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This implements issue #3.

This generalization is surprisingly easy in Iris 3.0, so I could not
resist not doing it :).

I do not know why we have to split the rewrite here, but it seems we do.

This is probably due to a bug in the rewrite of ssreflect 1.6 which has
been fixed in ssreflect master.

I cannot reproduce the error of the CI builder on my machine with the
same version of Coq (8.5pl2).

And make it Typeclasses Opaque to ensure that we indeed do not do
so using the proof mode.

Use it to prove that tests/barrier_client and tests/heap_lang are adequate.

This commit features:

- A simpler model. The recursive domain equation no longer involves a triple
  containing invariants, physical state and ghost state, but just ghost state.
  Invariants and physical state are encoded using (higher-order) ghost state.

- (Primitive) view shifts are formalized in the logic and all properties about
  it are proven in the logic instead of the model. Instead, the core logic
  features only a notion of raw view shifts which internalizing performing frame
  preserving updates.

- A better behaved notion of mask changing view shifts. In particular, we no
  longer have side-conditions on transitivity of view shifts, and we have a
  rule for introduction of mask changing view shifts |={E1,E2}=> P with
  E2 ⊆ E1 which allows to postpone performing a view shift.

- The weakest precondition connective is formalized in the logic using Banach's
  fixpoint. All properties about the connective are proven in the logic instead
  of directly in the model.

- Adequacy is proven in the logic and uses a primitive form of adequacy for
  uPred that only involves raw views shifts and laters.

Some remarks:

- I have removed binary view shifts. I did not see a way to describe all rules
  of the new mask changing view shifts using those.
- There is no longer the need for the notion of "frame shifting assertions" and
  these are thus removed. The rules for Hoare triples are thus also stated in
  terms of primitive view shifts.

TODO:

- Maybe rename primitive view shift into something more sensible
- Figure out a way to deal with closed proofs (see the commented out stuff in
  tests/heap_lang and tests/barrier_client).

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

We git this from monotonicity now.

That way, we do not have useless type annotations of the form
"v : language.val heap_lang" cluttering about any goal.

Note, that we could decide to eta expand everywhere (as we do for ∀
and ∃), and use the notation "WP e {{ Q }}" for "wp e ⊤ (λ _, Q)".

Thanks to Amin Timany for the suggestion.

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.

For consistency's sake.

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

The performance gain seems neglectable, unfortunatelly...

* Put level of the triple at 20, so we can write things like
  ▷ {{ P }} e @ E {{ Φ }} without parentheses.
* Use high levels for P, e and Φ.
* Allow @ E to be omitted in case E = ⊤.

This avoids ambiguity with P and Q that we were using before for both
uPreds/iProps and indexed uPreds/iProps.

It is doing much more than just dealing with ∈, it solves all kinds
of goals involving set operations (including ≡ and ⊆).

simplify_equality        => simplify_eq
simplify_equality'       => simplify_eq/=
simplify_map_equality    => simplify_map_eq
simplify_map_equality'   => simplify_map_eq/=
simplify_option_equality => simplify_option_eq
simplify_list_equality   => simplify_list_eq
f_equal'                 => f_equal/=

The /= suffixes (meaning: do simpl) are inspired by ssreflect.

Also, make our redefinition of done more robust under different
orders of Importing modules.

Also do some minor clean up.

This way we avoid many one-off indexes and no longer need special cases for
index 0 in many definitions. For example, the definition of the distance
relation on option and excl has become much easier. Also, uPreds no longer need
to hold at index 0.

In order to make this change possible, we had to change the notions of
"contractive functions" and "chains" slightly.

Thanks to Aleš Bizjak and Amin Timany for suggesting this change and to help
with the proofs.