We have developed a program for inductive theory formation, called IsaCoSy, which
synthesises conjectures 'bottom-up'from the available constants and free variables. The …

We present a succinct account of dynamic rippling, a technique used to guide the
automation of inductive proofs. This simplifies termination proofs for rippling and hence …

We present the systematic build-up in the Theorema system of the theory of lists. This was
carried out in parallel with the process of synthesis of some sorting algorithms in the same …

The discovery of unknown lemmas, case-splits and other so called eureka steps are
challenging problems for automated theorem proving and have generally been assumed to …

In the context of a scheme based exploration model proposed by Bruno Buchberger, we
investigate the idea of decomposition, applied in the exploration of natural numbers. The …

Lemma speculation has long been considered a promising technique to automate the
discovery of missing lemmas for inductive proofs. This technique involves speculating a …

In this paper, we present a case study of computer supported exploration of the theory of
natural numbers, using a theory exploration model based on knowledge schemes, proposed …

IsaCoSy is a theory formation system for inductive theories. It synthesises conjectures and
uses the ones that can be proved to produce a background theory for a new formalisation …

We construct in a systematic way a collection of properties of lists which are used for
synthesizing automatically several sorting algorithms. This is a novel case study in theory …

IsaCoSy is a theory formation system which synthesises and proves conjectures in order to
produce a background theory for a new formalisation within a proof assistant. To make …