On Tue, Mar 3, 2009 at 2:43 AM, Peter Verswyvelen <bugfact@gmail.com> wrote:

Lambda calculus is a nice theory in which every function always has
one input and one output. Functions with multiple arguments can be
simulated because functions are first class and hence a function can
"return" a function. Multiple outputs cannot be done, one must embed
these outputs in some data type, e.g. using a tuple, or one must use
continuation passing style.

Now, does a similar theory exist of functions that always have one
input and one output, but these inputs and outputs are *always*
tuples? Or maybe this does not make any sense?

Well, this is not quite an answer to your question, but the curried multiple arguments convention in Haskell is exactly that: a convention. For example, in ML, most functions which take multiple arguments take them in the form of a tuple. They could just as well be curried, but the culture prefers tuples.