I implemented my custom type in Elm:
type Bin = BEmpty | One Bin | Zero Bin
I want it to be showable when I use it in String context similar to:
main = 
  Html.p (text bin)
if, for example, following is defined:
bin : Bin
bin = One (One (Zero BEmpty))
If I try to define instance of Show as follows:
instance Show Bin
  show bin = show (binToDec bin)
I get following error:
-- NAMING ERROR --------------------------------------------------- src/Main.elm
I cannot find a `Bin` variant:
19| instance Show Bin 
                  ^^^
These names seem close though:
    EQ
    Err
    GT
    L
Is there an equivalent of Haskell's instance Show Bin where declaration in Elm?
No, Elm does not have this feature.  You need to implement your own toString function:
binToString : Bin -> String
binToString bin =
    binToDec bin
    |> String.fromInt
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