map(a, b, x, y, t) maps [a, b] -> [x, y] wrt t
in a map function, most importantly we want exactness:
map(a, b, x, y, a) = xmap(a, b, x, y, b) = y
another nice guarantee to have is consistency:
map(a, b, x, x, t) = x
because many algorithms assume going only forward or backward in time, monotonicity: