Declaration vs. expression style
There are two main styles of writing functional programs, which are both supported by Haskell mainly because several language designers preferred these different styles.
In the declaration style you formulate an algorithm in terms of several equations that shall be satisfied.
In the expression style you compose big expressions from small expressions.
1 ComparisonAs illustration for the two styles, Simon Peyton Jones give two implementations of the Prelude function
filter :: (a -> Bool) -> [a] -> [a]
1.1 Declaration style
filter p  =  filter p (x:xs) | p x = x : rest | otherwise = rest where rest = filter p xs
1.2 Expression style
filter = \p -> \ xs -> case xs of  ->  (x:xs) -> let rest = filter p xs in if p x then x : rest else rest
2 Syntactic elements
There are characteristic elements of both styles.
|Function arguments on left hand side:||
f x = x*x
|Lambda abstraction:|| |
f = \x -> x*x
|Pattern matching in function definitions:||
f  = 0
f xs = case xs of  -> 0
|Guards on function definitions:||
f [x] | x>0 = 'a'
f [x] = if x>0 then 'a' else ...