Implications of APL2 grammar

ABSTRACT

A subtle but pervasive feature of APL2 is its new way of describing syntax. It is based on an ordered list of ordered pairs of syntactic classes. Position in the list corresponds to the strength of the syntactic bond between objects of the classes in the pair. The single rule of execution is to scan from the right until the binding drops and then evaluate the pair of objects just scanned. The new simple view of syntax suggests some straightforward extensions to the language which do not complicate the syntax and address such areas as: specifying a variable number of iterations of EACH in a manner analogous to the way a power operator can specify iterations of a function. using similar and similarly simple expressions to apply structural functions and operators, for example (2 3 ↑)″ A B C and (2 3 /)″ A B C require, respectively, that the named objects be of rank 2 and of length 2 (after scalar extension). The first expression is, of course, not valid today; the second is, and the parentheses are redundant. creating arrays of objects other than data, a subject treated in several papers in recent years a number of identities involving functions and operators, including some which provide compact notation for concepts of elementary arithmetic. the elevators of Landaeta, which are only possible if a language contains identically structured expressions for objects of different symbolic classes, provide a way of describing analogues of an operation in different syntactic classes. These lead to an interesting new diagrammatic way of expressing identities.

REFERENCES

• APL2: IBM Corporation, APL2 Language Manual, Order 5820-9227.
• Be84: Robert Bernecky, Function arrays, ACM SIGAPL APL Quote Quad, v.14 n.4, p.53-56, June 1984
• BG84: J. D. Bunda , J. A. Gerth, APL two by two-syntax analysis by pairwise reduction, ACM SIGAPL APL Quote Quad, v.14 n.4, p.85-94, June 1984
• Bk83: J. Philip Benkard, Valence and precedence in APL extensions, ACM SIGAPL APL Quote Quad, v.13 n.3, p.233-242, March 1983
• Bk84: J. Philip Benkard, Syntactic experiments with arrays of functions and operators, ACM SIGAPL APL Quote Quad, v.14 n.4, p.41-51, June 1984
• Bk85: J. Philip Benkard, Structural experiments with arrays of functions, ACM SIGAPL APL Quote Quad, v.15 n.4, p.166-172, May 12, 1985
• Bk86: J. Philip Benkard, Analysis of function applications in deep arrays, ACM SIGAPL APL Quote Quad, v.16 n.4, p.202-210, 1986
• Bk87: J.P. Benkard, "Replicate Each, Anyone?", these Proesedings. 16. No. 4 (July 19861,
• Iv78: K. E. Iverson* Operators and Functions. IBM Research Rsport RC7091.
• Iv79: Kenneth E. Iverson, The role of operators in APL, ACM SIGAPL APL Quote Quad, v.9 n.4, p.128-133, June 1979
• Iv82: Kenneth E. Iverson , Arthur T. Whitney, Practical uses of a model of APL, ACM SIGAPL APL Quote Quad, v.13 n.1, p.140-145, September 1982
• Iv85: K. E. Ivsrson. "A Concise Dictionary of APL", I. P. Sharp Associates.
• Iv86: K. E. Ivarsonr "Core APL", in Suppleaent to iuforral Voluae for APL86 (July 19861, pp. - .
• Ka83: James T. Kajiya, Designing and implementing an array theory incorporating abstract datatypes, ACM SIGAPL APL Quote Quad, v.13 n.3, p.291-296, March 1983
• La86: David J. Landaeta, A notation for manipulating arrays of operations, ACM SIGAPL APL Quote Quad, v.16 n.4, p.21-29, 1986

INDEX TERMS

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

          Nouns: APL

General Terms:
Design, Languages, Theory