A
program transformation where several results are returned
from a single traversal of a data structure. E.g.
mean l = sum l / length l
==>
mean l = s/n
where
(s,n) = sumLen l
sumLen [] = (0,0)
sumLen (x:xs) = (s+x, n+1)
where
(s,n) = sumLen xs
In
procedural languages this technique is known as
horizontal loop combination because it uses one loop to
calculate several results.
Another form of tupling transformation is used to avoid
repeated evaluation where a function generates several
identical calls to itself. By analysing the pattern of
recursion (see
descent function) it is possible to arrange
for these identical calls to share results. E.g.
fib 0 = 1
fib 1 = 1
fib n = fib (n-1) + fib (n-2)
==>
fib n = v where (_,v) = fibt n
fibt 0 = (1,1)
fibt n = (u+v,u) where (u,v) = fibt (n-1)