Notation as a tool of thought
@article{Iverson2007NotationAA,
title={Notation as a tool of thought},
author={Kenneth E. Iverson},
journal={ACM SIGAPL APL Quote Quad},
year={2007},
volume={35},
pages={2-31}
}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.
218 Citations
Programming Languages as Ideal Languages
- Computer Science
- 2013
“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
- Computer ScienceSIGP
- 1998
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
- Computer Science
- 2003
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
- Computer ScienceAPL '81
- 1981
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
- Computer ScienceCHI
- 2020
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
- Computer Science
- 2005
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
- PsychologyMemory & cognition
- 2007
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
- Computer ScienceAPLQ
- 1990
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
- Computer Science, Education
- 2005
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
- Computer Science
- 2005
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…
References
SHOWING 1-10 OF 39 REFERENCES
A programming language
- Computer ScienceAIEE-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
- EducationAPL '86
- 1986
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
- MathematicsAPL '75
- 1975
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
- GeologySIGP
- 1970
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.
- Computer ScienceCARN
- 1977
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
- Computer ScienceAPLQ
- 1976
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.
A History of Mathematical Notations, Volume If
- Open Court Publishing Co., La Salle, Illinois,
- 1929