已完成Haskell版Delaunay三角剖分代码，求Prolog实现方法

Let's walk through translating your existing Haskell code into Prolog, step by step. Prolog's declarative, logic-driven paradigm is different from Haskell's functional style, but we can map each core concept directly using Prolog's structured terms and predicates.

1. Representing Types (Point, Pair, Triple) #

Unlike Haskell, Prolog doesn't require explicit algebraic data type declarations. Instead, we use structured compound terms to represent these types:

• A 2D point: point(X, Y) where X and Y are numeric coordinates
• A pair of points: pair(P1, P2) where P1 and P2 are point/2 terms
• A triple of points: triple(P1, P2, P3) where each argument is a point/2 term

2. Implementing Core Predicates #

isCCW: Check Counter-Clockwise Order #

This predicate checks if three points form a counter-clockwise turn using the cross product (same logic as your Haskell implementation). It succeeds if the cross product is positive.

% is_ccw(PointA, PointB, PointC) succeeds if A->B->C is counter-clockwise
is_ccw(point(Xa, Ya), point(Xb, Yb), point(Xc, Yc)) :-
    % Calculate cross product: (B - A) × (C - A)
    Cross is (Xb - Xa) * (Yc - Ya) - (Yb - Ya) * (Xc - Xa),
    Cross > 0.

toCCW: Normalize Triple to Counter-Clockwise Order #

This predicate takes any triple of points and returns an equivalent triple ordered counter-clockwise. It handles collinear points with a warning (adjust this logic if you need stricter behavior).

% to_ccw(OriginalTriple, CCWTriple) converts a triple to CCW order
to_ccw(triple(P1, P2, P3), triple(P1, P2, P3)) :-
    is_ccw(P1, P2, P3), !. % Cut to avoid backtracking if already CCW
to_ccw(triple(P1, P2, P3), triple(P1, P3, P2)) :-
    is_ccw(P1, P3, P2), !.
to_ccw(triple(P1, P2, P3), triple(P2, P3, P1)) :-
    is_ccw(P2, P3, P1), !.
% Fallback for collinear points
to_ccw(Triple, Triple) :-
    write('Warning: Collinear points detected; returning original triple'), nl.

pairsFromPoints: Generate Unique Point Pairs #

This predicate generates all unique unordered pairs from a list of points. We use @< to ensure we only generate each pair once (avoids duplicate pair(P2, P1) entries).

% pairs_from_points(PointList, UniquePairs) generates all unique unordered point pairs
pairs_from_points(Points, Pairs) :-
    findall(pair(P1, P2),
            (member(P1, Points), member(P2, Points), P1 @< P2),
            Pairs).

triplesFromPoints: Generate Unique CCW Triples #

This predicate generates all unique counter-clockwise triples from a point list. We first generate raw unordered triples, normalize each to CCW order, then sort to remove duplicates.

% triples_from_points(PointList, UniqueCCWTriples) generates unique CCW triples
triples_from_points(Points, UniqueCCWTriples) :-
    % Generate all unique unordered triples (no permutations)
    findall(triple(P1, P2, P3),
            (member(P1, Points), member(P2, Points), member(P3, Points),
             P1 @< P2, P2 @< P3), % Ensure strict ordering to avoid duplicates
            RawTriples),
    % Normalize each triple to CCW order
    maplist(to_ccw, RawTriples, CCWTriples),
    % Sort to remove duplicate CCW triples (sort automatically dedups)
    sort(CCWTriples, UniqueCCWTriples).

3. Key Differences from Haskell #

• Predicates vs. Functions: Prolog uses relations (predicates) instead of functions. Instead of returning a value, a predicate succeeds or fails, and can generate multiple solutions.
• Explicit Collection: Use findall/3 to collect results into a list (similar to Haskell's list comprehensions).
• Deduplication: Prolog's sort/2 not only sorts lists but removes duplicate elements, which is handy for ensuring unique triples/pairs.
• Term Order: The @< operator compares Prolog terms lexicographically, which works for point/2 terms since it compares X-coordinates first, then Y.

Example Usage #

% Define a test point set
test_points([point(0,0), point(1,0), point(0,1), point(1,1)]).

% Query to get unique CCW triples
?- test_points(Points), triples_from_points(Points, Triples).
Triples = [triple(point(0,0),point(0,1),point(1,0)), triple(point(0,0),point(1,0),point(1,1)), triple(point(0,1),point(1,0),point(1,1))] ;
false.

内容的提问来源于stack exchange，提问作者Ray Sousa