Coinduction Plain and Simple

Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming. Second, it reviews and slightly extends the formalism commonly used for specifying codata. Third, it generalizes the coinduction proof principle, which has been originally specified for the equality predicate only, to other predicates. This generalization makes the coinduction proof principle more intuitive and stresses its closeness with structural induction. The article finally suggests in its conclusion extensions of functional and logic programming with limited and decidable forms of the generalized coinduction proof principle

Infinite Computation, Co-induction and Computational Logic

Abstract. We give an overview of the coinductive logic programming paradigm. We discuss its applications to modeling ω-automata, model checking, verification, non-monotonic reasoning, developing SAT solvers, etc. We also discuss future research directions.