I want to wrap a function with keyword arguments. Here is what I am trying to do,

# Wraps `fk(x)` with `d`, i.e. `fn(x) = fk(d * x)`
function wrapper(fk)
function fn(x; d = 1)
@show d
fk(d * x)
end
end
# Wraps `fi`, `niter` times
wrap(fi, niter) = ∘([wrapper for _ in 1 : niter]...)(fi)
# Get wrapped function `h`
niter = 5;
f0(x) = x;
h = wrap(f0, niter);

and this is the output I get when I call h with d specified.

julia> h(5, d=10);
d = 10
d = 1
d = 1
d = 1
d = 1

The problem here is that the keyword parameter d is evaluated as 10 just once (I think just when the function is compiled), not 5 times. I wonder if it is possible to evaluate as 10 for 5 times, not just for once?

Neither of them, actually. Simply stated, consider that there is a mapping T[f_k; d[ that maps f_k to f_{k + 1} such that f_{k + 1}(x) = T[f_k; d](x) = f_k(d \cdot x). Here, d \in \mathbb{R} is a parameter of the mapping T[f_k; d]. Given an initial function f_0(x), I want to compute the limit f^* of the mapping T[f_k; d], i.e., f^*(x) = \lim\limits_{k \mapsto \infty} T[f_k; d](x) \approx T^{\circ N}[f_0; d] for some large N where \circ is the composition operator. So, what I really want is the limit f^* of T[f_k;d] (which is a composed function, not a sequence of numbers, or a vector of functions).

If the initial function f0(x) also accepts a keyword argument, I think the following works.

function wrapper(fk)
function fn(x; d = 1)
@show d
fk(d * x; d=d)
end
end
wrap(fi, niter) = ∘([wrapper for _ in 1 : niter]...)(fi)
niter = 5;
f0(x; d=1) = x;
h = wrap(f0, niter);
h(5, d = 10)

You probably realize this already, but I’ll just comment that the behavior you see is expected. If you unroll your original h (with niter = 2 for simplicity), you get

h = function fn(x; d = 1)
@show d
(function fn(x; d = 1)
@show d
f0(d * x)
end)(d * x)
end

so h(5, d = 10) only modifies the d of the outermost fn, not any of the inner ds.

I started this post before your most recent post, so it looks like you already figured it out. But I’ll leave this comment in case it helps someone else understand why.