Next we consider an alternate solution to the problem from Section 2.3 of computing the product of the integers 1 to k which does not use the divide and conquer strategy.
The definition
factorial_iter =: monad define script
('n' ; 'acc' ; 'i') =. y.
if. i > n
do. acc
else. factorial_iter n , (i * acc) , i + 1
end.
)
computes the product of the integers 1 to 5 when applied to the argument 5 1 1.
A cover function for factorial_iter may be defined as
factorial1 =: monad define 'factorial_iter y. , 1 1'
so that
factorial1 5 produces a result of 120.
The analysis of factorial_iter is similar to the analysis
of sum-iter in Section 5.1. The
continuation of the recursive call to factorial_iter in
the definition of factorial_iter is
monad define 'y.'
Hence, no continuations need be saved and an optimizing compiler or
interpreter will replace the recursion with iteration which directly
computes the product of the integers 1 to k using a single call to
factorial_iter.