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

Overemphasis of efficiency leads to an unfortunate circularity in design: for reasons of efficiency early programming languages reflected the charact….

The precision provided (or enforced) by programming languages and their execution can identify lacunas, ambiguities, and other areas of potential con….

The practice of first developing a clear and precise definition of a process without regard for efficiency, and then using it as a guide and a test i….

It is important to distinguish the difficulty of describing and learning a piece of notation from the difficulty of mastering its implications. [...]….

Most programming languages are decidedly inferior to mathematical notation and are little used as tools of thought in ways that would be considered s….

I was appalled to find that the mathematical notation on which I had been raised failed to fill the needs of the courses I was assigned, and I began ….

If it is to be effective as a tool of thought, a notation must allow convenient expression not only of notions arising directly from a problem, but a….

Although mathematical notation undoubtedly possesses parsing rules, they are rather loose, sometimes contradictory, and seldom clearly stated. [...] ….

The initial motive for developing APL was to provide a tool for writing and teaching. Although APL has been exploited mostly in commercial programmin….

The properties of executability and universality associated with programming languages can be combined, in a single language, with the well-known pro….

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 c….