This fixes issue #62.

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

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

Use COFEs only for the recursive domain equation solver

The old name didn't make much sense. Also now we can have
pure_False too.

This way we avoid the env_cbv tactic unfolding string related stuff
that appears in the goal and hypotheses of the proof mode.

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.

That's like what we are doing when instantiating an arrow or wand.

This is more consistent with our current consensus of not using
implication. Also, it allows one to reintroduce the persistent
hypothesis into the spatial context.

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.

Used in iRevert, iClear, iFrame, and for generalizing the IH in
iInduction and iLöb.

Before, it failed when these tactics were invoked with persistent
hypotheses. The new behavior is more convenient when using these
tactics to build other tactics.

This comment mostly addresses issue #34.

There are still some issues:

- For iLöb we can write `iLöb (x1 .. xn) as "IH"` to revert x1 .. xn
  before performing Löb induction. An analogue notation for iInduction
  results in parsing conflicts.
- The names of the induction hypotheses in the Coq intro pattern are
  ignored. Instead, when using `iInduction x as pat "IH"` the induction
  hypotheses are given fresh names starting with "IH". The problem here
  is that the names in the introduction pattern are idents, whereas the
  induction hypotheses are inserted into the proof mode context, and thus
  need to have strings as names.

This closes issue 32.

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.

Following the time anology of later, the step-index 0 corresponds does
not correspond to 'now', but rather to the end of time (i.e. 'last').

This is allowed as long as one of the conjuncts is thrown away (i.e. is a
wildcard _ in the introduction pattern). It corresponds to the principle of
"external choice" in linear logic.

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).

This avoids recompilation of coq_tactics each time an instance is added.

The new implementation ensures that type class arguments are only infered
in the very end. This avoids the need for the inG hack in a0348d7c.