Abstract. We consider formal provabil-ity with structural induction and related proof principles in the $\lambda$-calculus presented with first-0rder abstract syntax over one-sorted variable names. As well as sum-marising and elaborating on earlier, for-mally verified proofs (in $\mathrm

objects. Although PRMs are significantly more expressive than standard models, such as Bayesian networks, we show how to extend well-known statistical methods for learning Bayesian networks to learn these models. We describe both parameter estimation and structure learning — the automatic induction

This paper discusses the technique of structural induction for proving theorems about programs. This technique is closely related to recursion induction but makes use of the inductive definition of the data structures handled by the programs. It treats programs with recursion but without

approaches such as the Davis-Putnam procedure or resolution. We also show that GSAT can solve structured satisfiability problems quickly. In particular, we solve encodings of graph coloring problems, N-queens, and Boolean induction. General application strategies and limitations of the approach are also

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We develop a general logic-independent structural induction proof method at the level of abstract institutions. This provides a solid and uniform mathematical foundations to induction proof methodologies for a wide variety of actual logic-based formal specification frameworks. Our development

Abstract. System F supports induction over data types in a manner that is polymorphic with respect to the data held in the structure. Reduction is strongly normalising, so that operations on data always terminate. However, since the induction principles are encoded in the types, it is unable

We propose a uniform, category-theoretic account of structural induction for inductively defined data types. The account is based on the understanding of inductively defined data types as initial algebras for certain kind of endofunctors T : B !B on a bicartesian/distributive category B . Regarding

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. Recursive definitions and the associated inductive proofs are well established in mathematics and computer science. The term "structural induction" is used to describe inductive proof steps over recursively defined structures. In this paper we state and prove, using the Z notation