feat(allsat): add model enumeration over all solutions

src/Sift/Enumerate.hs

@@ -0,0 +1,38 @@
+module Sift.Enumerate
+  ( projectModel
+  , blockingClause
+  , allModels
+  , countModels
+  , countQueensSolutions
+  ) where
+
+import Sift.Types
+import Sift.Cdcl (CdclResult(..), solveCdcl)
+import Sift.Encode.Queens (queens, queensCell)
+import qualified Data.Map.Strict as Map
+
+projectModel :: [Var] -> Assignment -> Assignment
+projectModel vars model =
+  Map.fromList [ (v, Map.findWithDefault False v model) | v <- vars ]
+
+blockingClause :: [Var] -> Assignment -> Clause
+blockingClause vars model =
+  [ if Map.findWithDefault False v model then negLit v else posLit v | v <- vars ]
+
+allModels :: [Var] -> CNF -> [Assignment]
+allModels projVars (CNF cs0) = go cs0
+  where
+    go cs = case solveCdcl (CNF cs) of
+      CdclUnsat -> []
+      CdclSat model ->
+        let projected = projectModel projVars model
+        in projected : go (blockingClause projVars projected : cs)
+
+countModels :: [Var] -> CNF -> Int
+countModels projVars = length . allModels projVars
+
+countQueensSolutions :: Int -> Int
+countQueensSolutions n =
+  countModels boardVars (queens n)
+  where
+    boardVars = [ queensCell n r c | r <- [1 .. n], c <- [1 .. n] ]