This patch was created using

  find -name *.v | xargs -L 1 awk -i inplace '{from = 0} /^From/{ from = 1; ever_from = 1} { if (from == 0 && seen == 0 && ever_from == 1) { print "Set Default Proof Using \"Type*\"."; seen = 1 } }1 '

and some minor manual editing

Use COFEs only for the recursive domain equation solver

This allows us to factor out properties about connectives that
commute with the big operators.

This requirement was useful in Iris 2.0: in order to ensure that ownership of
the physical state was timeless, we required the ghost CMRA to have a timeless
unit. To avoid having additional type class parameters, or having to extend the
algebraic hierarchy, we required the units of any CMRA to be timeless.

In Iris 3.0, this issue no longer applies: ownership of the physical state is
ghost ownership in the global CMRA, whose unit is always timeless.

Thanks to Jeehoon Kang for spotting this unnecessary requirement.

This is more consistent with the definition of the extension order, which
is also defined in terms of an existential.

be the same as .

This is a fairly intrusive change, but at least makes notations more
consistent, and often shorter because fewer parentheses are needed. Note
that viewshifts already had the same precedence as →.

Based on an idea and WIP commits of J-H. Jourdan: the core of a CMRA
A is now a partial function A → option A.

TODO: define sum CMRA
TODO: remove one shot CMRA and define it in terms of sum

- Make the carrier argument of the constructors for the canonical structures
  cofeT and cmraT explicit. This way we make sure the carrier is properly
  exposed, instead of some alias of the carrier.
- Make derived constructions (such as discreteC and discreteR) notations
  instead of definitions. This is yet again to make sure that the carrier is
  properly exposed.
- Turn DRA into a canonical structure (it used to be a type class).

This fixes some issues, notably it fixes some broken rewrites in algebra/sts
and it makes canonical structures work properly with dec_agree.

The only drawback is that we have to restrict iprod to finite types,
but that is fine.

Thanks to Amin Timany for the suggestion.

So, only use the type class for contractive functors.

Add both non-expansive and contractive functors, and bundle them for the general Iris instance as well as the global functor construction

This allows us to move the \later in the user-defined functor to any place we want.
In particular, we can now have "\later (iProp -> iProp)" in the ghost CMRA.

Since functor instances are just used as combinators, there is really
no need for functors that are not contractive.

This cleans up some ad-hoc stuff and prepares for a generalization
of saved propositions.

It now also contains a non-expansiveness proof.

I have simplified the following CMRA axioms:

  cmra_unit_preservingN n x y : x ≼{n} y → unit x ≼{n} unit y;
  cmra_op_minus n x y : x ≼{n} y → x ⋅ y ⩪ x ≡{n}≡ y;

By dropping off the step-index, so into:

  cmra_unit_preservingN x y : x ≼ y → unit x ≼ unit y;
  cmra_op_minus x y : x ≼ y → x ⋅ y ⩪ x ≡ y;

The old axioms can be derived.

The performance gain seems neglectable, unfortunatelly...

This way it behaves better for discrete CMRAs.