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

The WP construction now takes an invariant on states as a parameter
(part of the irisG class) and no longer builds in the authoritative
ownership of the entire state. When instantiating WP with a concrete
language on can choose its state invariant. For example, for heap_lang
we directly use `auth (gmap loc (frac * dec_agree val))`, and avoid
the indirection through invariants entirely.

As a result, we no longer have to carry `heap_ctx` around.

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

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.

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

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.

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

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.