The utility of a language as a tool of thought increases with the range of topics it can treat, but decreases with the amount of vocabulary and the complexity of grammatical rules which the user must keep in mind. Economy… — Kenneth E. Iverson Copy Share Image
If it is to be effective as a tool of thought, a notation must allow convenient expression not only of notions arising directly from… — Kenneth E. Iverson Copy Share Image
The properties of executability and universality associated with programming languages can be combined, in a single language, with the well-known properties of mathematical notation… — Kenneth E. Iverson Copy Share Image
It is important to distinguish the difficulty of describing and learning a piece of notation from the difficulty of mastering its implications. [...] Indeed,… — Kenneth E. Iverson Copy Share Image
The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical]… — Kenneth E. Iverson Copy Share Image
With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The computer may,… — Kenneth E. Iverson Copy Share Image
Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered significant… — Kenneth E. Iverson Copy Share Image
Overemphasis of efficiency leads to an unfortunate circularity in design: for reasons of efficiency early programming languages reflected the characteristics of the early computers,… — Kenneth E. Iverson Copy Share Image
The utility of a language as a tool of thought increases with the range of topics it can treat, but decreases with the amount… — Kenneth E. Iverson Copy Share Image
The practice of first developing a clear and precise definition of a process without regard for efficiency, and then using it as a guide… — Kenneth E. Iverson Copy Share Image
Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows… — Kenneth E. Iverson Copy Share Image
I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I… — Kenneth E. Iverson Copy Share Image
The initial motive for developing APL was to provide a tool for writing and teaching. Although APL has been exploited mostly in commercial programming,… — Kenneth E. Iverson Copy Share Image
![“It is important to distinguish the difficulty of describing and learning a piece of notation from the difficulty of mastering its implications. [...] Indeed, the very suggestiveness of a notation may make it seem harder to learn because of the many properties it suggests for exploration.” quote by Kenneth E. Iverson](https://sms4smile.com/quotes/img-quotes/3f1/kenneth-e-iverson-37528_describing_it-is-important-to-distinguish-the-diffi_460789.jpg)
![“The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential confusion in conventional [mathematical] notation.” quote by Kenneth E. Iverson](https://sms4smile.com/quotes/img-quotes/d25/kenneth-e-iverson-37528_ambiguity_the-precision-provided-or-enforced-by-pr_471194.jpg)
![“Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] The proliferation of programming languages shows no more uniformity than mathematics. Nevertheless, programming languages do bring a different…” quote by Kenneth E. Iverson](https://sms4smile.com/quotes/img-quotes/1ab/kenneth-e-iverson-37528_application_although-mathematical-notation-undoubted_1904632.jpg)
