Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Communications of the ACM
Communications of the ACM
The denotational semantics of programming languages
Communications of the ACM
A relational model of data for large shared data banks
Communications of the ACM
Recursive functions of symbolic expressions and their computation by machine, Part I
Communications of the ACM
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
POPL '79 Proceedings of the 6th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
Array theory in an APL environment
APL '79 Proceedings of the international conference on APL: part 1
APL '79 Proceedings of the international conference on APL: part 1
APL '79 Proceedings of the international conference on APL: part 1
Nested rectangular arrays for measures, addresses, and paths
APL '79 Proceedings of the international conference on APL: part 1
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
The Undecidable: Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions
APL '86 Proceedings of the international conference on APL
The integration of relational database algebra into APL
APL '86 Proceedings of the international conference on APL
An object oriented extension to APL
APL '87 Proceedings of the international conference on APL: APL in transition
Transforming high-level data-parallel programs into vector operations
PPOPP '93 Proceedings of the fourth ACM SIGPLAN symposium on Principles and practice of parallel programming
Connection Machine Lisp: fine-grained parallel symbolic processing
LFP '86 Proceedings of the 1986 ACM conference on LISP and functional programming
Carrier arrays: an idiom-preserving extension to APL
POPL '81 Proceedings of the 8th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
A new calculus for multidimensional arrays
APL '02 Proceedings of the 2002 conference on APL: array processing languages: lore, problems, and applications
Polyvalent functions, operators, strand notation and their precedence
APL '84 Proceedings of the international conference on APL
Rectangularly arranged collections of collections
APL '82 Proceedings of the international conference on APL
APL '82 Proceedings of the international conference on APL
Array diagrams and the Nial approach
APL '82 Proceedings of the international conference on APL
Nested rectangular arrays for measures, addresses, and paths
APL '79 Proceedings of the international conference on APL: part 1
Representations for enclosed arrays
APL '81 Proceedings of the international conference on APL
A development system for testing array theory concepts
APL '81 Proceedings of the international conference on APL
Nial: A candidate language for fifth generation computer systems
ACM '84 Proceedings of the 1984 annual conference of the ACM on The fifth generation challenge
Useful formulas for multidimensional arrays
Proceedings of the 2003 conference on APL: stretching the mind
Irregular computations in Fortran - expression and implementation strategies
Scientific Programming
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Data, like electricity and gravity, are part of the world in which we live. Some occur naturally, as in the genetic code, while most occur as a consequence of language and social organization. The search for a theory of data, which begins with the choice of a model, is as important and interesting as the development of theories in physics, economics, and psychology. Most models of data are collections, such as the unnested array of APL, the one-axis nested list of LISP, and the set, which is nested but lacks the properties of order, repetitions, type, and multiple axes inherent in rectangular arrangement. Nested rectangular arrays have all these properties. The existence of simple, universally valid equations in both set theory and linear algebra suggests that equally simple equations may hold for all arrays. The principles of nested collections developed in set theory apply with few changes to the nesting of arrays. A one-sorted theory of arrays, in which type is preserved for empty arrays, provides an algebra of operations interpreted not only for data but also types of data.