Haskell non-exhaustive patterns and converting function output - haskell

Question

I have a function that wants to list all of a dataType.
fn [] = []
fn (dt#(DataType t d y [(f,r)]):dts) = ["T:" ++ t ++ " D: " ++ d ++ " R: " ++ show y ++ "Ra" ++ show (fnAvg dt)] ++ fn dts
Where t and d are strings, y is an int, f is a string and r is an int (not sure f and r matter though, will explain furthur on).
I got the error non-exhaustive patterns, and presumed it was because I didn't have one for when there was only one element in the list, so I added this between the other patterns:
fn [dt#(DataType t d y [(f,r)])] = ["T:" ++ t ++ " D: " ++ d ++ " R: " ++ show y ++ "Ra" ++ show (fnAvg dt)]
It compiled, but when I called the function it once again told me 'non-exhaustive patterns'. I'm struggling to think of what pattern i've missed, should I add a wildcard pattern afterward to catch everything? I'm not looking for someone to type out the answer, but hints or suggestions are welcome.

Answer 1

The pattern [(f,r)] only matches when the list contains one element. If it contains zero, or two, or any other number, you have a pattern match failure.
What the code should do in this instance, I couldn't say...

Answer 2

You do already cover the one-element-list case: that matches fn (dt#(DataType t d y [(f,r)]):[]), since dts can be anything including the empty list.
Indeed there's no reason to use explicit recursion here: you basically have something like
f [] = []
f (x:xs) = g x ++ f xs
Compare that to the monad instance of lists:
instance Monad [] where
return x = [x]
[] >>= _ = []
(x:xs) >>= g = g x ++ (xs >>= g)
So you should write you function as
fn l = l >>= \dt#( DataType t d y [(f,r)] )
-> ["T:" ++ t ++ " D: " ++ d ++ " R: " ++ show y ++ "Ra" ++ show (fnAvg dt)]
That won't fix your problem though, but it makes it obvious what's going on: evidently, DataType t d y [(f,r)] is not the only valid pattern for that type. As MathematicalOrchid points out, [(f,r)] matches only a list with length 1, but you need to cover other lengths as well.
fn l = l >>= \dt -> case dt of
DataType t d y [(f,r)]
-> ["T:" ++ t ++ " D: " ++ d ++ " R: " ++ show y ++ "Ra" ++ show (fnAvg dt)]
DataType t d y []
-> ["Some other stuff"]
DataType t d y [(f,r), ...]
-> ["Yet other stuff"]
or whatever.
Indeed, if you only ever return [ ("stuff") ] here, then you're not really using the monadic bind functionality at all: you could have written the recursive version without ++, only reconstruct the thing with :, and in fact you have simply a map operation:
fn = map $ \dt -> case dt of
DataType t d y [(f,r)]
-> "T:" ++ t ++ " D: " ++ d ++ " R: " ++ show y ++ "Ra" ++ show (fnAvg dt)
DataType t d y []
-> "Some other stuff"
DataType t d y [(f,r), ...]
-> "Yet other stuff"