The general idea is to first import/export modules which are further
than the current one, and then import/export modules which are close
dependencies.

This commit tries to use the same order of imports for every file, and
describes the convention in ProofGuide.md. There is one exception,
where we do not follow said convention: in program_logic/weakestpre.v,
using that order would break printing of texan triples (??).

This is in preparation for coq/coq#9274.

New IntoAcc typeclass to decouple creating and elliminating accessors; ElimInv supports both with and without Hclose

This is to be used on top of stdpp's 4b5d254e.

Thanks to Janno.

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

Robbert Krebbers authored 8 years ago and Ralf Jung committed 8 years ago

We do this by introducing a type class UpClose with notation ↑.

The reason for this change is as follows: since `nclose : namespace
→ coPset` is declared as a coercion, the notation `nclose N ⊆ E` was
pretty printed as `N ⊆ E`. However, `N ⊆ E` could not be typechecked
because type checking goes from left to right, and as such would look
for an instance `SubsetEq namespace`, which causes the right hand side
to be ill-typed.

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.

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.

Initial proof by Jan-Oliver Kaiser, adapted by Robbert Krebbers.

Before this commit, given "HP" : P and "H" : P -★ Q with Q persistent, one
could write:

  iSpecialize ("H" with "#HP")

to eliminate the wand in "H" while keeping the resource "HP". The lemma:

  own_valid : own γ x ⊢ ✓ x

was the prototypical example where this pattern (using the #) was used.

However, the pattern was too limited. For example, given "H" : P₁ -★ P₂ -★ Q",
one could not write iSpecialize ("H" with "#HP₁") because P₂ -★ Q is not
persistent, even when Q is.

So, instead, this commit introduces the following tactic:

  iSpecialize pm_trm as #

which allows one to eliminate implications and wands while being able to use
all hypotheses to prove the premises, as well as being able to use all
hypotheses to prove the resulting goal.

In the case of iDestruct, we now check whether all branches of the introduction
pattern start with an `#` (moving the hypothesis to the persistent context) or
`%` (moving the hypothesis to the pure Coq context). If this is the case, we
allow one to use all hypotheses for proving the premises, as well as for proving
the resulting goal.

By using the global ghost maps instead of our own ones.

This makes stuff more uniform and also removes the need for the [inGFs]
type class. Instead, there is now a type class [subG Σ1 Σ2] which expresses
that a list of functors [Σ1] is contained in [Σ2].

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).