Would you still consider this semantics restrictive if the default were private scope and a programmer could intentionally expose API functionality using "package," "protected," and "public"?

IMO, anonymous functions make OO-style private scope easy and implicit, without feeling like a limitation on the programmer.

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"It seems to me, intuitively, that the kinds of mistakes that can be easily caught by the compiler at compile time are in general the kinds of mistakes that are easily caught, period."

I think that's true, yet not as trivial as you suggest. In general, the properties a compiler can verify are those that can be "easily" expressed in mathematics, where "easily" means the proof-theoretical algorithms of finding proofs, verifying proofs, etc. (whatever the compiler needs to do) have reasonable computational complexity. Mathematics as a whole is arbitrarily hard, but I believe human effort has computational complexity limits too, and I see no clear place to draw the line between what computers can verify and what humans can verify. Our type systems and other tech will keep getting better.

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"The kinds of bugs that are hard to find are the ones that happen at runtime and propagate before showing themselves, and they are literally impossible for the compiler to find, because that would require the compiler to solve problems that are provably uncomputable."

I believe you're assuming a program must run Turing-complete computations at run time. While Turing-completeness is an extremely common feature of programming languages, not all languages encourage it, especially not if their type system is used for theorem proving. From a theorems-as-types point of view, the run time behavior of a mathematical proof is just the comfort in knowing its theorem is provable. :-p If you delay that comfort forever in a nonterminating computation, you're not proving anything.

Functional programming with guaranteed termination is known as total FP. "Epigram [a total FP language] has more static information than we know what to do with." http://strictlypositive.org/publications.html

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"PHP is actually an interesting example, because in PHP, the rules for variable declarations are basically inverted from normal: you have to declare global variables in every function that you use them (or access them through the $GLOBALS array), but you don't have to declare function-scope variables at all. It makes a lot of sense if you think about it."

I find this annoying. My style of programming isn't absolutely pure functional programming, but it often approximates it. In pure FP, there's no need to have the assignment syntax automatically declare a local variable. That's because there's no assignment syntax! Accordingly, if a variable is used but not defined, it must be captured from a surrounding scope, so it's extraneous to have to declare it as a nonlocal variable.