Question to famous computer scientist Tony Hoare (British computer scientist) . Why is it so hard to teach (or require) beginning programmers top-down programming?

You cannot teach beginners top-down programming, because they don't know which end is up. Tony Hoare.

Problem-solving methodology:

• Identify the problem.
• Define the problem.
• Design top-down solution (decomposition).
• Implement bottom-up implementation (composition).
• Evaluate the results.

Compare to Waterfall method, SDLC (Systems Development Life Cycle), etc.

In the development of the understanding of complex phenomena, the most powerful tool available to the human intellect is abstraction. Tony Hoare (British computer scientist)

Dahl, O., Dijkstra, E., & Hoare, C. (1972). Structured programming. New York: Academic Press., p. 83.

In simple terms, abstraction is looking at similarities and ignoring differences.
Abstraction arises from a recognition of similarities between certain objects, situations, or processes in the real world, and the decision to concentrate on these similarities, and to ignore for the time being the differences. Tony Hoare (British computer scientist)

Dahl, O., Dijkstra, E., & Hoare, C. (1972). Structured programming. New York: Academic Press., p. 83.

I was eventually persuaded of the need to design programming notations so as to maximize the number of errors which cannot be made, or if made, can be reliably detected at compile time. Tony Hoare (British computer scientist)

Inside every well-written large program is a well-written small program. Tony Hoare (British computer scientist)

Premature optimization is the root of all evil in programming. Tony Hoare (British computer scientist)

The price of reliability is the pursuit of the utmost simplicity. It is a price which the very rich may find hard to pay. Tony Hoare (British computer scientist)

Some problems are better evaded than solved Tony Hoare (British computer scientist)

The real value of tests is not that they detect bugs in the code but that they detect inadequacies in the methods, concentration, and skills of those who design and produce the code. Tony Hoare (British computer scientist)

There are two ways of constructing a software design: One way is to make it so simple that there are obviously no deficiencies, and the other way is to make it so complicated that there are no obvious deficiencies. The first method is far more difficult. Tony Hoare (British computer scientist)

Programmers are always surrounded by complexity; we cannot avoid it.... If our basic tool, the language in which we design and code our programs, is also complicated, the language itself becomes part of the problem rather than part of its solution. Tony Hoare (British computer scientist)

The job of formal methods is to elucidate the assumptions upon which formal correctness depends. Tony Hoare (British computer scientist)

To "sort" is to "arrange" into "order" using some "criteria". In the seventh kingdom parable, the harvest at the end of the age, the "angels" "arrange" or "order" items into "good" and "rotten". This is the basic idea of the first iteration of quicksort that was developed by Tony Hoare in 1959 and published in 1961.

If the "greatest" and the "least" are the same value, then sorting on that value results in n! orderings for n items, all of which are valid sorts or arrangements. In such a case, there is no need to ever sort on that value.

More: Matthew 13:47-50: KP7 Parable of the harvest at the end of the age

More: Matthew: First last and last first