Abstract
A spatial object consists of data assigned to points in a space. Spatial objects, such as memory states and three dimensional graphical scenes, are diverse and ubiquitous in computing. We develop a general theory of spatial objects by modelling abstract data types of spatial objects as topological algebras of functions. One useful algebra is that of continuous functions, with operations derived from operations on space and data, and equipped with the compact-open topology. Terms are used as abstract syntax for defining spatial objects and conditional equational specifications are used for reasoning. We pose a completeness problem: Given a selection of operations on spatial objects, do the terms approximate all the spatial objects to arbitrary accuracy? We give some general methods for solving the problem and consider their application to spatial objects with real number attributes.
| Original language | English |
|---|---|
| Pages (from-to) | 189-218 |
| Number of pages | 30 |
| Journal | Formal Aspects of Computing |
| Volume | 25 |
| Issue number | 2 |
| Early online date | 19 Jul 2011 |
| DOIs | |
| Publication status | Published - Mar 2013 |
Keywords
- abstract data types
- algebras
- approximation by terms
- compact-open topology
- conditional equations
- continuous functions
- dense subalgebras
- equations
- space
- spatial objects
- terms
- topological algebras