Poly1305-Equivalence

Steps to machine-check the proofs:

# The clone might take a while since it pulls vale and hacl* as well
git clone --recursive https://github.com/jaybosamiya/poly1305-equivalence
cd poly1305-equivalence

# Apply minor patch to squash some trivial warnings and errors
git apply --directory=hacl-star hacl-star-0001-Squash-some-errors-warnings.patch

# Apply minor patch to de-anonymize a function, to make it possible to prove stuff
git apply --directory=hacl-star hacl-star-0002-de-anonymize-function.patch

# Run fstar on all fst files in current directory, using hints
find -maxdepth 1 -type f -name '*.fst' -exec fstar --use_hints {} \;

Expected output:

Verified module: Poly1305.Equivalence (253 milliseconds)
All verification conditions discharged successfully
Verified module: TagEquivalence (135 milliseconds)
All verification conditions discharged successfully
Verified module: MsgEquivalence (32622 milliseconds)
All verification conditions discharged successfully
Verified module: UsefulLemmas (1152 milliseconds)
All verification conditions discharged successfully
Verified module: Axioms (924 milliseconds)
All verification conditions discharged successfully
Verified module: KeyEquivalence (947 milliseconds)
All verification conditions discharged successfully
Verified module: ThirdSpec (3913 milliseconds)
All verification conditions discharged successfully

FStar Version:

F* 0.9.5.0
platform=Linux_x86_64
compiler=OCaml 4.05.0
date=2017-08-23T11:19:43-07:00
commit=fa9b1fd

HACL* Commit: 3b72903e + minor patch + minor patch

Vale Commit: 5aab381

Notes:

1. To simplify fstar finding everything, I have simply symlinked all relevant files from the Vale and HACL* directories into the root directory of this repository. I will hopefully clean that up at some point.
2. Imho, the proof should be read starting from Poly1305.Equivalence.fst, since it provides the overall goal of the proof, as well as links into lemmas that are used to achieve it.
3. A bunch of the *_semantics lemmas in Axioms.fst exist only because HACL* decides not to reveal the implementations for IntSeq and IntTypes. I've manually checked them a bunch of times to ensure that they match with the implementation, but it'd be nice to have a better way to have them be machine-checked against the implementation.
4. I am using ocp-indent for indentation, and overall, it works out great! However, for certain trivial edge cases, it leads to weird indentations (nothing unreadable, but it troubles me to see the aesthetics be spoilt). Either fstar --indent must be improved (it kills all my newlines, which I dislike), or ocp-indent must be modified to support fstar's differences from OCaml. Just felt like this should be written down somewhere :P