With the computer and programming languages, mathematics has newly-acquired tools, and its notation should be reviewed in the light of them. The… — 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
