Iterated functions in Julia

IteratedFunctions.jl

module IteratedFunctions

export IteratedFunction, iterated

struct IteratedFunction{F} <: Function
    f::F
    n::UInt # ensure non-negative
end

IteratedFunction(f, n::Integer) = IteratedFunction(f, UInt(n))

# make it callable
(itfun::IteratedFunction)(x) = foldl((y,_) -> itfun.f(y), 1:itfun.n; init=x)

iterated(f, n=1) = IteratedFunction(f, n)

# collapse nested iterations if possible (does not overflow)
function iterated(itfun::IteratedFunction, n::Int)
    n = UInt(n)
    n <= typemax(UInt) ÷ itfun.n ?
        IteratedFunction(itfun.f, itfun.n * n) :
        IteratedFunction(itfun, n)
end

# do this if you love a thrilling life
Base.:^(f::Function, n) = iterated(f, n)

end # module