The idea on magic wand is to use it for curried lemmas and use ⊢ for uncurried lemmas.

This reverts commit 2a7755fe because
it is no longer needed after Matthieu Sozeau reverted this change in
Coq 8.6. See also the discussion:

  [Coq-Club] Coq 8.6 typeclasses behavior change

at 11/16/2016 02:14 PM.

In Coq 8.6 type class search is not called recursively on premises
that are not type classes. To that end, we use a hint extern to invoke
an ordinary auto.

The old choice for ★ was a arbitrary: the precedence of the ASCII asterisk *
was fixed at a wrong level in Coq, so we had to pick another symbol. The ★ was
a random choice from a unicode chart.

The new symbol ∗ (as proposed by David Swasey) corresponds better to
conventional practise and matches the symbol we use on paper.

This should make theme asier to parse, "{{{ v, v; l |-> v }}}" looks rather funny.

There are now two proof mode tactics for dealing with modalities:

- `iModIntro` : introduction of a modality
- `iMod pm_trm as (x1 ... xn) "ipat"` : eliminate a modality

The behavior of these tactics can be controlled by instances of the `IntroModal`
and `ElimModal` type class. We have declared instances for later, except 0,
basic updates and fancy updates. The tactic `iMod` is flexible enough that it
can also eliminate an updates around a weakest pre, and so forth.

The corresponding introduction patterns of these tactics are `!>` and `>`.

These tactics replace the tactics `iUpdIntro`, `iUpd` and `iTimeless`.

Source of backwards incompatability: the introduction pattern `!>` is used for
introduction of arbitrary modalities. It used to introduce laters by stripping
of a later of each hypotheses.

And also rename the corresponding proof mode tactics.

rename program_logic.{ownership -> wsat}. It really is about world satisfaction and invariants more than about ownership.

As proposed by JH Jourdan in issue 34.

This also removes the double use of the name 'wp_fork' in both
program_logic/weakestpre and heap_lang/lifting.

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

Also make those for introduction and elimination more symmetric:

  !%   pure introduction         %        pure elimination
  !#   always introduction       #        always elimination
  !>   later introduction        > pat    timeless later elimination
  !==> view shift introduction   ==> pat  view shift elimination

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).

In particular, remove ectx_language.atomic, because it seems unused
expect for a smart constructor for language.atomic.

* Values are considered as atomic expressions (this does not hurt, and
  this makes the proofs of atomicity simpler).

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 →.