Tupling
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)
