findType passing every test I've thrown at it!

app/Check.hs

@@ -1,4 +1,3 @@
-{-# LANGUAGE BangPatterns #-}
 module Check where
 
 import Control.Monad.Except
@@ -6,7 +5,6 @@ import Data.List (intercalate, (!?))
 
 import Control.Monad (unless)
 import Expr
-import Debug.Trace
 
 type Context = [Expr]
 
@@ -22,34 +20,27 @@ matchPi e = Left $ ExpectedFunctionType e
 showContext :: Context -> String
 showContext g = "[" ++ intercalate ", " (map show g) ++ "]"
 
--- TODO: Debug these problem cases
--- λ (S : *) (P : S -> *) (H : forall (x : S), P x) (y : S) => P y
 findType :: Context -> Expr -> CheckResult Expr
-findType _ Star = trace "star" $ Right Square
-findType _ Square = trace "square" $ Left SquareUntyped
+findType _ Star = Right Square
+findType _ Square = Left SquareUntyped
 findType g (Var n _) = do
-    !_ <- trace ("var:\t" ++ showContext g ++ "\n  n:\t" ++ show n) (Right Star)
     t <- maybe (Left UnboundVariable) Right $ g !? fromInteger n
     s <- findType g t
     unless (isSort s) $ throwError $ NotASort s 32
     pure t
 findType g (App m n) = do
-    !_ <- trace ("app:\t" ++ showContext g ++ "\n  m:\t" ++ show m ++ "\n  n: \t" ++ show n) (Right Star)
     (a, b) <- findType g m >>= matchPi
     a' <- findType g n
     unless (betaEquiv a a') $ throwError $ NotEquivalent a a'
-    pure $ subst n b
+    pure $ subst 0 n b
 findType g (Abs x a m) = do
-    !_ <- trace ("abs:\t" ++ showContext g ++ "\n  a:\t" ++ show a ++ "\n  m:\t" ++ show m) (Right Star)
     s1 <- findType g a
-    !_ <- trace ("back in abs:\t" ++ showContext g ++ "\n\t\t" ++ show a ++ " : " ++ show s1) (Right Star)
     unless (isSort s1) $ throwError $ NotASort s1 43
     b <- findType (incIndices a : map incIndices g) m
     s2 <- findType g (Pi x a b)
     unless (isSort s2) $ throwError $ NotASort s2 46
     pure $ if occursFree 0 b then Pi x a b else Pi "" a b
 findType g (Pi _ a b) = do
-    !_ <- trace ("pi:\t" ++ showContext g ++ "\n  a:\t" ++ show a ++ "\n  b:\t" ++ show b) (Right Star)
     s1 <- findType g a
     unless (isSort s1) $ throwError $ NotASort s1 51
     s2 <- findType (incIndices a : map incIndices g) b

app/Expr.hs

@@ -11,7 +11,16 @@ data Expr where
     App :: Expr -> Expr -> Expr
     Abs :: String -> Expr -> Expr -> Expr
     Pi :: String -> Expr -> Expr -> Expr
-    deriving (Show, Eq)
+    deriving (Show)
+
+instance Eq Expr where
+    (Var n _) == (Var m _) = n == m
+    Star == Star = True
+    Square == Square = True
+    (App e1 e2) == (App f1 f2) = e1 == f1 && e2 == f2
+    (Abs _ t1 b1) == (Abs _ t2 b2) = t1 == t2 && b1 == b2
+    (Pi _ t1 b1) == (Pi _ t2 b2) = t1 == t2 && b1 == b2
+    _ == _ = False
 
 infixl 4 <.>
 
@@ -55,7 +64,7 @@ groupParams = foldr addParam []
     addParam :: (String, Expr) -> [([String], Expr)] -> [([String], Expr)]
     addParam (x, t) [] = [([x], t)]
     addParam (x, t) l@((xs, s) : rest)
-        | t == s = (x : xs, t) : rest
+        | incIndices t == s = (x : xs, t) : rest
         | otherwise = ([x], t) : l
 
 showParamGroup :: ([String], Expr) -> String
@@ -69,8 +78,8 @@ helper k (App e1 e2) = if k > 3 then parenthesize res else res
   where
     res = helper 3 e1 ++ " " ++ helper 4 e2
 helper k (Pi "" t1 t2) = if k > 2 then parenthesize res else res
-    where
-        res = helper 3 t1 ++ " -> " ++ helper 2 t2
+  where
+    res = helper 3 t1 ++ " -> " ++ helper 2 t2
 helper k e@(Pi{}) = if k > 2 then parenthesize res else res
   where
     (params, body) = collectPis e
@@ -92,38 +101,35 @@ isSort Star = True
 isSort Square = True
 isSort _ = False
 
+shiftIndices :: Integer -> Integer -> Expr -> Expr
+shiftIndices d c (Var k x)
+    | k >= c = Var (k + d) x
+    | otherwise = Var k x
+shiftIndices _ _ Star = Star
+shiftIndices _ _ Square = Square
+shiftIndices d c (App m n) = App (shiftIndices d c m) (shiftIndices d c n)
+shiftIndices d c (Abs x m n) = Abs x (shiftIndices d c m) (shiftIndices d (c + 1) n)
+shiftIndices d c (Pi x m n) = Pi x (shiftIndices d c m) (shiftIndices d (c + 1) n)
+
 incIndices :: Expr -> Expr
-incIndices (Var n x) = Var (n + 1) x
-incIndices Star = Star
-incIndices Square = Square
-incIndices (App m n) = App (incIndices m) (incIndices n)
-incIndices (Abs x m n) = Abs x (incIndices m) (incIndices n)
-incIndices (Pi x m n) = Pi x (incIndices m) (incIndices n)
+incIndices = shiftIndices 1 0
 
--- substitute s for 0 *AND* decrement indices; only use after reducing a redex.
-subst :: Expr -> Expr -> Expr
-subst s (Var 0 _) = s
-subst _ (Var n s) = Var (n - 1) s
-subst _ Star = Star
-subst _ Square = Square
-subst s (App m n) = App (subst s m) (subst s n)
-subst s (Abs x m n) = Abs x (subst s m) (subst s n)
-subst s (Pi x m n) = Pi x (subst s m) (subst s n)
-
-substnd :: Expr -> Expr -> Expr
-substnd s (Var 0 _) = s
-substnd _ (Var n s) = Var (n - 1) s
-substnd _ Star = Star
-substnd _ Square = Square
-substnd s (App m n) = App (substnd s m) (substnd s n)
-substnd s (Abs x m n) = Abs x (substnd s m) (substnd s n)
-substnd s (Pi x m n) = Pi x (substnd s m) (substnd s n)
+-- substitute s for k *AND* decrement indices; only use after reducing a redex.
+subst :: Integer -> Expr -> Expr -> Expr
+subst k s (Var n x)
+    | k == n = s
+    | otherwise = Var (n - 1) x
+subst _ _ Star = Star
+subst _ _ Square = Square
+subst k s (App m n) = App (subst k s m) (subst k s n)
+subst k s (Abs x m n) = Abs x (subst k s m) (subst (k + 1) (incIndices s) n)
+subst k s (Pi x m n) = Pi x (subst k s m) (subst (k + 1) (incIndices s) n)
 
 betaReduce :: Expr -> Expr
 betaReduce (Var k s) = Var k s
 betaReduce Star = Star
 betaReduce Square = Square
-betaReduce (App (Abs _ _ v) n) = subst n v
+betaReduce (App (Abs _ _ v) n) = subst 0 n v
 betaReduce (App m n) = App (betaReduce m) (betaReduce n)
 betaReduce (Abs x t v) = Abs x (betaReduce t) (betaReduce v)
 betaReduce (Pi x t v) = Pi x (betaReduce t) (betaReduce v)

app/Main.hs

@@ -12,7 +12,7 @@ main = do
     input <- getLine
     case pAll input of
         Left err -> putStrLn err
-        Right expr -> print expr >> case findType [] expr of
+        Right expr -> case findType [] expr of
             Right ty -> putStrLn $ pretty expr ++ " : " ++ pretty ty
             Left err -> print err
     main

app/Parser.hs

@@ -7,7 +7,7 @@ import Data.Functor.Identity
 import Data.List (elemIndex)
 import Data.List.NonEmpty (NonEmpty ((:|)))
 import qualified Data.List.NonEmpty as NE
-import Expr (Expr (..), (.->), incIndices)
+import Expr (Expr (..), incIndices, (.->))
 import Text.Megaparsec hiding (State)
 import Text.Megaparsec.Char
 import qualified Text.Megaparsec.Char.Lexer as L
@@ -56,7 +56,7 @@ pParamGroup = lexeme $ label "parameter group" $ between (char '(') (char ')') $
     idents <- some pIdentifier
     _ <- defChoice $ ":" :| []
     ty <- pExpr
-    modify (idents ++)
+    modify (flip (foldl $ flip (:)) idents)
     pure $ zip idents (iterate incIndices ty)
 
 pParams :: Parser [(String, Expr)]