It seems to have quickly "infected" literature on dependent types at large---not to the point of having replaced the normal terminology, but instead as forming a sort of common framework for examining those fields.
Which is definitely a point on the side of "has no impact".
But on the other hand, I think studying dependent types is a fantastic way to get some perspective as an intermediate to advanced Haskell or OCaml programmer. Software Foundations and Certified Programming with Dependent Types are both great books to read.
HoTT won't be on that list for some time if ever, but once you've got a good mental model for dependent types it's illuminating to see them worked out "from scratch" as HoTT does.
So, the best I can say is that it can be influential in the way that you view types if you're someone who frequently programs and thinks in a nicely typed language like Haskell/OCaml and maybe Scala.
Which is definitely a point on the side of "has no impact".
But on the other hand, I think studying dependent types is a fantastic way to get some perspective as an intermediate to advanced Haskell or OCaml programmer. Software Foundations and Certified Programming with Dependent Types are both great books to read.
HoTT won't be on that list for some time if ever, but once you've got a good mental model for dependent types it's illuminating to see them worked out "from scratch" as HoTT does.
So, the best I can say is that it can be influential in the way that you view types if you're someone who frequently programs and thinks in a nicely typed language like Haskell/OCaml and maybe Scala.