ACM SIGAPL APL Quote Quad
Conception, evolution, and application of functional programming languages
ACM Computing Surveys (CSUR)
APL '89 Conference proceedings on APL as a tool of thought
APL '89 Conference proceedings on APL as a tool of thought
APL '90 Conference proceedings on APL 90: for the future
APL '90 Conference proceedings on APL 90: for the future
APL '90 Conference proceedings on APL 90: for the future
ACM Transactions on Programming Languages and Systems (TOPLAS)
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)
The Implementation of Functional Programming Languages (Prentice-Hall International Series in Computer Science)
Walks into the APL design space
APL '92 Proceedings of the international conference on APL
The CTalk programming language: a strategic evolution of APL
APL '92 Proceedings of the international conference on APL
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Any expression in combinatory logic made up of combinators and variables can be abstracted into a pure combinator expression applied to a sequence of variables. Because there are great similarities between combinators and certain APL operators, a similar result obtains in many APL dialects. However, rewriting arbitrary APL expressions as pure functions requires new operators, not provided as primitives by any dialect. This paper defines functional completeness, gives a construction for achieving it, proves a conjecture of Kenneth Iverson that J is functionally complete, and shows how closely the major APL dialects have approached these conditions.