Miles Sabin implemented a nice selection sort example in Scala's type system. See:
http://www.chuusai.com/2012/01/27/type-level-sorting-in-shapeless/
To get a better understanding how that works I ported the algorithm to Prolog.
selectleast([H|T], TM, [H|TRem]):-
selectleast(T, TM, TRem), TM < H.
selectleast([H|T], H, T).
selectionsort(L, [M|ST]):-
selectleast(L, M, Rem), selectionsort(Rem, ST).
selectionsort(S, S).
To test it use a Prolog interpreter:
?- selectleast([3, 1, 4, 0, 2, 5], H, T).
H = 0,
T = [3, 1, 4, 2, 5] .
?- selectionsort([3, 1, 4, 0, 2, 5], Sorted).
Sorted = [0, 1, 2, 3, 4, 5] .
The implementation is perhaps not very idiomatic Prolog code but that's not the point. The nice thing is that the translation from Scala type system syntax is completely straightforward.
Let's start with SelectLeast rule and convert it to Prolog.
/* hlistSelectLeast3(implicit tsl : SelectLeast[T, TM, TRem], ev : TM < H): SelectLeast[H :: T, TM, H :: TRem] */
==>
selectleast([H|T], TM, [H|TRem]):-
selectleast(T, TM, TRem), TM < H.
The return type of 'hlistSelectLeast3' is rule's head. The implicit parameters are the predicates. Lower priority 'hlistSelectLeast1' is simply a Prolog fact.
/* hlistSelectLeast1: SelectLeast[H :: T, H, T] */
==>
selectleast([H|T], H, T).
SelectionSort is converted in a same way.
/* hlistSelectionSort2(implicit sl : SelectLeast[L, M, Rem], sr : SelectionSort[Rem, ST]): SelectionSort[L, M :: ST] */
==>
selectionsort(L, [M|ST]):-
selectleast(L, M, Rem), selectionsort(Rem, ST).
/* hlistSelectionSort1: SelectionSort[S, S] */
==>
selectionsort(S, S).
Miles, I did a little bit Prolog some 15 years ago. So please take my view on what is idiomatic and what is not with a grain of salt :) I think some folks would prefer to make non-recursive cases more explicit. As in this implementation:
That translates to following Shapeless code (seems to work without prioritizing the implicits, I added GT to my Shapeless build):