[putzdown]

It looks to me as if there’s a solution to this problem based on the precompilation of sparse matrices. I’ll explain. If you have a function (or operator) call of the form fn(a, b), and you know that fn might accept 19 types (say) in the “a” place and 57 types in the “b” place, then in effect you have a large 2d matrix of the a types and the b types. (For functions taking a larger number of arguments you have a matrix with larger dimensionality.) The compiler’s problem is to find the matrix cell (indeed the first cell by some ordering) that is non-empty. If all the cells are empty, then you have a compiler error. If at least one cell is non-empty (the function is implemented for this type combination), then you ask “downward” whether the given arguments values can conform to the acceptable types. I know that there’s complexity in this “downward” search, but I’m guessing that the bulk of the time is spent on searching this large matrix. If so, then it’s worth noting that there are good ways of making this kind of sparse matrix search very fast, almost constant time.