On 15 Jul 2009, at 13:22, Luke Palmer wrote:
If ++ could be pattern matched, what should have been the result of "let (x++y)=[1,2,3] in (x,y)"?
It will branch. In terms of unification, you get a list of substitutions.
f :: [a] -> ([a],[a]) f (x ++ y) = (x,y)
For an argument s, any pair (x, y) satisfying s = x ++ y will match. That is, if s = [s_1, ..., s_k], the solutions j = 0, ..., k, x = [s_1, ..., s_j], y = [s_(j+1), ..., s_k]. And for each one, a potentially different value could given. That is, s could produce multiple values.
If this pattern branches, it could hardly be considered a function which takes lists and returns pairs. It would have to return something else.
So this would be a multi-valued function, which sometime is useful as a concept. But if the choices are indexed, they can be reduced to a single valued function. Like g(x,y) with the requirement that if x ++ y = x' ++ y', then g(x, y) = g(x', y'). This branching is what would happen if one tries to make a type theory based on sets. (It is possible to implement Horn clauses as unification branching.) The selection of branches correspond to a choice in the proof tree. Hans