Recursive functions of symbolic expressions and their computation by machine, Part I
Communications of the ACM
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
The Calculi of Lambda Conversion. (AM-6) (Annals of Mathematics Studies)
A programming language
General arrays, operators and functions
IBM Journal of Research and Development
Beyond rasters: introducing the new OGC web coverage service 2.0
Proceedings of the 18th SIGSPATIAL International Conference on Advances in Geographic Information Systems
RAM: a multidimensional array DBMS
EDBT'04 Proceedings of the 2004 international conference on Current Trends in Database Technology
An axiomatization of arrays for kleene algebra with tests
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
A familial specification language for database application systems
Computer Languages
Recent developments in the theory of data structures
Computer Languages
Survey: A survey of state vectors
Computer Science Review
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Array theory combines APL with set theory, transfinite arithmetic, and operationally transformed functions to produce an axiomatic theory in which the theorems hold for all arrays having any finite number of axes of arbitrary countable ordinal lengths. The items of an array are again arrays. The treatment of ordinal numbers and letters is similar to Quine's treatment of individuals in set theory. The theory is developed first as a theory of lists. This paper relates the theory to the eight axioms of Zermelo-Fraenkel set theory, describes the structure of arrays, interprets empty arrays in terms of vector spaces, presents a system of axioms for certain properties of operations related to the APL function of reshaping, deduces a few hundred theorems and corollaries, develops an algebra for determining the behavior of operations applied to empty arrays, begins the axiomatic development of a replacement operator, and provides an informal account of unions, Cartesian products, Cartesian arrays, and outer, positional, separation, and reduction transforms.