True QuickSort in Standard ML - quicksort

Question

Since RosettaCode's Standard ML solution is a very slow version of Quicksort according to the question (and discussion) "Why is the minimalist, example Haskell quicksort not a "true" quicksort?", how would a functional Quicksort look like in Standard ML if it behaved according to the complexity of Hoare's algoritm?
fun quicksort [] = []
| quicksort (x::xs) =
let
val (left, right) = List.partition (fn y => y<x) xs
in
quicksort left # [x] # quicksort right
end
That is, one that employs some aspects of functional programming where it makes sense. Unlike the Haskell version that needs to encapsulate its in-place partitioning, would there be any need for a Quicksort in SML to vary in any way from the C version besides syntax? Whether the function accepts an array/vector or spends O(n) time converting the list is less relevant.
Edit: Rephrased question with regards to John Coleman's comments.

Answer 1

Here is my attempt:
fun swap(A,i,j) =
let
val t = Array.sub(A,i)
in
Array.update(A,i,Array.sub(A,j));
Array.update(A,j,t)
end
fun firstAfter(A,i,f) =
if f(Array.sub(A,i)) then i else firstAfter(A,i+1,f)
fun lastBefore(A,j,f) =
if f(Array.sub(A,j)) then j else lastBefore(A,j-1,f)
fun partition(A,lo,hi)=
let
fun partition'(A,lo,hi,pivot) =
let
val i = firstAfter(A,lo,fn k => k >= pivot)
val j = lastBefore(A,hi,fn k => k <= pivot)
in
if i >= j then
j
else
(
swap(A,i,j);
partition'(A,i+1,j-1,pivot)
)
end
in
partition'(A,lo,hi,Array.sub(A,lo))
end
fun quicksort(A,lo,hi) =
if hi <= lo then
()
else
let
val p = partition(A,lo,hi)
in
(
quicksort(A,lo,p);
quicksort(A,p+1,hi)
)
end;
fun qsort A = quicksort(A,0,Array.length A - 1);
It follows Hoare's algorithm as described in Wikipedia fairly closely but uses recursion rather than loops, and has a somewhat functional approach for looking for pairs of indices to swap. There is no question that this is nowhere nearly as elegant as the 2 or 3 line pseudo-quicksort which is often taught in introductory treatments of functional programming and it doesn't really showcase the powers of functional programming. Hopefully someone who knows more SML than I can come up with a more idiomatic SML qsort.

Answer 2

You can find some of sorting algorithms written in Standard ML in my github repository https://github.com/Khanzadeh-AH/sorting_algorithms_SML
fun pivot_split([], pivot) = ([],[])
| pivot_split(h::t, pivot) =
let
val (L,R) = pivot_split(t, pivot)
in
if h < pivot then (h::L, R)
else (L, h::R)
end;
fun quicksort([]) = []
| quicksort([a]) = [a]
| quicksort(h::t) =
let
val (L, R) = pivot_split(t, h)
in
quicksort(L)#[h]#quicksort(R)
end;
pivot_split([12,3,5,67,1,2,3,5,7],3);
quicksort([12,3,5,67,1,2,3,5,7]);