One of the authors introduced in [Santocanale, FoSSaCS, 2002] a calculus of circular proofs
for studying the computability arising from the following categorical operations: finite …

We introduce AmiCo, a tool that extends a proof assistant, Isabelle/HOL, with flexible
function definitions well beyond primitive corecursion. All definitions are certified by the …

Coinductive definitions, such as that of an infinite stream, may often be described by elegant
logic programs, but ones for which SLD-refutation is of no value as SLD-derivations fall into …

Functional languages offer a high level of abstraction, which results in programs that are
elegant and easy to understand. Central to the development of functional programming are …

We present two methods for defining corecursive functions that go beyond what is accepted
by the builtin corecursion mechanisms of the Coq proof assistant. This gain in …

Coinductive predicates express persisting 'safety'specifications of transition systems.
Previous observations by Hermida and Jacobs identify coinductive predicates as suitable …

Coinductive predicates express persisting “safety” specifications of transition systems.
Previous observations by Hermida and Jacobs identify coinductive predicates as suitable …

In this paper, we develop a general theory of fixed point combinators, in higher-order logic
equipped with Hilbert's epsilon operator. This combinator allows for a direct and effective …

We propose a (limited) solution to the problem of constructing stream values defined by
recursive equations that do not respect the guardedness condition. The guardedness …

In logic and computer science one often needs to constructivize a theorem∀ f∃ gP (f, g),
stating that for every infinite sequence f there is an infinite sequence g such that P (f, g). Here …