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-implementation module StdGameTree
-
-import StdRoseTree
-import StdEnv
-
-// bereken game tree met moves functie en begin toestand:
-gametree :: (Moves s) s -> RoseTree s
-gametree moves s = iteratetree moves s
-
-// bereken minimax-waarde van de root van de game tree:
-minimaxvalue :: (RoseTree w) -> w | Ord,~ w
-minimaxvalue (Node w []) = w
-minimaxvalue (Node _ ts) = w
-where ws = map minimaxvalue ts
- w = ~(minList ws)
-
-// bereken minimax-waarde m.b.v. alpha-beta pruning:
-ab_minimaxvalue :: (w,w) (RoseTree w) -> w | Ord,~,Eq w
-ab_minimaxvalue (a,b) (Node w [ ]) = max a (min w b)
-ab_minimaxvalue (a,b) (Node _ ts) = bound (a,b) ts
-where
- bound :: (w,w) [RoseTree w] -> w | Ord,~,Eq w
- bound (a,b) [] = a
- bound (a,b) [t : ts] = if (a` == b) a` (bound (a`,b) ts)
- where a` = ~ (ab_minimaxvalue (~b,~a) t)
-
-// bereken minimax-waarden van alle nodes van de game tree:
-minimaxtree :: (RoseTree w) -> RoseTree w | Ord,~ w
-minimaxtree (Node w []) = Node w []
-minimaxtree (Node _ ts) = Node w ts`
-where ts` = map minimaxtree ts
- w = ~(minList (map root ts`))
-
-// bereken look-ahead van n ronden, en bereken alle minimax-waarden van de nodes:
-minimax :: PruneDepth (Worth s w) (Moves s) -> s -> RoseTree w | Ord, ~ w
-minimax n w moves = minimaxtree
- o (maptree w)
- o (prunetree (2*n))
- o (gametree moves)
-
-// selecteer optimale volgende zet, met look-ahead n ronden, gebruik makend van minimax waarden
-// van alle nodes van de game tree:
-nextmoves :: PruneDepth (Worth s w) (Moves s) s -> [s] | Ord,~,Eq w
-nextmoves n w moves s = [ s` \\ s` <- moves s
- & w` <- children mtree
- | ~(root w`) == root mtree
- ]
-where mtree = minimax n w moves s
-
-// sorting sub trees for better states first:
-high (Node w ts) = Node w (sortBy higher (map low ts))
-low (Node w ts) = Node w (sortBy lower (map high ts))
-higher t1 t2 = root t1 > root t2
-lower t1 t2 = root t1 <= root t2