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Without having run the whole company twice in parallel, once using Haskell and again in some other language, and without having measured both runs exactly the same way, I don't think metrics like you're interested in could possibly have sufficient context to mean anything reliable.

Obviously Mercury is successful, and obviously Haskell is how they did it. So it's essential to their success. Would it be instrumental to anyone else's anywhere else doing anything else? Can't possibly know, I don't think.

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I’m asking for solutions and answers. Yeah. I’m aware of how hard it is to get metrics.

You can still compare lines of code and bug rate over the same period of time.

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The irony of these fancy FP languages that were designed to develop compilers or to get PL academics off is that they're actually also really good at the most mundane code imaginable.

Being able to minimize boilerplate and have strong refactoring and bug resistant types is a huge edge.

The only problem is their ecosystems are limited so you might spend more time than you like implementing an API or binding a system library.

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It's probably more likely it comes down to: if your programmers are capable of learning and working in Haskell, they're likely a cut above in terms of keenosity and nerdiness and motivation around programming, and you're likely to early-cull the people who just got into CS because mom and dad told them it paid well. That's likely to help produce better overall code health.
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