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Results 1 - 10
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252
The Continuum as a Final Coalgebra
, 1999
"... We define the continuum up to order isomorphism, and hence up to homeomorphism via the order topology, in terms of the final coalgebra of either the functor N X, product with the set of natural numbers, or the functor 1 + N X. This makes an attractive analogy with the definition of N itself as the i ..."
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Cited by 5 (3 self)
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We define the continuum up to order isomorphism, and hence up to homeomorphism via the order topology, in terms of the final coalgebra of either the functor N X, product with the set of natural numbers, or the functor 1 + N X. This makes an attractive analogy with the definition of N itself
FINAL COALGEBRAS IN ACCESSIBLE CATEGORIES
, 905
"... Abstract. We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra in ..."
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Abstract. We give conditions on a finitary endofunctor of a finitely accessible category to admit a final coalgebra. Our conditions always apply to the case of a finitary endofunctor of a locally finitely presentable (l.f.p.) category and they bring an explicit construction of the final coalgebra
Logical Construction of Final Coalgebras
, 2003
"... We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and is an extensive category, it has a natural number object. ..."
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Cited by 1 (0 self)
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We prove that every finitary polynomial endofunctor of a category C has a final coalgebra, provided that C is locally Cartesian closed, it has finite coproducts and is an extensive category, it has a natural number object.
Continuous functions on final coalgebras
, 2007
"... In a previous paper we have given a representation of continuous functions on streams, both discrete-valued functions, and functions between streams. the topology on streams is the ‘Baire ’ topology induced by taking as a basic neighbourhood the set of streams that share a given finite prefix. We ga ..."
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Cited by 12 (1 self)
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gave also a combinator on the representations of stream processing functions that reflects composition. Streams are the simplest example of a non-trivial final coalgebras, playing in the coalgebraic realm the same role as do the natural numbers in the algebraic realm. Here we extend our previous
Similarity Quotients as Final Coalgebras
"... Abstract. We give a general framework relating a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity (a well known example), similarity, upper and lower similarity for transition sys ..."
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Cited by 8 (0 self)
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Abstract. We give a general framework relating a branching time relation on nodes of a transition system to a final coalgebra for a suitable endofunctor. Examples of relations treated by our theory include bisimilarity (a well known example), similarity, upper and lower similarity for transition
On The Final Coalgebra Of Automatic Sequences
, 2011
"... Abstract. Streams are omnipresent in both mathematics and theoretical computer science. Automatic sequences form a particularly interesting class of streams that live in both worlds at the same time: they are defined in terms of finite automata, which are basic computational structures in computer s ..."
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Cited by 6 (4 self)
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that the set of automatic sequences carries a final coalgebra structure, consisting of the operations of head, even, and odd. This will allow us to show that automatic sequences are to (general) streams what rational languages are to (arbitrary) languages. 1
A Small Final Coalgebra Theorem
- Theoretical Computer Science
, 1998
"... This paper presents an elementary and self-contained proof of an existence theorem of final coalgebras for endofunctors on the category of sets and functions. ..."
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Cited by 11 (0 self)
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This paper presents an elementary and self-contained proof of an existence theorem of final coalgebras for endofunctors on the category of sets and functions.
Guarded Induction on Final Coalgebras
, 1998
"... We make an initial step towards a categorical semantics of guarded induction. While ordinary induction is usually modelled in terms of the least fixpoints and the initial algebras, guarded induction is based on the unique fixpoints of certain operations, called guarded, on the final coalgebras. So f ..."
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We make an initial step towards a categorical semantics of guarded induction. While ordinary induction is usually modelled in terms of the least fixpoints and the initial algebras, guarded induction is based on the unique fixpoints of certain operations, called guarded, on the final coalgebras. So
Initial Algebra, Final Coalgebra and Datatype
, 2011
"... Induction ” in which they provided a brief introduction to initial algebras and final coalgebras[1]. Induction is used both as a definition principle, and as a proof principle for algebraic structures. But there are also important dual “coalgebraic” ..."
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Induction ” in which they provided a brief introduction to initial algebras and final coalgebras[1]. Induction is used both as a definition principle, and as a proof principle for algebraic structures. But there are also important dual “coalgebraic”
A Thesis Proposal on Final Coalgebras
, 1998
"... I present an overview of final coalgebras together with a description of initial algebras, showing the analogies between the two. In particular, I show how initiality of algebras leads to the properties of definition by recursion and proof by induction. I then show how final coalgebras have the anal ..."
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I present an overview of final coalgebras together with a description of initial algebras, showing the analogies between the two. In particular, I show how initiality of algebras leads to the properties of definition by recursion and proof by induction. I then show how final coalgebras have
Results 1 - 10
of
252
