We consider a cyclic approach to inductive reasoning in the setting of first-order logic with
inductive definitions. We present a proof system for this language in which proofs are …

Inductive definitions are the most natural means by which to represent many families of
structures occurring in mathematics and computer science, and their corresponding …

Induction plays a key role in reasoning in many areas of mathematics and computer science.
A central problem in the automation of proof by induction is the non-analytic nature of …

This article formalizes and compares two different styles of reasoning with inductively
defined predicates, each style being encapsulated by a corresponding sequent calculus …

We describe the design and implementation of an automated theorem prover realising a
fully general notion of cyclic proof. Our tool, called Cyclist, is able to construct proofs obeying …

Inductive definitions and rule inductions are two fundamental reasoning tools in logic and
computer science. When inductive definitions involve binders, then Barendregt's variable …

We show how codatatypes can be employed to produce compact, high-level proofs of key
results in logic: the soundness and completeness of proof systems for variations of first-order …

Cyclic proof provides a style of proof for logics with inductive (and coinductive) definitions, in
which proofs are cyclic graphs representing a form of argument by infinite descent. It is …

The eld of automated deduction has reached a state of maturity and seriousness, in which
the hope for nding a proof method which is simple, uniform, and successful in general has …

We describe rippling: a tactic for the heuristic control of the key part of proofs by
mathematical induction. This tactic significantly reduces the search for a proof of a wide …