(i) Higher-order functions: Yes, slam-dunk win. Essentially all new languages have them, Java and C++ retrofit them.
(ii) Lazy evaluation order by default: mostly dead. All new language use eager evaluation, even SPJ is sceptical that lazy evaluation should be the default. Scala has an interesting approach: eager by default, but you can switch to CBN (although not full laziness) if required. This hybrid form enables you to define control-operators easily, while keeping the simplicity and efficiency of eager evaluation. Exceptions are languages with dependent types that are really theorem provers (e.g. Agda).
(iii) Purity: dead. All new languages have side-effects. The widely used FP languages like Haskell, Ocaml and F# have side-effects. Exceptions are languages with dependent types for Curry-Howard-based theorem provers (e.g. Agda), because there is no convincing Curry-Howard correspondence using state.
(iv) Everything is function application: open. This may work reasonably well in purely sequential languages, but there are theoretical reasons to believe that message passing is not function application (while function application is a special case of message passing).
(v) Types. The answer on this one depends on whether one is a proponent of statically typed languages or not, clearly an unresolved question. For dynamically typed languages, the question is moot, so the rest of the discussion is irrelevant to those who think that static typing is a bad idea.
(vi) Types (1), type inference: Slam dunk winner. All new languages have inference or wish they could have it but don't know how to do it (Scala). There are probably some hard trade-offs between expressivity of types and efficient decidability of type inference (B Pierce termed Hindley-Milner a "sweet spot"), so we might have to tolerate some type annotation being required, e.g. in local or bidirectional inference.
(vii) Types (2), algebraic data types, pattern matching: winner. Most new languages have them in some form.
(viii) Types (3), monadic encapsulation of effects: open. Most new languages have not yet embraced this. Some conceptual problems not yet solved, e.g. destructors for state monads. There are also expressivity problems, e.g. not all effects can easily be expressed as monads, and composition of monads doesn't always work as desired. Moreover there are pragmatic questions about whether monadic encapsulation should be required or optional.
(ix) Types (4), higher-kinded types: open. Not all new languages have them, but HKTs are generally considered useful, but not super important, cf Rust's evolution. If monadic encapsulation of effects is used, then HKTs become highly desirable, cf the recent Scala fork.
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