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According to most sources, with all else equal, programming languages that use dynamic typing instead of static typing should be more productive. Not that all else ever is equal, but that's the theory. I've seen statistics advanced by fairly intelligent people to back it up, and for the most part I believe it. I just don't understand it, and highly doubt it applies to me with my personal coding style. I hate doing type discovery code, and despise finding out at runtime an error that could have been detected at compile time had static typing been employed. I'll admit some environments are more friendly with respect to these issues than others, but it still just pisses me off.

Yes, it would probably take ten times as long to write the program to provide overloads for the hundred different types needed, but I'd still have more confidence in the final program.
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I think the idea is that you never have to perform type discovery. The only time you have multiple types is when you're using polymorphism and then your language's dispatch mechanism takes over. If you pass the wrong thing to a function you usually get an exception raised straight away. It's one of those things that appears to always be fine in practice, even though it seems loose and lazy in theory.

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