Communication and concurrency
Exact Real Computer Arithmetic with Continued Fractions
IEEE Transactions on Computers
Infinite objects in type theory
TYPES '93 Proceedings of the international workshop on Types for proofs and programs
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
Coalgebraic Specifications and Models of Determinatistic Hybrid Systems
AMAST '96 Proceedings of the 5th International Conference on Algebraic Methodology and Software Technology
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
Coalgebraic Representation Theory of Fractals
Electronic Notes in Theoretical Computer Science (ENTCS)
| Hi-index | 5.23 |
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 NX, product with the set of natural numbers, or the functor 1+NX. This makes an attractive analogy with the definition of N itself as the initial algebra of the functor 1+X, disjoint union with a singleton. We similarly specify Baire space and Cantor space in terms of these final coalgebras. We identify two variants of this approach, a coinductive definition based on final coalgebraic structure in the category of sets, and a direct definition as a final coalgebra in the category of posets. We conclude with some paradoxical discrepancies between continuity and constructiveness in this setting.