Roger K. W. Hui

Gerunds and representations

Gerunds, verbal forms that can be used as nouns, are recognized as having utility in the realm of programming languages. We show that gerunds can be viewed as arrays of atomic representations of verbs (functions), in a way which is consistent with the syntax and semantics of APL, and which allows verbs to be first class objects in the language. We define derivations of verbs from gerunds in the J dialect of APL, and show how these derivations provide control structures for sequencing, selection (in the sense of generalized forms of CASE or SWITCH statements and IF/THEN/ELSE), iteration (DO UNTIL), recursion, and parallel computation (MIMD, or Multiple Instruction, Multiple Data). We conclude with alternative representations of verbs which are useful in other contexts.

Tacit definition

Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. ~ 1991 ACM 0-89791 -441-4/91 /0008/0202 ...

Some uses of { and }

1 .50

Design: a financial modelling system

We believe that the design of APL was also affected in important respects by a number of procedures and circumstances. Firstly, from its inception APL has been developed by using it in a succession of areas. This emphasis on application clearly favors practicality and simplicity. The treatment of many different areas fostered generalization … — Falkoff and Iverson, “The Design of APL”

J for the APL programmer

A non-procedural financial modelling system is presented. The financial models can be deterministic or probabilistic. Some issues in the design and implementation of this system are discussed.

TAGS: trains, agendas, and gerunds

Though J shares many concepts with APL, in many respects it is radically different, and almost all APL constructions that are in J differ in some way. These differences can be a stumbling block to the newcomer who thinks that J is simply an ASCII version of APL, prompting questions such as:• How do I save my workspace?• Why do J functions work along the columns and not the rows?• Can I have a version of J with □io←1?• Can I have a version of J with real APL characters?

Recreation: explorations in determinants

Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission. APL 94”9/94 Antwerp Belgium Q 1994 ACM 0-89791 -675-1 /94/0009..

Rank and uniformity

3.50 Software

Representations of recursion

The dyad aU. ym derived from the dot operator is inner product. For example, a+. x~ is the matrix multipfi-cation of finear algebra. A dictionary of APL ([] 18 1) defines the monad O. Y~ on matrices ~ thus: