Esoteric programming paradigms

First, declarative programming is a generic name which includes a broad range of paradigms - from functional to logic programming. Logic programming is something that deserves a special mention and discussion, because there are a number of interesting and unique concepts that deserve a more in-depth explanation.

Second, "dependent types" is better understood as a feature of a language (or better yet, of a type system) than a paradigm by itself.

Some of the other "paradigms" also seem more like characteristics of languages, and not really something that structures the way solutions are expressed/understood.

Of course, always remember that "can be compiled" != "can be synthesized".

[0] http://www.asic-world.com/verilog/index.html

Forth is known by name and reputation but very few people have ever tried to write anything in it - let alone delve into it's strange bootstrapped nature.

First, the article claims: "the sudoku solver above does a brute force search", but that is specifically not the case. In fact, quite the opposite holds: The Prolog Sudoku formulation shown in the article uses a powerful technique known as Constraint Logic Programming over Finite Domains, which automatically performs pruning before and also during the search for solutions. This effectively eliminates large portions of the search space in practice, and degenerates to brute force only in those cases where almost nothing can be deduced from initial constraints. In the particular case of Sudoku, the pruning is especially effective and can in many cases eliminate the search entirely, since the initial constraints (hints) basically determine the whole solution.

Second, yes, it is easy to write an O(n!) search algorithm in Prolog. However, it is almost as easy to implement much more efficient search algorithms in Prolog. For example, here is Quicksort in Prolog:

    quicksort([])     --> [].
    quicksort([L|Ls]) -->
            { partition(Ls, L, Smalls, Bigs) },
            quicksort(Smalls), [L], quicksort(Bigs).

https://esolangs.org/wiki/Rail https://esolangs.org/wiki/Billiard_ball_machine