It's quite difficult to explain how much work a very strong type system can do for you if you're used to something like C as your definition of "static typing". I mean this comment comment completely straight and polite, and I'm trying to help people answer your very reasonable question by asking you for some details that will help calibrate the answer.
Technically that would be something like Haskell's, but I only have surface-level fluency. More to the point would be the most complex stuff I've had reason to do with a type system, which caps at around this generic state machine:
Absolutely. It's little different than asking whether you can solve a problem once you have the appropriate data structure. Solving the problem when the right data structure is available becomes almost trivial -- most of the difficult of programming is recognizing what data structures are needed.
Very few of the problems we encounter in every day programming don't fall when the right data structure is available.
It's not the same at all; data structures frequently actually are half the problem, though that's not to say that insight buys you anything.
Let's say I want to stream logging data at a massive rate (~peak core-core bandwidth) to another core and perform complex queries and visualisations on it in sub-frame times. If I have the data structure for that, the rest is bookwork. If I have the type... what have I gained?
Let's say I want to find the best way to represent my data in a way that's amiable to GPU operations. If I find a data structure for that, I'm left with the other half of the job in mapping the transformations I need to GPU calls. If I write some types for it, it's not like GPUs start being any less buggy.
Let's say I'm writing an extension for a Java program with an API not designed for my use-case, and I want to work out how to access stuff that's not directly intended to be exposed. A data structure design isn't much good, since it's an exploratory problem, but neither is assigning types to random things. I still need to figure out how to abuse the API.
Let's say I'm trying to solve the Halting Problem. If I have a data structure for that, I've pretty much proven FALSE, and literally everything is provable. Conversely, I can already give you the type and I'm no closer to solving it.
> Let's say I want to stream logging data at a massive rate (~peak core-core bandwidth) to another core and perform complex queries and visualisations on it in sub-frame times. If I have the data structure for that, the rest is bookwork. If I have the type... what have I gained?
It depends on how you're using "type" vs how I'm using it.
If you mean the "publicly visible type", ie. the left hand side of "newtype Foo a = ...", my claim is weaker. Even so, the public interface for your type specifies the operations and implies their approximate time and space complexity (1), which points rather suggestively at the types of internal data structures that will be needed to satisfy these properties (2), which as you've said, is at least half the problem.
If by "type", the actual data type definitions needed to satisfy this interface, ie. the right hand side of "newtype Foo a = ...", which is what I originally meant, then you're already at (2) above, from which the conclusion follows almost trivially.
It's quite difficult to explain how much work a very strong type system can do for you if you're used to something like C as your definition of "static typing". I mean this comment comment completely straight and polite, and I'm trying to help people answer your very reasonable question by asking you for some details that will help calibrate the answer.