GitLab

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

Using this new definition we can express being contractive using a
Proper. This has the following advantages:

- It makes it easier to state that a function with multiple arguments
  is contractive (in all or some arguments).
- A solve_contractive tactic can be implemented by extending the
  solve_proper tactic.

No longer `put box_own_prop γ P` in the invariant, it is persistent.

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

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.

We need instances like EqDecision and Countable for it. We could
redeclare those instead, though.

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.

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.

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