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.