From e7bed242ba52e6d3233928f2c6189e701cfa5e4c Mon Sep 17 00:00:00 2001
From: Tom Smeding <tom@tomsmeding.com>
Date: Thu, 14 Mar 2024 23:21:53 +0100
Subject: Some typechecker work

---
 src/HSVIS/Typecheck/Solve.hs | 103 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 103 insertions(+)
 create mode 100644 src/HSVIS/Typecheck/Solve.hs

(limited to 'src/HSVIS/Typecheck')

diff --git a/src/HSVIS/Typecheck/Solve.hs b/src/HSVIS/Typecheck/Solve.hs
new file mode 100644
index 0000000..184937c
--- /dev/null
+++ b/src/HSVIS/Typecheck/Solve.hs
@@ -0,0 +1,103 @@
+{-# LANGUAGE ScopedTypeVariables #-}
+module HSVIS.Typecheck.Solve where
+
+import Control.Monad (guard, (>=>))
+import Data.Bifunctor (second)
+import Data.Foldable (toList, foldl')
+import Data.List (sort)
+import Data.Ord (comparing)
+import Data.Map.Strict (Map)
+import qualified Data.Map.Strict as Map
+
+import Debug.Trace
+
+import Data.Bag
+import Data.List (minimumBy)
+
+
+data UnifyErr v t
+  = UEUnequal t t
+  | UERecursive v t
+  deriving (Show)
+
+-- | Returns a pair of:
+-- 1. A set of unification errors;
+-- 2. An assignment of the variables that had any constraints on them.
+-- The producedure was successful if the set of errors is empty. Note that
+-- unconstrained variables do not appear in the output.
+solveConstraints
+  :: forall v t. (Ord v, Ord t, Show v, Show t)
+     -- | reduce: take two types and unify them, resulting in:
+     -- 1. A bag of resulting constraints on variables;
+     -- 2. A bag of errors: pairs of two types that are provably distinct but
+     --    need to be equal for the input types to unify.
+  => (t -> t -> (Bag (v, t), Bag (t, t)))
+     -- | Free variables in a type
+  -> (t -> Bag v)
+     -- | \v repl term -> Substitute v by repl in term
+  -> (v -> t -> t -> t)
+     -- | Detect bare-variable types
+  -> (t -> Maybe v)
+     -- | Some kind of size measure on types
+  -> (t -> Int)
+     -- | Equality constraints to solve
+  -> [(t, t)]
+  -> (Map v t, Bag (UnifyErr v t))
+solveConstraints reduce frees subst detect size = \cs ->
+  let (vcs, errs) = foldMap (uncurry reduce) cs
+      asg = Map.fromListWith (<>) (map (second pure) (toList vcs))
+      (errs', asg') = loop asg []
+      errs'' = fmap (uncurry UEUnequal) errs <> errs'
+  in trace ("[solver] Solving:" ++ concat ["\n- " ++ show a ++ "  ==  " ++ show b | (a, b) <- cs]) $
+     trace ("[solver] Result: (with " ++ show (length errs'') ++ " errors)" ++
+              concat ["\n- " ++ show v ++ " = " ++ show t | (v, t) <- Map.assocs asg'])
+     (asg', errs'')
+  where
+    loop :: Map v (Bag t) -> [(v, t)] -> (Bag (UnifyErr v t), Map v t)
+    loop m eqlog = do
+      traceM $ "[solver] Step:" ++ concat ["\n- " ++ show v ++ " == " ++ show t | (v, t) <- Map.assocs m]
+      m' <- Map.traverseWithKey
+              (\v ts ->
+                let ts' = bagFromList (dedup (toList ts))
+                    -- filter out recursive equations
+                    (recs, nonrecs) = bagPartition (\t -> if v `elem` frees t then Just t else Nothing) ts'
+                    -- filter out trivial equations (v = v)
+                    (_, nonrecs') = bagPartition (detect >=> guard . (== v)) nonrecs
+                in (UERecursive v <$> recs, nonrecs'))
+              m
+
+      let msmallestvar = -- var with its smallest RHS, if such a var exists
+            minimumByMay (comparing (size . snd))
+            . map (second (minimumBy (comparing size)))
+            . filter (not . null . snd)
+            $ Map.assocs m'
+
+      case msmallestvar of
+        Nothing -> return $ applyLog eqlog mempty
+        Just (var, smallrhs) -> do
+          let (_, otherrhss) = bagPartition (guard . (== smallrhs)) (m' Map.! var)
+          let (newcs, errs) = foldMap (reduce smallrhs) (dedup (toList otherrhss))
+          (fmap (uncurry UEUnequal) errs, ())  -- write the errors
+          let m'' = Map.unionWith (<>)
+                      (Map.map (fmap (subst var smallrhs)) (Map.delete var m'))
+                      (Map.fromListWith (<>) (map (second pure) (toList newcs)))
+          loop m'' ((var, smallrhs) : eqlog)
+
+    applyLog :: [(v, t)] -> Map v t -> Map v t
+    applyLog ((v, t) : l) m = applyLog l $ Map.insert v t (Map.map (subst v t) m)
+    applyLog [] m = m
+
+    dedup :: Ord t => [t] -> [t]
+    dedup = uniq . sort
+
+    uniq :: Eq a => [a] -> [a]
+    uniq (x:y:xs) | x == y = uniq (x : xs)
+                  | otherwise = x : uniq (y : xs)
+    uniq l = l
+
+    minimumByMay :: Foldable t' => (a -> a -> Ordering) -> t' a -> Maybe a
+    minimumByMay cmp = foldl' min' Nothing
+      where min' mx y = Just $! case mx of
+                                  Nothing -> y
+                                  Just x | GT <- cmp x y -> y
+                                         | otherwise -> x
-- 
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