Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and first-class phantom types, and are closely related to inductive types. They have the distinguishing feature that, when typechecking a function defined by cases, every branch may be checked under different typing assumptions. This mechanism allows exploiting th...

Abstract. Let A (ε) be an analytic square matrix and λ0 an eigenvalue of A (0) of algebraic multiplicity m ≥ 1. Then under the condition, ∂ ∂ε det (λI − A (ε)) |(ε,λ)=(0,λ0) 6= 0, we prove that the Jordan normal form of A (0) corresponding to the eigenvalue λ0 consists of a single m×m Jordan block, the perturbed eigenvalues near λ0 and their corresponding eigenvectors can be represented by a si...

B. Courcelle studied algebraic trees as precisely the solutions of all recursive program schemes for a given signature in Set. He proved that the corresponding monad is iterative. We generalize this to recursive program schemes over a given finitary endofunctor H of a ”suitable” category. A monad is called second-order iterative if every guarded recursive program scheme (w.r.t. H) has a unique ...

Hypercomputation refers to computation surpassing the Turing model, not just exceeding the von Neumann architecture. Algebraic constructions yield a $nitely based pseudorecursive equational theory (Internat. J. Algebra Comput. 6 (1996) 457–510). It is not recursive, although for each given number n, its equations in n variables form a recursive set. Hypercomputation is therefore required for an...

Recently, due to integration requirements, manufacturing industry is faced with the problem of controlling, monitoring, optimizing and supporting business and production processes. Among methods and techniques dealing with workflow management, those allowing a correct flexibility description are the more suitable for this industrial context. The aim of this paper is to show the interest of our ...

Final coalgebras for a functor serve as semantic domains for state based systems of various types. For example, formal languages, streams, nonwell-founded sets and behaviors of CCS processes form final coalgebras. We present a uniform account of the semantics of recursive definitions in final coalgebras by combining two ideas: (1) final coalgebras are also initial completely iterative algebras ...