GitLab

This approach is originally by Robbert

There are certainly more places this is useful, but let's start with this simple test

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.

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

There is no way to infer the cmra A, so we make it explicit.

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.

And also rename the corresponding proof mode tactics.

This allows us to factor out properties about connectives that
commute with the big operators.

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].

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 way type class inference is not invokved when used in tactics
like iPvs while not having to write an @.

(Idea suggested by Ralf.)

This way, it won't pick arbitrary (and possibly wrong!) inG instances
when multiple ones are available. We achieve this by declaring:

  Hint Mode inG - - +

So that type class inference only succeeds when the type of the ghost
variable does not include any evars.

This required me to make some minor changes throughout the whole
development making some types explicit.

This is more consistent with the proofmode, where we also call it pure.

Fixes issue #20.

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 →.

It used to be: (P ={E}=> Q) := (True ⊢ (P → |={E}=> Q))
Now it is: (P ={E}=> Q) := (P ⊢ |={E}=> Q)