The power of parameterization in coinductive proof

Abstract

Coinduction is one of the most basic concepts in computer science. It is therefore surprising that the commonly-known lattice-theoretic accounts of the principles underlying coinductive proofs are lacking in two key respects: they do not support compositional reasoning (i.e. breaking proofs into separate pieces that can be developed in isolation), and they do not support incremental reasoning (i.e. developing proofs interactively by starting from the goal and generalizing the coinduction hypothesis repeatedly as necessary).