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https://github.com/distributedcomponents/infseqext
A Coq library for reasoning (co)inductively on infinite sequences using LTL-like modal operators
https://github.com/distributedcomponents/infseqext
coq coq-library ltl modal-logic proof temporal-logic
Last synced: 21 days ago
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A Coq library for reasoning (co)inductively on infinite sequences using LTL-like modal operators
- Host: GitHub
- URL: https://github.com/distributedcomponents/infseqext
- Owner: DistributedComponents
- Created: 2016-11-20T20:58:15.000Z (about 8 years ago)
- Default Branch: master
- Last Pushed: 2023-01-07T12:58:58.000Z (almost 2 years ago)
- Last Synced: 2023-08-11T00:17:39.885Z (over 1 year ago)
- Topics: coq, coq-library, ltl, modal-logic, proof, temporal-logic
- Language: Coq
- Homepage:
- Size: 88.9 KB
- Stars: 13
- Watchers: 3
- Forks: 4
- Open Issues: 1
-
Metadata Files:
- Readme: README.md
Awesome Lists containing this project
README
# InfSeqExt
[![Docker CI][docker-action-shield]][docker-action-link]
[docker-action-shield]: https://github.com/DistributedComponents/InfSeqExt/workflows/Docker%20CI/badge.svg?branch=master
[docker-action-link]: https://github.com/DistributedComponents/InfSeqExt/actions?query=workflow:"Docker%20CI"
Coq library for reasoning inductively and coinductively on infinite sequences,
using modal operators similar to those in linear temporal logic (LTL).
## Meta
- Author(s):
- Yuxin Deng (initial)
- Jean-Francois Monin (initial)
- Karl Palmskog
- Ryan Doenges
- Compatible Coq versions: 8.9 or later
- Additional dependencies: none
- Coq namespace: `InfSeqExt`
- Related publication(s): none
## Building and installation instructions
The easiest way to install InfSeqExt is via
[OPAM](https://opam.ocaml.org/doc/Install.html):
```shell
opam repo add coq-extra-dev https://coq.inria.fr/opam/extra-dev
opam install coq-inf-seq-ext
```
To instead build and install manually, do:
```shell
git clone https://github.com/DistributedComponents/InfSeqExt.git
cd InfSeqExt
make # or make -j
make install
```
## Documentation
InfSeqExt is based on an [earlier library][infseq-paper] by Deng and Monin.
It is intended as a more comprehensive alternative to [Streams][streams-link]
in the Coq standard library. In particular, InfSeqExt provides machinery commonly
used when reasoning about temporal properties of system execution traces, and
follows the modal operator [name conventions][spin-ltl-link] used in the Spin model checker.
### Files
- `infseq.v`: main definitions and results
- coinductive definition of infinite sequences
- definitions and notations for modal operators and connectors
- basic modal operators: `now`, `next`, `consecutive`, `always1`, `always`, `weak_until`, `until`, `release`, `eventually`
- composite modal operators: `inf_often`, `continuously`
- modal connectors: `impl_tl` (`->_`), `and_tl` (`/\_`), `or_tl` (`\/_`), `not_tl` (`~_`)
- lemmas about modal operators and connectors
- tactics
- `map.v`: corecursive definitions of the `map` and `zip` functions for use on infinite sequences, and related lemmas
- `exteq.v`: coinductive definition of extensional equality (`exteq`) for infinite sequences, and related lemmas
- `subseq.v`: coinductive definitions of infinite subsequences and related lemmas
- `classical.v`: lemmas about modal operators and connectors when assuming classical logic (excluded middle)
### Related libraries
InfSeqExt has some overlap with the less exhaustive [CTLTCTL][ctltctl-link]
and [LTL][ltl-link] Coq contributions, which provide similar machinery.
In contrast to CTLTCTL and LTL, InfSeqExt does not provide a definition
of traces following some labeled reduction relation, nor an explicit
notion of time. Fairness is also left up to library users to define.
[infseq-paper]: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5198503
[streams-link]: https://coq.inria.fr/library/Coq.Lists.Streams.html
[spin-ltl-link]: http://spinroot.com/spin/Man/ltl.html
[ctltctl-link]: https://github.com/coq-contribs/ctltctl
[ltl-link]: https://github.com/coq-contribs/ltl