Higher Dimensional Trees, Algebraically

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Higher Dimensional Trees, Algebraically
In formal language theory, James Rogers published a series of innovative papers generalising strings and trees to higher dimensions.Motivated by applications in linguistics, his goal was to smoothly extend the core theory of the formal languages of strings and trees to these higher dimensions. Rogers’ definitions focussed on a specific representation of higher dimensional trees. This paper presents an alternative approach which focusses more on their universal properties and is based upon category theory, algebras, coalgebras and containers. Our approach reveals that Rogers’ trees are canonical constructions which are also particularly beautiful. We also provide new theoretical results concerning higher dimensional trees. Finally, we provide evidence for our devout conviction that clean mathematical theories the basis for clean implementations by showing how our abstract presentation makes computing with higher dimensional trees easier.
Neil Ghani, Alexander Kurz
Added 07 Jun 2010
Updated 07 Jun 2010
Type Conference
Year 2007
Authors Neil Ghani, Alexander Kurz
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