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This problem has been reported by Léon Gondelman.

Before, when using, for example wp_alloc, in an expression like:

  ref (ref v)

It would apply `tac_wp_alloc` to the outermost ref, after which it
fails to establish that the argument `ref v` is a value. In this
commit, other evaluation positions will be tried whenever it turn
out that the argument of the construct is not a value. The same
applies to store/cas/...

I have implemented this by making use of the new `IntoVal` class.

This way `IntoLaterNEnvs` is ought to be computed less frequently

The tactic was doing something weird and only once used.

- Get rid of wp_finish, which was a hack.
- Write the wp_ tactics for stateful steps in the same style as
  wp_pure, i.e. by taking the context into account.
- Make use of the context K in wp_pure.

Instead of writing a separate tactic lemma for each pure reduction,
there is a single tactic lemma for performing all of them.

The instances of PureExec can be shared between WP tactics and, e.g.
symbolic execution in the ghost  threadpool

We now first iPoseProof the lemma and instantiate its premises before trying
to search for the sub-term where to apply. As a result, instantiation of the
premises of the applied lemmas happens only once, instead of it being done for
each sub-term as obtained by reshape_expr.

wp_apply often results in an of_val that should be simplified.

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

Also:

- Remove the wp_strip_later hack.
- Let wp_lam, wp_rec, wp_... initiate the proof mode.

I also renamed `iProof` into `iStartProof`, as it is supposed to be
something internal, and not a substitute of Coq's `Proof` command (as
originally intended).

Really, *all* of our files contain proof rules

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.

Robbert Krebbers authored Nov 18, 2016 and Ralf Jung committed Nov 22, 2016

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.

Now we try to avoid adding them unnecessarily, so we don't have to remove them automatically any more.

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 better reflects the name of the bind rule.

I renamed an internal tactic that was previously called wp_bind into
wp_bind_core.

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).

Concretely, when execution of any of the wp_ tactics does not yield
another wp, it will make sure that a view shift is kept. This
behavior was already partially there, but now it is hopefully more
consistent.

We are now using the prefixes Into, From, and Is (the first two are
inspired by the names of some traits in the Rust stdlib), and hopefully
doing that consistenly.