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.
Kenneth E. IversonOveremphasis of efficiency leads to an unfortunate circularity in design: for reasons of efficiency early programming languages reflected the characteristics of the early computers, and each generation of computers reflects the needs of the programming languages of the preceding generation.
Kenneth E. IversonThe initial motive for developing APL was to provide a tool for writing and teaching. Although APL has been exploited mostly in commercial programming, I continue to believe that its most important use remains to be exploited: as a simple, precise, executable notation for the teaching of a wide range of subjects.
Kenneth E. IversonAlthough 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 perspective. [...] Because of their application to a broad range of topics, their strict grammar, and their strict interpretation, programming languages can provide new insights into mathematical notation.
Kenneth E. IversonThe 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 of notation is therefore important.
Kenneth E. Iverson