foo :: a -> (b -> c) Not saying it's wrong, but "foo is a second-order function" is a distinctly minority opinion. To a useful first approximation, Haskell wo

foo :: a -> (b -> c) Not saying it's wrong, but "foo is a second-order function" is a distinctly minority opinion. To a useful first approximation, Haskell works as a cartesian-closed category, which basically means we have tuples and that tuples harmonize with functions so that foo behaves just like uncurry foo :: (a,b) -> c which is a first-order function. So the majority opinion calls foo a first-order arity-2 function. Here's a bar function that's truly second-order: bar :: (a -> b) -> c In general, the order of a function is the count of parens nesting the leftmost innermost arrow. It is invariant to currying/uncurrying as well as permutation of arguments. The same counting principle applies to other invariants such as ranks and kinds. "How high can the order of a function go?" is the question explored in this blog post [0]. Note how the author's definition of order -- essentially the same given here -- got left and right mixed up. [0] http://math.andrej.com/2006/03/21/interesting-higher-order-functionals/ http://math.andrej.com/2006/03/21/interesting-higher-order-f...