diff --git a/app/Main.hs b/app/Main.hs
index 92531bf..32976de 100644
--- a/app/Main.hs
+++ b/app/Main.hs
@@ -1,8 +1,6 @@
 module Main where
 
-import Check
 import qualified Data.Text.IO as T
-import Expr
 import Parser
 import Repl
 import System.Environment
@@ -23,8 +21,4 @@ handleFile fileName =
         input <- T.hGetContents fileH
         case pAll input of
             Left err -> putStrLn err
-            Right expr -> case findType [] expr of
-                Left err -> print err
-                Right ty -> do
-                    putStrLn $ "expr:\t" ++ prettyS expr
-                    putStrLn $ "type:\t" ++ prettyS ty
+            Right () -> putStrLn "success!"
diff --git a/app/Repl.hs b/app/Repl.hs
index fee1189..97989be 100644
--- a/app/Repl.hs
+++ b/app/Repl.hs
@@ -2,6 +2,7 @@ module Repl (repl) where
 
 import Check
 import qualified Data.Text as T
+import qualified Data.Map as M
 import Expr
 import Parser
 import System.Console.Haskeline
@@ -23,12 +24,7 @@ parseCommand (Just input) = Just (Input input)
 handleInput :: ReplState -> String -> InputT IO ()
 handleInput state input = case pAll (T.pack input) of
     Left err -> outputStrLn err
-    Right expr -> case findType [] expr of
-        Left err -> outputStrLn $ show err
-        Right ty ->
-            if debugMode state
-                then printDebugInfo expr ty
-                else outputStrLn $ prettyS ty
+    Right () -> pure ()
 
 printDebugInfo :: Expr -> Expr -> InputT IO ()
 printDebugInfo expr ty = do
diff --git a/dependent-lambda.cabal b/dependent-lambda.cabal
index 29901be..8d40e74 100644
--- a/dependent-lambda.cabal
+++ b/dependent-lambda.cabal
@@ -24,13 +24,15 @@ build-type:         Simple
 extra-doc-files:    CHANGELOG.md
                   , README.md
 
--- Extra source files to be distributed with the package, such as examples, or a tutorial module.
--- extra-source-files:
+common warnings
+    ghc-options: -Wall
 
 library dependent-lambda-lib
+    import:             warnings
     exposed-modules:    Check
                         Parser
                         Expr
+                        Eval
 
     hs-source-dirs:     lib
     build-depends:      base ^>=4.19.1.0
@@ -38,13 +40,11 @@ library dependent-lambda-lib
                       , text
                       , parser-combinators
                       , mtl
+                      , containers
     default-language:   Haskell2010
     default-extensions: OverloadedStrings
                       , GADTs
 
-common warnings
-    ghc-options: -Wall
-
 executable dependent-lambda
     import:             warnings
     main-is:            Main.hs
@@ -53,6 +53,7 @@ executable dependent-lambda
     build-depends:      base ^>=4.19.1.0
                       , dependent-lambda-lib
                       , text
+                      , containers
                       , haskeline
                       , directory
                       , filepath
@@ -62,6 +63,7 @@ executable dependent-lambda
                       , GADTs
 
 test-suite tests
+    import:             warnings
     type:               exitcode-stdio-1.0
     main-is:            Tests.hs
     other-modules:      ExprTests
@@ -70,6 +72,7 @@ test-suite tests
     build-depends:      base ^>=4.19.1.0
                       , HUnit
                       , text
+                      , containers
                       , dependent-lambda-lib
     hs-source-dirs:     tests
     default-language:   Haskell2010
diff --git a/lib/Check.hs b/lib/Check.hs
index aca307c..bcf8278 100644
--- a/lib/Check.hs
+++ b/lib/Check.hs
@@ -1,16 +1,19 @@
-module Check (TypeCheckError (..), CheckResult (..), findType) where
+module Check (TypeCheckError (..), CheckResult, checkType) where
 
+import Control.Monad (unless)
 import Control.Monad.Except (MonadError (throwError))
-import Data.List (intercalate, (!?))
+import Control.Monad.Reader
+import Data.List ((!?))
+import qualified Data.Map as M
 import Data.Text (Text)
 import qualified Data.Text as T
 
-import Control.Monad (unless)
+import Eval
 import Expr
 
 type Context = [Expr]
 
-data TypeCheckError = SquareUntyped | UnboundVariable Text | NotASort Expr Expr | ExpectedPiType Expr Expr | NotEquivalent Expr Expr Expr deriving (Eq)
+data TypeCheckError = SquareUntyped | UnboundVariable Text | NotASort Expr Expr | ExpectedPiType Expr Expr | NotEquivalent Expr Expr Expr deriving (Eq, Ord)
 
 instance Show TypeCheckError where
     show SquareUntyped = "□ does not have a type"
@@ -21,25 +24,24 @@ instance Show TypeCheckError where
 
 type CheckResult = Either TypeCheckError
 
-matchPi :: Expr -> Expr -> CheckResult (Expr, Expr)
-matchPi _ (Pi _ a b) = Right (a, b)
-matchPi m e = Left $ ExpectedPiType m e
+matchPi :: Expr -> Expr -> ReaderT Env CheckResult (Expr, Expr)
+matchPi _ (Pi _ a b) = pure (a, b)
+matchPi m e = throwError $ ExpectedPiType m e
 
-showContext :: Context -> String
-showContext g = "[" ++ intercalate ", " (map show g) ++ "]"
-
-findType :: Context -> Expr -> CheckResult Expr
-findType _ Star = Right Square
-findType _ Square = Left SquareUntyped
+findType :: Context -> Expr -> ReaderT Env CheckResult Expr
+findType _ Star = pure Square
+findType _ Square = throwError SquareUntyped
 findType g (Var n x) = do
-    t <- maybe (Left $ UnboundVariable x) Right $ g !? fromInteger n
+    t <- maybe (throwError $ UnboundVariable x) pure $ g !? fromInteger n
     s <- findType g t
     unless (isSort s) $ throwError $ NotASort t s
     pure t
+findType g (Free n) = asks (M.lookup n) >>= maybe (throwError $ UnboundVariable n) (findType g)
 findType g e@(App m n) = do
     (a, b) <- findType g m >>= matchPi m
     a' <- findType g n
-    unless (betaEquiv a a') $ throwError $ NotEquivalent a a' e
+    equiv <- asks $ runReader (betaEquiv a a')
+    unless equiv $ throwError $ NotEquivalent a a' e
     pure $ subst 0 n b
 findType g (Abs x a m) = do
     s1 <- findType g a
@@ -54,3 +56,6 @@ findType g (Pi _ a b) = do
     s2 <- findType (incIndices a : map incIndices g) b
     unless (isSort s2) $ throwError $ NotASort b s2
     pure s2
+
+checkType :: Env -> Context -> Expr -> CheckResult Expr
+checkType env g t = runReaderT (findType g t) env
diff --git a/lib/Eval.hs b/lib/Eval.hs
new file mode 100644
index 0000000..ee3ab51
--- /dev/null
+++ b/lib/Eval.hs
@@ -0,0 +1,39 @@
+module Eval where
+
+import Control.Monad.Reader
+import qualified Data.Map as M
+import Data.Maybe
+import Data.Text (Text)
+import Expr
+
+type Env = M.Map Text Expr
+
+-- 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
+    | n > k = Var (n - 1) x
+    | otherwise = Var n x
+subst _ _ (Free s) = Free s
+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)
+
+whnf :: Expr -> Expr
+whnf (App (Abs _ _ v) n) = whnf $ subst 0 n v
+whnf e = e
+
+betaEquiv :: Expr -> Expr -> Reader Env Bool
+betaEquiv e1 e2
+    | e1 == e2 = pure True
+    | otherwise = case (whnf e1, whnf e2) of
+        (Var k1 _, Var k2 _) -> pure $ k1 == k2
+        (Free n, Free m) -> pure $ n == m
+        (Free n, e) -> fromMaybe False <$> (asks (M.lookup n) >>= traverse (`betaEquiv` e))
+        (e, Free n) -> fromMaybe False <$> (asks (M.lookup n) >>= traverse (`betaEquiv` e))
+        (Star, Star) -> pure True
+        (Abs _ t1 v1, Abs _ t2 v2) -> (&&) <$> betaEquiv t1 t2 <*> betaEquiv v1 v2 -- i want idiom brackets
+        (Pi _ t1 v1, Pi _ t2 v2) -> (&&) <$> betaEquiv t1 t2 <*> betaEquiv v1 v2
+        _ -> pure False -- remaining cases impossible or false
diff --git a/lib/Expr.hs b/lib/Expr.hs
index 9994281..ac41840 100644
--- a/lib/Expr.hs
+++ b/lib/Expr.hs
@@ -6,12 +6,13 @@ import qualified Data.Text as T
 
 data Expr where
     Var :: Integer -> Text -> Expr
+    Free :: Text -> Expr
     Star :: Expr
     Square :: Expr
     App :: Expr -> Expr -> Expr
     Abs :: Text -> Expr -> Expr -> Expr
     Pi :: Text -> Expr -> Expr -> Expr
-    deriving (Show)
+    deriving (Show, Ord)
 
 instance Eq Expr where
     (Var n _) == (Var m _) = n == m
@@ -24,12 +25,32 @@ instance Eq Expr where
 
 occursFree :: Integer -> Expr -> Bool
 occursFree n (Var k _) = n == k
+occursFree _ (Free _) = False
 occursFree _ Star = False
 occursFree _ Square = False
 occursFree n (App a b) = on (||) (occursFree n) a b
 occursFree n (Abs _ a b) = occursFree n a || occursFree (n + 1) b
 occursFree n (Pi _ a b) = occursFree n a || occursFree (n + 1) b
 
+isSort :: Expr -> Bool
+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 _ _ (Free s) = Free s
+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 = shiftIndices 1 0
+
 {- --------------------- PRETTY PRINTING ----------------------------- -}
 
 parenthesize :: Text -> Text
@@ -62,6 +83,7 @@ showParamGroup (ids, ty) = parenthesize $ T.unwords ids <> " : " <> pretty ty
 
 helper :: Integer -> Expr -> Text
 helper _ (Var _ s) = s
+helper _ (Free s) = s
 helper _ Star = "*"
 helper _ Square = "□"
 helper k (App e1 e2) = if k > 3 then parenthesize res else res
@@ -86,63 +108,3 @@ pretty = helper 0
 
 prettyS :: Expr -> String
 prettyS = T.unpack . pretty
-
-{- --------------- ACTUAL MATH STUFF ---------------- -}
-
-isSort :: Expr -> Bool
-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 = shiftIndices 1 0
-
--- 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
-    | n > k = Var (n - 1) x
-    | otherwise = Var n 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 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)
-
-betaNF :: Expr -> Expr
-betaNF e = if e == e' then e else betaNF e'
-  where
-    e' = betaReduce e
-
-whnf :: Expr -> Expr
-whnf (App (Abs _ _ v) n) = whnf $ subst 0 n v
-whnf e = e
-
-betaEquiv :: Expr -> Expr -> Bool
-betaEquiv e1 e2
-    | e1 == e2 = True
-    | otherwise = case (whnf e1, whnf e2) of
-        (Var k1 _, Var k2 _) -> k1 == k2
-        (Star, Star) -> True
-        (Abs _ t1 v1, Abs _ t2 v2) -> betaEquiv t1 t2 && betaEquiv v1 v2
-        (Pi _ t1 v1, Pi _ t2 v2) -> betaEquiv t1 t2 && betaEquiv v1 v2
-        _ -> False -- remaining cases impossible or false
diff --git a/lib/Parser.hs b/lib/Parser.hs
index c17260c..d00c4b3 100644
--- a/lib/Parser.hs
+++ b/lib/Parser.hs
@@ -1,5 +1,8 @@
+{-# LANGUAGE NamedFieldPuns #-}
+
 module Parser (pAll) where
 
+import Check
 import Control.Monad
 import Control.Monad.State.Strict
 import Data.Bifunctor (first)
@@ -7,22 +10,30 @@ import Data.Functor.Identity
 import Data.List (elemIndex)
 import Data.List.NonEmpty (NonEmpty ((:|)))
 import qualified Data.List.NonEmpty as NE
+import qualified Data.Map as M
 import Data.Text (Text)
 import qualified Data.Text as T
+import Eval
 import Expr (Expr (..), incIndices)
 import Text.Megaparsec hiding (State)
 import Text.Megaparsec.Char
 import qualified Text.Megaparsec.Char.Lexer as L
 
-type InnerState = [Text]
+data InnerState = IS {_binds :: [Text], _defs :: Env}
 
-data CustomErrors = UnboundVariable Text [Text] deriving (Eq, Ord, Show)
+newtype TypeError = TE TypeCheckError
+    deriving (Eq, Ord, Show)
 
-instance ShowErrorComponent CustomErrors where
-    showErrorComponent (UnboundVariable var bound) =
-        "Unbound variable: " ++ T.unpack var ++ ". Did you mean one of: " ++ T.unpack (T.unwords bound) ++ "?"
+type Parser = ParsecT TypeError Text (State InnerState)
 
-type Parser = ParsecT CustomErrors Text (State InnerState)
+instance ShowErrorComponent TypeError where
+  showErrorComponent (TE e) = show e
+
+bindsToIS :: ([Text] -> [Text]) -> InnerState -> InnerState
+bindsToIS f x@(IS{_binds}) = x{_binds = f _binds}
+
+defsToIS :: (Env -> Env) -> InnerState -> InnerState
+defsToIS f x@(IS{_defs}) = x{_defs = f _defs}
 
 skipSpace :: Parser ()
 skipSpace =
@@ -38,15 +49,15 @@ pIdentifier :: Parser Text
 pIdentifier = label "identifier" $ lexeme $ do
     firstChar <- letterChar <|> char '_'
     rest <- many $ alphaNumChar <|> char '_'
-    return $ T.pack (firstChar : rest) -- Still need T.pack here as we're building from chars
+    return $ T.pack (firstChar : rest)
 
 pVar :: Parser Expr
 pVar = label "variable" $ lexeme $ do
     var <- pIdentifier
-    binders <- get
-    case elemIndex var binders of
-        Just i -> return $ Var (fromIntegral i) var
-        Nothing -> customFailure $ UnboundVariable var binders
+    binders <- _binds <$> get
+    pure $ case elemIndex var binders of
+        Just i -> Var (fromIntegral i) var
+        Nothing -> Free var
 
 defChoice :: NE.NonEmpty Text -> Parser ()
 defChoice options = lexeme $ label (T.unpack $ NE.head options) $ void $ choice $ NE.map chunk options
@@ -56,7 +67,7 @@ pParamGroup = lexeme $ label "parameter group" $ between (char '(') (char ')') $
     idents <- some pIdentifier
     _ <- defChoice $ ":" :| []
     ty <- pExpr
-    modify (flip (foldl $ flip (:)) idents)
+    modify $ bindsToIS $ flip (foldl $ flip (:)) idents
     pure $ zip idents (iterate incIndices ty)
 
 pParams :: Parser [(Text, Expr)]
@@ -68,7 +79,7 @@ pLAbs = lexeme $ label "λ-abstraction" $ do
     params <- pParams
     _ <- defChoice $ "." :| ["=>", "⇒"]
     body <- pExpr
-    modify (drop $ length params)
+    modify $ bindsToIS $ drop $ length params
     pure $ foldr (uncurry Abs) body params
 
 pPAbs :: Parser Expr
@@ -77,7 +88,7 @@ pPAbs = lexeme $ label "Π-abstraction" $ do
     params <- pParams
     _ <- defChoice $ "." :| [","]
     body <- pExpr
-    modify (drop $ length params)
+    modify $ bindsToIS $ drop $ length params
     pure $ foldr (uncurry Pi) body params
 
 pArrow :: Parser Expr
@@ -112,5 +123,20 @@ pAppTerm = lexeme $ pLAbs <|> pPAbs <|> pApp
 pExpr :: Parser Expr
 pExpr = lexeme $ try pArrow <|> pAppTerm
 
-pAll :: Text -> Either String Expr
-pAll input = first errorBundlePretty $ fst $ runIdentity $ runStateT (runParserT pExpr "" input) []
+pDef :: Parser ()
+pDef = lexeme $ label "definition" $ do
+    ident <- pIdentifier
+    _ <- defChoice $ ":=" :| []
+    value <- pExpr
+    _ <- defChoice $ ";" :| []
+    foo <- get
+    let ty = checkType (_defs foo) [] value
+    case ty of
+        Left err -> customFailure $ TE err
+        Right _ -> modify $ defsToIS $ M.insert ident value
+
+pProgram :: Parser ()
+pProgram = void $ many pDef
+
+pAll :: Text -> Either String ()
+pAll input = first errorBundlePretty $ fst $ runIdentity $ runStateT (runParserT pProgram "" input) $ IS{_binds = [], _defs = M.empty}
diff --git a/test.pg b/test.pg
new file mode 100644
index 0000000..0db99c5
--- /dev/null
+++ b/test.pg
@@ -0,0 +1,2 @@
+id := fun (A : *) (x : A) . x ;
+foo := fun (A B : *) (f : A -> B) (x : A) . id (A -> B) f (id A x) ;
diff --git a/tests/CheckTests.hs b/tests/CheckTests.hs
index 9607ef0..c79bc3b 100644
--- a/tests/CheckTests.hs
+++ b/tests/CheckTests.hs
@@ -1,11 +1,12 @@
 module CheckTests (tests) where
 
 import Check
+import qualified Data.Map as M
 import Expr (Expr (..))
 import Test.HUnit
 
 sort :: Test
-sort = TestCase $ assertEqual "*" (Right Square) (findType [] Star)
+sort = TestCase $ assertEqual "*" (Right Square) (checkType M.empty [] Star)
 
 stlc :: Test
 stlc =
@@ -13,7 +14,12 @@ stlc =
         assertEqual
             "fun (x : A) (y : B) . x"
             (Right $ Pi "" (Var 0 "A") (Pi "" (Var 2 "B") (Var 2 "A")))
-            (findType [Star, Star] $ Abs "x" (Var 0 "A") (Abs "y" (Var 2 "B") (Var 1 "x")))
+            (checkType M.empty [Star, Star] $ Abs "x" (Var 0 "A") (Abs "y" (Var 2 "B") (Var 1 "x")))
+
+freeVar :: Test
+freeVar =
+    TestCase $
+        assertEqual "{x = *} , [] |- x : □" (Right Square) (checkType (M.singleton "x" Star) [] (Free "x"))
 
 polyIdent :: Test
 polyIdent =
@@ -21,7 +27,7 @@ polyIdent =
         assertEqual
             "fun (A : *) (x : A) . x"
             (Right $ Pi "A" Star (Pi "" (Var 0 "A") (Var 1 "A")))
-            (findType [] (Abs "A" Star (Abs "x" (Var 0 "A") (Var 0 "x"))))
+            (checkType M.empty [] (Abs "A" Star (Abs "x" (Var 0 "A") (Var 0 "x"))))
 
 typeCons :: Test
 typeCons =
@@ -29,7 +35,7 @@ typeCons =
         assertEqual
             "fun (A B : *) . A -> B"
             (Right $ Pi "" Star (Pi "" Star Star))
-            (findType [] (Abs "A" Star (Abs "B" Star (Pi "" (Var 1 "A") (Var 1 "B")))))
+            (checkType M.empty [] (Abs "A" Star (Abs "B" Star (Pi "" (Var 1 "A") (Var 1 "B")))))
 
 useTypeCons :: Test
 useTypeCons =
@@ -37,7 +43,7 @@ useTypeCons =
         assertEqual
             "fun (C : * -> *) (A : *) (x : C A) . x"
             (Right $ Pi "C" (Pi "" Star Star) (Pi "A" Star (Pi "" (App (Var 1 "C") (Var 0 "A")) (App (Var 2 "C") (Var 1 "A")))))
-            (findType [] $ Abs "C" (Pi "" Star Star) (Abs "A" Star (Abs "x" (App (Var 1 "C") (Var 0 "A")) (Var 0 "x"))))
+            (checkType M.empty [] $ Abs "C" (Pi "" Star Star) (Abs "A" Star (Abs "x" (App (Var 1 "C") (Var 0 "A")) (Var 0 "x"))))
 
 dependent :: Test
 dependent =
@@ -45,7 +51,7 @@ dependent =
         assertEqual
             "fun (S : *) (x : S) . S -> S"
             (Right $ Pi "S" Star (Pi "" (Var 0 "S") Star))
-            (findType [] $ Abs "S" Star (Abs "x" (Var 0 "S") (Pi "" (Var 1 "S") (Var 2 "S"))))
+            (checkType M.empty [] $ Abs "S" Star (Abs "x" (Var 0 "S") (Pi "" (Var 1 "S") (Var 2 "S"))))
 
 useDependent :: Test
 useDependent =
@@ -53,7 +59,7 @@ useDependent =
         assertEqual
             "fun (S : *) (P : S -> *) (x : S) . P x"
             (Right $ Pi "S" Star (Pi "" (Pi "" (Var 0 "S") Star) (Pi "" (Var 1 "S") Star)))
-            (findType [] $ Abs "S" Star (Abs "P" (Pi "" (Var 0 "S") Star) (Abs "x" (Var 1 "S") (App (Var 1 "P") (Var 0 "x")))))
+            (checkType M.empty [] $ Abs "S" Star (Abs "P" (Pi "" (Var 0 "S") Star) (Abs "x" (Var 1 "S") (App (Var 1 "P") (Var 0 "x")))))
 
 big :: Test
 big =
@@ -61,15 +67,15 @@ big =
         assertEqual
             "fun (S : *) (P Q : S -> *) (H : forall (x : S), P x -> Q x) (G : forall (x : S), P x) (x : S) . H x (G x)"
             (Right $ Pi "S" Star (Pi "P" (Pi "" (Var 0 "S") Star) (Pi "Q" (Pi "" (Var 1 "S") Star) (Pi "" (Pi "x" (Var 2 "S") (Pi "" (App (Var 2 "P") (Var 0 "x")) (App (Var 2 "Q") (Var 1 "x")))) (Pi "" (Pi "x" (Var 3 "S") (App (Var 3 "P") (Var 0 "x"))) (Pi "x" (Var 4 "S") (App (Var 3 "Q") (Var 0 "x"))))))))
-            (findType [] $ Abs "S" Star (Abs "P" (Pi "" (Var 0 "S") Star) (Abs "Q" (Pi "" (Var 1 "S") Star) (Abs "H" (Pi "x" (Var 2 "S") (Pi "" (App (Var 2 "P") (Var 0 "x")) (App (Var 2 "Q") (Var 1 "x")))) (Abs "G" (Pi "x" (Var 3 "S") (App (Var 3 "P") (Var 0 "x"))) (Abs "x" (Var 4 "S") (App (App (Var 2 "H") (Var 0 "x")) (App (Var 1 "G") (Var 0 "x")))))))))
+            (checkType M.empty [] $ Abs "S" Star (Abs "P" (Pi "" (Var 0 "S") Star) (Abs "Q" (Pi "" (Var 1 "S") Star) (Abs "H" (Pi "x" (Var 2 "S") (Pi "" (App (Var 2 "P") (Var 0 "x")) (App (Var 2 "Q") (Var 1 "x")))) (Abs "G" (Pi "x" (Var 3 "S") (App (Var 3 "P") (Var 0 "x"))) (Abs "x" (Var 4 "S") (App (App (Var 2 "H") (Var 0 "x")) (App (Var 1 "G") (Var 0 "x")))))))))
 
 tests :: Test
 tests =
     TestList
         [ TestLabel "sort" sort
-        , TestLabel "λ→" stlc
+        , TestLabel "λ→" $ TestList [stlc, freeVar]
         , TestLabel "λ2" polyIdent
-        , TestLabel "λω" (TestList [typeCons, useTypeCons])
-        , TestLabel "λP2" (TestList [dependent, useDependent])
+        , TestLabel "λω" $ TestList [typeCons, useTypeCons]
+        , TestLabel "λP2" $ TestList [dependent, useDependent]
         , TestLabel "λC" big
         ]
diff --git a/tests/ExprTests.hs b/tests/ExprTests.hs
index a3c518e..0d3edb2 100644
--- a/tests/ExprTests.hs
+++ b/tests/ExprTests.hs
@@ -1,6 +1,7 @@
 module ExprTests (tests) where
 
 import Expr
+import Eval
 import Test.HUnit
 
 inner :: Expr
@@ -34,13 +35,13 @@ substE1 =
             after
             (subst 0 (Var 2 "B") inner)
 
-betaNFe1 :: Test
-betaNFe1 =
+whnfE1 :: Test
+whnfE1 =
     TestCase $
         assertEqual
             "e1 B"
             after
-            (betaNF $ App e1 $ Var 2 "B")
+            (whnf $ App e1 $ Var 2 "B")
 
 tests :: Test
 tests =
@@ -48,5 +49,5 @@ tests =
         [ TestLabel "fFree" fFree
         , TestLabel "incE1" incE1
         , TestLabel "substE1" substE1
-        , TestLabel "betaNFe1" betaNFe1
+        , TestLabel "whnfE1" whnfE1
         ]
diff --git a/tests/ParserTests.hs b/tests/ParserTests.hs
index bb620ca..8e8d916 100644
--- a/tests/ParserTests.hs
+++ b/tests/ParserTests.hs
@@ -1,7 +1,5 @@
 module ParserTests (tests) where
 
-import Data.Text (Text)
-import qualified Data.Text as T
 import Expr (Expr (..))
 import Parser (pAll)
 import Test.HUnit