Notation as a tool of thought

  title={Notation as a tool of thought},
  author={Kenneth E. Iverson},
  journal={ACM SIGAPL APL Quote Quad},
  • K. Iverson
  • Published 1 August 1980
  • Art
  • ACM SIGAPL APL Quote Quad
The importance of nomenclature, notation, and language as tools of thought has long been recognized. In chemistry and in botany, for example, the establishment of systems of nomenclature by Lavoisier and Linnaeus did much to stimulate and to channel later investigation. Concerning language, George Boole in his Laws of Thought [1, p.21] asserted "That language is an instrument of human reason, and not merely a medium for the expression of thought, is a truth generally admitted. 
Programming Languages as Ideal Languages
“So-called ’natural language’ is wonderful for the purposes it was created for, such as to be rude in, to tell jokes, to cheat or to make love in (and Theorists of Literary Criticism can even be
Putting more meaning in expressions
Several constructs are proposed that enrich the semantics of expressions in expression-oriented languages, to extend the possibilities for explicit specification of properties and interrelations between program objects, thus conveying more meaning to the reader of a program.
Syntax Extension as a Tool for Application Programming
The largely unexploited issue is the notion of having one programming language but with a run-time mutable syntax, which seems especially plausible to provide when the language must address an application whose own notational syntax can mutate, even over a short textual span.
The use of APL as an executable formal language in economics demonstrated by an example
It is shown that the use of APL in the presentation of the ideas of the model and in the proof of the related theorems leads to directly executable steps in the formal proofs, and hence to a better understanding of the idea behind them.
To Write Code: The Cultural Fabrication of Programming Notation and Practice
It is argued that translation work is a fundamental property of the practice of writing code by advancing an intercultural lens on programming practice rooted in history by Questioning long-standing terminology, dichotomies, and epistemological tendencies in the field of computer programming.
The de Bruijn principle and the compositional design of programming languages
Initial work is described on a system that encapsulates component-oriented language design, which can generate language tools and their associated proof systems by composing descriptions of feature sets, and is designed to modularise the development and proof processes.
Formal notations are diagrams: Evidence from a production task
The primary goal of this article is to establish, using behavioral measures on naturalistic tasks, that some of the same cognitive resources involved in representing spatial relations and proximities are also involved in represents symbolic notations—in short, that formal notations are a kind of diagram.
Considered harmful—still
The adoption of new, ASCII-based dialects of APL, such as J, is suggested as one solution to the character-set problem.
An Experiment in Program Annotation
A formal notation that can most naturally be provided by the written tradition of mathematics is provided, for various reasons that will be mentioned later on, borrowing from traditional mathematical notation without modifying it may not be just what the authors need.
Languages and metamodels for modelling frameworks
ions in these layers. In the layered set of languages suggested by this view, the abstractions of various modelling paradigms would be defined by providing mappings from the language encoding these


A programming language
  • K. Iverson
  • Computer Science
    AIEE-IRE '62 (Spring)
  • 1962
The paper describes a succinct problem-oriented programming language that relies heavily on a systematic extension of a small set of basic operations to vectors, matrices, and trees, and on a family of flexible selection operations controlled by logical vectors.
Style and literacy in APL
A persistent belief in the APL community, reflecting perhaps some of the prejudice against APL outside that community, that “good style” in APL involves writing very short statements, using as few primitives as possible in each is explored.
A notation for the GCD and LCM functions
P proofs of some of the basic theorems concerning gcd and lcm are given to insure that they are valid for the entire domain of values for which it is proposed the APL functions be defined.
APL Quote-Quad
The APL Quote-Quad is an informal publication for APL Users that is in need of high quality material for publication on these pages and does not represent the opinions or policy of an y company or organization.
Review of Digital system implementation by Gerrit A. Blaauw. Prentice Hall, Series in Automatic Computatin 1976.
In order to define the architecture of the adder (chapter 2) a diagram is given which is immediately translated into a APL Program (which makes it necessary to interrupt the flow of presentation by a
Digital System Implementation
Eight chapters following an introductory chapter consider the architecture and implementation of addition, multiplication, division, datapaths of the arithmetic and logic unit, internal control of the datapath, storage, and communication among system components.
Ein Gesamtschrittverfahren zur Berechnung der Nullstellen von Polynomen
A History of Mathematical Notations, Volume If
  • Open Court Publishing Co., La Salle, Illinois,
  • 1929
Mathematical Analysis
Summation of Series.