We add a specific constructor to the type of expressions for injecting
values in expressions.

The advantage are :
- Values can be assumed to be always closed when performing
  substitutions (even though they could contain free variables, but it
  turns out it does not cause any problem in the proofs in
  practice). This means that we no longer need the `Closed` typeclass
  and everything that comes with it (all the reflection-based machinery
  contained in tactics.v is no longer necessary). I have not measured
  anything, but I guess this would have a significant performance
  impact.

- There is only one constructor for values. As a result, the AsVal and
  IntoVal typeclasses are no longer necessary: an expression which is
  a value will always unify with `Val _`, and therefore lemmas can be
  stated using this constructor.

Of course, this means that there are two ways of writing such a thing
as "The pair of integers 1 and 2": Either by using the value
constructor applied to the pair represented as a value, or by using
the expression pair constructor. So we add reduction rules that
transform reduced pair, injection and closure expressions into values.
At first, this seems weird, because of the redundancy. But in fact,
this has some meaning, since the machine migth actually be doing
something to e.g., allocate the pair or the closure.

These additional steps of computation show up in the proofs, and some
additional wp_* tactics need to be called.

Snapshot will re-appear in iris-examples eventually

Marianna Rapoport authored 6 years ago and Ralf Jung committed 6 years ago

- Removing admitted prophecy spec and making prophecy-related examples (coin-flip and atomic-pair-snapshot) work with the new prophecy support in heap_lang
- Adjusting heap_lang tactics for automation of substitution, closedness, etc. to support prophecy syntax
- Adding notation for prophecy syntax

Marianna Rapoport authored 6 years ago and Ralf Jung committed 6 years ago

- Added my version of increment.v for practicing working with logically atomic triples
- Added implementation of coin-flip spec from Turon et al. (POPL'13) with an assumed spec for prophecy variables