[Haskell-beginners] Type classes and synonyms

[Philip Scott]

Hello all,

Quick one for you. I have a list of (<timestamp>,<value>) pairs, and I have 
defined lots of nice functions for doing various tricks with them. I'd like to 
define a custom data type which is an instance of 'Num' so I can conveniently 
do arithmetic on them. (I have written some tools for merging two time series 
etc...)

e.g.

t (x,y) = x
v (x,y) = y
mergeSkip _  [] = []
mergeSkip [] _  = []
mergeSkip (x:xs) (y:ys)
    | t x == t y = ( t x, (v x, v y) ) : (mergeSkip xs ys)
    | t x > t y  = mergeSkip xs (y:ys)    
    | t x < t y  = mergeSkip (x:xs) ys

binaryValueFunc f [] = []
binaryValueFunc f ((t,(a,b)):xs) = (t, f a b):binaryValueFunc f xs

add xs = binaryValueFunc (+) xs

addSkip xs ys = add $ mergeSkip xs ys

So addSkip will nicely take two of my time series, merge them by throwing out 
any pairs which don't have a time stamp that exists in both and then add the 
values to return a new series. All is well. But how do I make it so that I can 
use the + operator to add two of them?

Well of course, I tried making a custom data type:

data Ts a b = Ts [(a,b)]
intance Ts Num where
   <blaa blaa blaa>

But then I have to rewrite all of my functions to pattern match on Ts instead 
of just the list. Worse, when I am writing recursive functions I have to 
construct a Ts again for the recursive call. I guess I could make my own 
'list-like' datastructure

data Ts a b = Empty
  |           Cons ((a,b), Ts)

But that seems rather clumsy.

So I tried to make 'Ts' a type synonym for [(a,b)] which worked, but then
I couldn't declare it an instance of 'Num'.

So I guess the question is, is there any way of making a type synonym for a 
type which I can define as an instance of another class? So I can use my 
values of the type synonym for functions which expect the 'vanilla' type, but 
define 'extra' stuff my type synonym can do?

Any help or advice greatly appreciated.

- Philip