A library for doing proofs by (enhanced) coinduction.
It is based on the notion of 'companion' from the paper Coinduction All the Way Up. Damien Pous. In Proc. LICS, 2016.
It contains:
- enhancements of the coinductive proof method
- second order coinduction reasonning about enhancements
- parametrised coinduction, as proposed by Hur et al.
- powerful symmetry arguments
- compatibility and respectfulness
Examples on how to use the library may be found in the associated coq-coinduction-examples package:
- a formalisation of Hur et al's toy example on divergence
- a formalisation of Rutten's stream calculus
- a formalisation of Milner's calculus of communicating systems (CCS)
- a formalisation of Automata and regular expression equivalence
lattice.v: complete lattices, monotone functions in such latticestower.v: abstract theory of coinduction via tower inductionrel.v: tools for the complete lattice of binary relationstactics.v: tactics for coinductive predicates/relationscompanion.v: abstract theory of the companion (no longer used)tests.v: sanity checksall.v: single module to load the library (despite the name, excludes companion and tests)
- Author(s):
- Damien Pous (initial)
- Coq-community maintainer(s):
- Damien Pous (@damien-pous)
- License: [GNU LGPL3+]
- Coq namespace:
Coinduction - Related publication(s):
The easiest way to install the latest released version of Coinduction is via OPAM:
opam repo add coq-released https://coq.inria.fr/opam/released
opam install coq-coinductionTo instead build and install manually, do:
git clone https://github.com/damien-pous/coinduction.git
cd coinduction
make
make install- versions v1.6, v1.7 and v1.8 all compile with Coq 8.16.1, 8.17.1 and 8.18.0
- v1.7 is feature equivalent but not backward-compatible with v1.6
- the master branch of this git repository should compile with Coq master