Automatic synthesis of the inverses of APL functions

ABSTRACT

APL is used to facilitate the automatic inversion and execution of programs which are constructed by strict functional composition. Programs for performing high level functions and their inverses can be logically synthesized and then tested in arbitrary instances. APL is used to compose higher level functions by repeated left application of functions and operators designed expressly so that their syntax is limited to be monadic.A small system of auxiliary functions are sufficient to do the synthesis of inverse programs. This system operates on sequences of applicative functions which must be provided originally with their forward form coded in functional style APL. The system inverts higher level user-defined functions and generates correctly sequenced function calls which are used in testing the synthesized inverses.Using this system, the mechanistic re-formulation of the forward functions and either their exact or even their approximate inverses can be produced and then checked for consistency. Consistency in performance can be randomly tested by evaluating and confirming the validity of the identity R ≡ F^-1 F R. This may be done for acceptable comparison tolerances over a representative number of objects named R to which the function F and its inverse F^-1 are applied in tandem.

REFERENCES

• 1: James A. Brown , Sandra Pakin , Raymond P. Polivka, APL2: at a glance, Prentice-Hall, Inc., Upper Saddle River, NJ, 1988
• 2: Hudak, P., Wadler, P. (editors) Report on the Programming Language HaskeU, Version 1.0 April 1, 1990, Yale University Document YALEU/DCS/RR-777.
• 3: Iverson, Kenneth, The Principles of J, pp 1-15, APL News, Volume 22 Number 3, 1990.
• 4: Raymond P. Polivka , Sandra Pakin, APL: The Language and Its Usage, Prentice Hall Professional Technical Reference, 1975
• 5: Rumelhart, D.E., McClelland J. L., Parallel Distributed Processing, Vol. I, Foundations, page 329, 1988 MIT Press.

INDEX TERMS

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

          Nouns: APL

Additional Classification:
  D. Software
  D.1 PROGRAMMING TECHNIQUES
  D.3 PROGRAMMING LANGUAGES
      D.3.3 Language Constructs and Features
          Subjects: Procedures, functions, and subroutines

  I. Computing Methodologies
  I.2 ARTIFICIAL INTELLIGENCE
      I.2.2 Automatic Programming
          Subjects: Program synthesis

General Terms:
Languages