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I've been writing software for over 20 years, and with every day that goes by I grow more certain that strong static typing is not just a good idea, but also almost always the right choice.
There are definitely uses for untyped languages (or language variants), for example they are much nicer when using a REPL, or for throwaway scripts in environments that are already hopelessly untyped (e.g. the shell). In almost every other case, however, strong typing is strongly preferred.
There are advantages to not using types, such as a faster development speed, but they pale in comparison to all of the advantages. To that I say:
Writing software without types lets you go at full speed. Full speed towards the cliff.
The question around strong static typing is simple: would you rather work a bit more and get invariants checked at compile-time (or type-checking time for non-compiled languages), or work a bit less and have them be enforced at runtime, or even worse not enforced even at runtime (JavaScript, I'm looking at you...
1 + "2" == 12
).Getting errors at runtime is a terrible idea. First, it means that you won't always catch them during development. Second, when you do catch them, it will happen in a customer facing manner. Yes, tests help, but writing tests for every possible mistyped function parameter is impossible given the endless possibilities. Even if you could, having types is much easier than testing for wrong types.
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