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Terminal coalgebras for a functor serve as semantic domains for state-based systems of various types. For example, behaviors of CCS processes, streams, infinite trees, formal languages and non-well-founded sets form terminal coalgebras. We present a uniform account of the semantics of recursive definitions in terminal coalgebras by combining two ideas: (1)… (More)

Completely iterative algebras (cias) are those algebras in which recur-sive equations have unique solutions. In this paper we study complete iterativity for algebras with computational effects (described by a monad). First, we prove that for every analytic endofunctor on Set there exists a canonical distributive law over any commutative monad M , hence a… (More)

Covarieties of coalgebras are those classes of coalgebras for an endofunctor H on the category of sets that are closed under coproducts, subcoalgebras and quotients. Equivalently, covarieties are classes of H-coalgebras that can be presented by co-equations. Adámek introduced a logic of coequations and proved soundness and completeness for all polynomial… (More)

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

Introduction Motivation Goal Deduce properties of (state-based) systems from known properties of these systems. Introduction Motivation Goal Deduce properties of (state-based) systems from known properties of these systems. concept model as example system coalgebra deterministic automaton system property coequation each state accepts the empty word… (More)

Deterministic recursive program schemes (RPS's) have a clear category theoretic semantics presented by Ghani et al. and by Milius and Moss. Here we extend it to nondeterministic RPS's. We provide a category theoretic notion of guardedness and of solutions. Our main result is a description of the canonical greatest solution for every guarded nondeterministic… (More)

- Daniel Schwencke
- 2014

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