Coinduction

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 rocq-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

Modules

• lattice.v : complete lattices, monotone functions in such lattices
• tower.v : abstract theory of coinduction via tower induction
• rel.v : tools for the complete lattice of binary relations
• tactics.v : tactics for coinductive predicates/relations
• companion.v : abstract theory of the companion (no longer used)
• tests.v : sanity checks
• all.v : single module to load the library (despite the name, excludes companion and tests)

Meta

• Author(s):
  • Damien Pous (initial)
• Rocq-community maintainer(s):
  • Damien Pous (@damien-pous)
• License: [GNU LGPL3+]
• Rocq namespace: Coinduction
• Related publication(s):
  • Coinduction All the Way Up doi:10.1145/2933575.2934564

Building and installation instructions

The easiest way to install the latest released version of Coinduction is via OPAM:

opam repo add rocq-released https://rocq-prover.org/opam/released
opam install rocq-coinduction

To instead build and install manually, do:

git clone https://github.com/damien-pous/coinduction.git
cd coinduction
make
make install

Compatibility

• versions v1.21 compiles with Rocq 9.0 without transition packages
• versions v1.20 compiles with Coq 8.20 and Rocq 9.0 with transition packages
• 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