\DOC funpow
\TYPE {Compat.funpow : (int -> ('a -> 'a) -> 'a -> 'a)}
\SYNOPSIS
Iterates a function a fixed number of times.
\DESCRIBE
{funpow n f x} applies {f} to {x}, {n} times, giving the result {f (f ...
(f
x)...)} where the number of {f}'s is {n}. {funpow 0 f x} returns {x}. If
{n} is
negative, {funpow n f x} will either fail or loop indefinitely, depending
on
the values of {f} and {x}.
\FAILURE
{funpow n f x} fails if any of the {n} applications of f fail. It will
not be
in the ML environment if the {hol88} library has not been loaded.
\EXAMPLE
Apply {tl} three times to a list:
{
- funpow 3 tl [1,2,3,4,5];
[4, 5] : int list
}
Apply {tl} zero times:
{
- funpow 0 tl [1,2,3,4,5];
[1, 2, 3, 4, 5] : int list
}
Apply {tl} six times to a list of only five elements:
{
- funpow 6 tl [1,2,3,4,5];
uncaught exception Tl
}
Next, an application of {funpow} in which the integer argument is
negative. Since the function cannot be applied to the argument an
arbitrary
number of times, the application of {funpow} fails.
{
- funpow ~1 tl [1,2,3,4,5];
uncaught exception Tl
}
An example that causes indefinite looping:
{
- funpow ~1 I [1,2,3,4,5];
}
\ENDDOC