Terminal coalgebras in well-founded set theory
Theoretical Computer Science
Discrete iterated function systems
Discrete iterated function systems
Dynamical systems, measures, and fractals via domain theory
Information and Computation
Axiomatic domain theory in categories of partial maps
Axiomatic domain theory in categories of partial maps
Universal coalgebra: a theory of systems
Theoretical Computer Science - Modern algebra and its applications
The continuum as a final coalgebra
Theoretical Computer Science
Real number computation through gray code embedding
Theoretical Computer Science
Applied Semantics, International Summer School, APPSEM 2000, Caminha, Portugal, September 9-15, 2000, Advanced Lectures
A Universal Characterization of the Closed Euclidean Interval
LICS '01 Proceedings of the 16th Annual IEEE Symposium on Logic in Computer Science
A Functional Algorithm for Exact Real Integration with Invariant Measures
Electronic Notes in Theoretical Computer Science (ENTCS)
Corecursive Algebras: A Study of General Structured Corecursion
Formal Methods: Foundations and Applications
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We develop a representation theory in which a point of a fractal specified by metric means (by a variant of an iterated function system, (IFS) is represented by a suitable equivalence class of infinite streams of symbols. The framework is categorical: symbolic representatives carry a final coalgebra; an IFS-like metric specification of a fractal is an algebra for the same functor. Relating the two there canonically arises a representation map, much like in America and Rutten's use of metric enrichment in denotational semantics. A distinctive feature of our framework is that the canonical representation map is bijective. In the technical development, gluing of shapes in a fractal specification is a major challenge. On the metric side we introduce the notion of injective IFS to be used in place of conventional IFSs. On the symbolic side we employ Leinster's presheaf framework that uniformly addresses necessary identification of streams-such as .0111...=.1000... in the binary expansion of real numbers. Our leading example is the unit interval I=[0,1].