The role of composition in computer programming

ABSTRACT

Iverson has greatly enlarged the mathematical notion of function composition and made it available to computer programmers. This paper explains the concept, and uses practical examples to show how concise, powerful programs can be written and read. Alternative forms are given, and ways of overcoming initial difficulties are explained.The systematic use of composition extends the well-known advantages of APL; namely conciseness, consistency, and generality.

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INDEX TERMS

Primary Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: APL

Additional Classification:
  D. Software
  D.3 PROGRAMMING LANGUAGES
      D.3.2 Language Classifications

          Nouns: J
      D.3.3 Language Constructs and Features
          Subjects: Procedures, functions, and subroutines

  F. Theory of Computation
  F.2 ANALYSIS OF ALGORITHMS AND PROBLEM COMPLEXITY
      F.2.2 Nonnumerical Algorithms and Problems
          Subjects: Geometrical problems and computations
  F.3 LOGICS AND MEANINGS OF PROGRAMS
      F.3.3 Studies of Program Constructs
          Subjects: Functional constructs

General Terms:
Algorithms, Languages

Keywords:
APL, Iverson, J, adverbs, composite verbs, conjunctions, executable mathematical notation, forks, function composition, geometry, gerunds, hooks, trains