatches onto the function defined on Styles or in all levels?

An example, how the restriction only for the topmost function in the call tree looks like, is

function environments(above::AbstractMPS, op::AbstractMPO, below::AbstractMPS)
    return environments(GeometryStyle(above, op, below), OperatorStyle(op), above, op, below)
end

and then

function environments(::InfiniteChainStyle, ::HamiltonianStyle, above, op, below)
 ...
end