Hmmm scanning the paper I think it easier to read the code and follow the paper. The paper is a little intractable.
the 1st link is a bit challenging... You may want to read 3rd chapter of Okasaki's "Purely Functional Data Structures" - it describes weight-biased lefitsh heaps without any type-level magic.
the 2nd I can probably cope with for the moment, though I may be asking questions. As you probably noticed this is based on paper "Why Dependent Types Matter", so you should probably read the paper and follow the code.
If you have any beginner level tutorial, then that’s even better.. I personally learned all these things in Agda. It's a bit easier because it's a fully-fledged dependently-typed language and things are just easier to write. Only then I moved to Haskell.
Janek
I can just about cope with associated types, type families and GADT...some of the other extensions I suspect disbelief for.
What does “~” mean…(it’s something that comes out in error messages when my types are all messed up)….
It means GHC knows that two types are equal.
and then there’s a “=>” going on…in the middle of a signature….I know “=>” in the context of “Num a => a -> a -> a”
Yeah, that looks scary. You use gcastWith when you need a value of type a but you have a value of type b with a proof that a and b are equal (here a proof is a value of a :~: b). I have a practical example, though perhaps it's not the simplest one:
https://github.com/jstolarek/dep-typed-wbl-heaps-hs/blob/master/src/Two Pass Merge/RankProof.hs#L361
This code is thought as an intermediate level tutorial - you might want to give it a try. Another example I have is here (I use the name subst, but it's identical to gcastWith):
https://github.com/jstolarek/why-dependent-types-matter/blob/master/Why Depe ndentTypesMatter.hs#L220
HTH
Janek
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