Add IdempP instances for min_nat and max_nat.

Move additional numbers related lemmas and instances into the numbers file.

Gregory Malecha authored 5 years ago and Robbert Krebbers committed 5 years ago

- remove "odd" comment
- move atomic triples to bi_scope

Tej Chajed authored 5 years ago and Ralf Jung committed 5 years ago

Add array_copy_to (copy in-place to destination array) and array_clone
(copy to a freshly allocated array). The heap_lang spec and proof for
array_copy_to are inspired by
https://gitlab.mpi-sws.org/iris/lambda-rust/blob/3b4ae69fa3be1344245245bf05e5e80e790e064d/theories/lang/lib/memcpy.v.

Fixes #293.

The general idea is to first import/export modules which are further
than the current one, and then import/export modules which are close
dependencies.

This commit tries to use the same order of imports for every file, and
describes the convention in ProofGuide.md. There is one exception,
where we do not follow said convention: in program_logic/weakestpre.v,
using that order would break printing of texan triples (??).

This also gets rid of [val_for_compare]-normalization; instead we introduce a
[LitErased] literal that is suited for use by erasure theorems.

This is the name used by x86 (CMPXCHG) and LLVM.  Also reorder the result (value
first, boolean second) for consistency with LLVM, because why not.

Used the following script:

sed '
s/\bCofeMor/OfeMor/g;
s/\-c>/\-d>/g;
s/\bcFunctor/oFunctor/g;
s/\bCFunctor/OFunctor/g;
s/\b\%CF/\%OF/g;
s/\bconstCF/constOF/g;
s/\bidCF/idOF/g
s/\bdiscreteC/discreteO/g;
s/\bleibnizC/leibnizO/g;
s/\bunitC/unitO/g;
s/\bprodC/prodO/g;
s/\bsumC/sumO/g;
s/\bboolC/boolO/g;
s/\bnatC/natO/g;
s/\bpositiveC/positiveO/g;
s/\bNC/NO/g;
s/\bZC/ZO/g;
s/\boptionC/optionO/g;
s/\blaterC/laterO/g;
s/\bofe\_fun/discrete\_fun/g;
s/\bdiscrete\_funC/discrete\_funO/g;
s/\bofe\_morC/ofe\_morO/g;
s/\bsigC/sigO/g;
s/\buPredC/uPredO/g;
s/\bcsumC/csumO/g;
s/\bagreeC/agreeO/g;
s/\bauthC/authO/g;
s/\bnamespace_mapC/namespace\_mapO/g;
s/\bcmra\_ofeC/cmra\_ofeO/g;
s/\bucmra\_ofeC/ucmra\_ofeO/g;
s/\bexclC/exclO/g;
s/\bgmapC/gmapO/g;
s/\blistC/listO/g;
s/\bvecC/vecO/g;
s/\bgsetC/gsetO/g;
s/\bgset\_disjC/gset\_disjO/g;
s/\bcoPsetC/coPsetO/g;
s/\bgmultisetC/gmultisetO/g;
s/\bufracC/ufracO/g
s/\bfracC/fracO/g;
s/\bvalidityC/validityO/g;
s/\bbi\_ofeC/bi\_ofeO/g;
s/\bsbi\_ofeC/sbi\_ofeO/g;
s/\bmonPredC/monPredO/g;
s/\bstateC/stateO/g;
s/\bvalC/valO/g;
s/\bexprC/exprO/g;
s/\blocC/locO/g;
' -i $(find theories -name "*.v")

This MR is a follow up on the renamings performed (implicitly) as part of
!215. This MR makes the following changes:

- `auth_both_frac_valid` and `auth_both_valid` are now of the same shape
  as `auth_both_frac_validN` and `auth_both_validN`. That is, both are
  now biimplications.
- The left-to-right  direction of `auth_both_frac_valid` and
  `auth_both_valid` only holds in case the camera is discrete. The
  right-to-left versions for non-discrete cameras are prefixed `_2`, the
  convention that we use throughout the development.
- Change the direction of lemmas like `auth_frag_valid` and
  `auth_auth_valid` so that it's consistent with the other lemmas. I.e.
  make sure that the ◯ and ● are always on the LHS of the biimplication.