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Scala type system -> Prolog

View scalatoprolog.md

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.

Breakdown

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).
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