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meta.yml
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---
fullname: Bits
shortname: bits
organization: coq-community
community: true
action: true
coqdoc: false
doi: 10.1007/978-3-319-29604-3_2
synopsis: >-
Coq bit vector library
description: |-
A formalization of bitset operations in Coq with a corresponding
axiomatization and extraction to OCaml native integers.
publications:
- pub_url: https://hal.archives-ouvertes.fr/hal-01251943/document
pub_title: "From Sets to Bits in Coq"
pub_doi: 10.1007/978-3-319-29604-3_2
- pub_url: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/12/coqasm.pdf
pub_title: "Coq: The world's best macro assembler?"
pub_doi: 10.1145/2505879.2505897
authors:
- name: Andrew Kennedy
email: [email protected]
initial: true
- name: Arthur Blot
email: [email protected]
initial: true
- name: Pierre-Évariste Dagand
email: [email protected]
initial: true
maintainers:
- name: Anton Trunov
nickname: anton-trunov
opam-file-maintainer: [email protected]
opam-file-version: dev
license:
fullname: Apache License 2.0
identifier: Apache-2.0
file: LICENSE
supported_coq_versions:
text: 8.16 or later (use releases for other Coq versions)
opam: '{>= "8.16"}'
tested_coq_opam_versions:
- version: '2.0.0-coq-8.16'
repo: 'mathcomp/mathcomp'
- version: '2.0.0-coq-8.18'
repo: 'mathcomp/mathcomp'
- version: '2.1.0-coq-8.16'
repo: 'mathcomp/mathcomp'
- version: '2.1.0-coq-8.18'
repo: 'mathcomp/mathcomp'
- version: '2.2.0-coq-8.16'
repo: 'mathcomp/mathcomp'
- version: '2.2.0-coq-8.19'
repo: 'mathcomp/mathcomp'
- version: '2.2.0-coq-dev'
repo: 'mathcomp/mathcomp'
- version: 'coq-8.19'
repo: 'mathcomp/mathcomp-dev'
- version: 'coq-dev'
repo: 'mathcomp/mathcomp-dev'
dependencies:
- opam:
name: ocamlbuild
description: OCamlbuild
- opam:
name: coq-mathcomp-algebra
version: '{>= "2.0"}'
description: |-
[MathComp](https://math-comp.github.io) 2.0 or later (`algebra` suffices)
namespace: Bits
keywords:
- name: bit arithmetic
- name: bitset
- name: bit vector
- name: extraction
categories:
- name: Computer Science/Data Types and Data Structures
documentation: |-
## Origins
This library has been extracted from Andrew Kennedy et al. ['x86proved' fork][xprovedkennedy].
This link presently redirects to https://github.com/nbenton/x86proved repository.
The main paper for this project is [Coq: The world’s best macro assembler?][coqasm].
## Using the library
To import the main library, do:
```coq
From Bits Require Import bits.
```
An axiomatic interface supporting efficient extraction to OCaml can be
loaded with:
```coq
From Bits Require Import extraction.axioms8. (* or 16 or 32 *)
```
## Organization
This library, briefly described in the paper [From Sets to Bits in Coq][bitstosets],
helps to model operations on bitsets. It's a formalization of
logical and arithmetic operations on bit vectors. A bit vector is defined as an
SSReflect tuple of bits, i.e. a list of booleans of fixed (word) size.
The key abstractions offered by this library are as follows:
- `BITS n : Type` - vector of `n` bits
- `getBit bs k` - test the `k`-th bit of `bs` bit vector
- `andB xs ys` - bitwise "and"
- `orB xs ys` - bitwise "or"
- `xorB xs ys` - bitwise "xor"
- `invB xs` - bitwise negation
- `shrB xs k` - right shift by `k` bits
- `shlB xs k` - left shift by `k` bits
The library characterizes the interactions between these elementary operations
and provides embeddings to and from the additive group ℤ/(2ⁿ)ℤ.
The overall structure of the code is as follows:
- [src/ssrextra](src/ssrextra): complements to the [Mathcomp][mathcomp] library
- [src/spec](src/spec): specification of bit vectors
- [src/extraction](src/extraction): axiomatic interface to OCaml, for extraction
For a specific formalization developed in a file `A.v`, one will find its
associated properties in the file `A/properties.v`. For example, bit-level
operations are defined in [src/spec/operations.v](src/spec/operations.v),
therefore their properties can be found in
[src/spec/operations/properties.v](src/spec/operations/properties.v).
## Verification axioms
Axioms can be verified for 8-bit and 16-bit (using only extracted code) using
the following command:
```shell
make verify
```
For 8bit, the verification process should finish in few seconds. However
for 16-bit, depending on your computer speed, it could take more than 6
hours.
[bitstosets]: https://hal.archives-ouvertes.fr/hal-01251943/document
[coqasm]: https://www.microsoft.com/en-us/research/wp-content/uploads/2016/12/coqasm.pdf
[xprovedkennedy]: https://x86proved.codeplex.com/SourceControl/network/forks/andrewjkennedy/x86proved/latest#src/bits.v
[mathcomp]: https://github.com/math-comp/math-comp
---