[Haskell-cafe] working my way through Data.Type.Equality...my head hurts...

[Nicholls, Mark]

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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