Lambda the Ultimate

Can anyone tell me which functional languages support a non-order-specific fold, and what the name of those operations are? I read somewhere that sometimes reduce is non-order specific, but other places claims it is the same as foldl. Clearly it depends on the languages, but I don't trust those source, so I thought I'd ask my favourite group of egg-heads. :-)

It seems that specifying left or right folds when the function being used is associative is over-specifying the solution to a problem. In other words you are solving a more specific problem than stated. Commonplace in imperative code, but it should be more easily avoided in functional code. Perhaps this is moot because it might be an "easy" problem for compilers to figure out if a "clean" function (e.g. pure functional) is associative and/or commutative based on the primitives.

I am studying the problem of optimizing / parallelizing pure functional code. So any good pointers to basic primers on the internet would be much appreciated. I am particularly interested in those common-knowledge optimizations of functional code. I don't have time to purchase any books, so online references would be most appreciated. It would be cool to gather a compendium of functional optimization tips and tricks on this thread, but that might be hoping for too much.

Thanks in advance.