diff --git a/src/Elab.hs b/src/Elab.hs
index e719da7..6a24ab7 100644
--- a/src/Elab.hs
+++ b/src/Elab.hs
@@ -24,6 +24,8 @@ import Prettyprinter
 
 import Syntax.Pretty
 import Syntax
+import Data.Map (Map)
+import Data.Text (Text)
 
 infer :: P.Expr -> ElabM (Term, NFType)
 infer (P.Span ex a b) = withSpan a b $ infer ex
@@ -132,6 +134,11 @@ check (P.Sigma s d r) ty = do
     r <- check r ty
     pure (Sigma var d r)
 
+check (P.Let items body) ty = do
+  checkLetItems mempty items \decs -> do
+    body <- check body ty
+    pure (Let decs body)
+
 check (P.LamSystem bs) ty = do
   (extent, dom) <- isPartialType ty
   let dom_q = quote dom
@@ -188,6 +195,30 @@ check exp ty = do
   wp <- isConvertibleTo has ty
   pure (wp tm)
 
+checkLetItems :: Map Text (Maybe NFType) -> [P.LetItem] -> ([(Name, Term, Term)] -> ElabM a) -> ElabM a
+checkLetItems _   [] cont = cont []
+checkLetItems map (P.LetDecl v t:xs) cont = do
+  t <- check t VTypeω
+  t_nf <- eval t
+  assume (Defined v 0) t_nf \_ ->
+    checkLetItems (Map.insert v (Just t_nf) map) xs cont
+
+checkLetItems map (P.LetBind name rhs:xs) cont = do
+  case Map.lookup name map of
+    Nothing -> do
+      (tm, ty) <- infer rhs
+      tm_nf <- eval tm
+      define (Defined name 0) ty tm_nf \name' ->
+        checkLetItems map xs \xs ->
+          cont ((name', quote ty, tm):xs)
+    Just Nothing -> throwElab $ Redefinition (Defined name 0)
+    Just (Just ty_nf) -> do
+      rhs <- check rhs ty_nf
+      rhs_nf <- eval rhs
+      define (Defined name 0) ty_nf rhs_nf \name' ->
+        checkLetItems (Map.insert name Nothing map) xs \xs ->
+          cont ((name', quote ty_nf, rhs):xs)
+
 checkFormula :: P.Formula -> ElabM Value
 checkFormula P.FTop = pure VI1
 checkFormula P.FBot = pure VI0
@@ -296,7 +327,8 @@ checkStatement (P.Defn name rhs) k = do
 
       rhs <- check rhs ty_nf
       rhs_nf <- eval rhs
-      define (Defined name 0) ty_nf rhs_nf (const k)
+      define (Defined name 0) ty_nf rhs_nf $ \name ->
+        local (\e -> e { definedNames = Set.insert name (definedNames e) }) k
 
 checkStatement (P.Builtin winame var) k = do
   wi <-
@@ -316,7 +348,8 @@ checkStatement (P.Builtin winame var) k = do
   liftIO $
     runElab check env `catch` \(_ :: NotInScope) -> pure ()
 
-  define (Defined var 0) (wiType wi) (wiValue wi) (const k)
+  define (Defined var 0) (wiType wi) (wiValue wi) $ \name ->
+    local (\e -> e { definedNames = Set.insert name (definedNames e) }) k
 
 checkStatement (P.ReplNf e) k = do
   (e, _) <- infer e
diff --git a/src/Elab/Eval.hs b/src/Elab/Eval.hs
index 60b2886..8b59f0d 100644
--- a/src/Elab/Eval.hs
+++ b/src/Elab/Eval.hs
@@ -184,6 +184,9 @@ eval' e (Comp a phi u a0) = comp (eval' e a) (eval' e phi) (eval' e u) (eval' e
 eval' e (GlueTy a phi tys f) = glueType (eval' e a) (eval' e phi) (eval' e tys) (eval' e f)
 eval' e (Glue a phi tys eqvs t x) = glueElem (eval' e a) (eval' e phi) (eval' e tys) (eval' e eqvs) (eval' e t) (eval' e x)
 eval' e (Unglue a phi tys f x) = unglue (eval' e a) (eval' e phi) (eval' e tys) (eval' e f) (eval' e x)
+eval' e (Let ns x) =
+  let env' = foldl (\newe (n, ty, x) -> newe { getEnv = Map.insert n (eval' newe ty, eval' newe x) (getEnv newe) }) e ns
+   in eval' env' x
 
 vApp :: HasCallStack => Plicity -> Value -> Value -> Value
 vApp p (VLam p' k) arg
diff --git a/src/Elab/Eval/Formula.hs b/src/Elab/Eval/Formula.hs
index ae95e7a..4958f07 100644
--- a/src/Elab/Eval/Formula.hs
+++ b/src/Elab/Eval/Formula.hs
@@ -62,7 +62,7 @@ truthAssignments (VIOr x y) m = truthAssignments x m ++ truthAssignments y m
 truthAssignments (VIAnd x y) m = truthAssignments x =<< truthAssignments y m
 truthAssignments (VNe (HVar x) Seq.Empty) m = pure (Map.insert x (VI, VI1) m)
 truthAssignments (VINot (VNe (HVar x) Seq.Empty)) m = pure (Map.insert x (VI, VI0) m)
-truthAssignments x _ = error $ "impossible formula: " ++ show x
+truthAssignments _ m = pure m
 
 idist :: Value -> Value -> Value
 idist (VIOr x y) z = (x `idist` z) `ior` (y `idist` z)
diff --git a/src/Elab/WiredIn.hs b/src/Elab/WiredIn.hs
index 5e36794..e156dbc 100644
--- a/src/Elab/WiredIn.hs
+++ b/src/Elab/WiredIn.hs
@@ -22,6 +22,7 @@ import qualified Presyntax.Presyntax as P
 import Syntax
 
 import System.IO.Unsafe
+import GHC.Stack
 
 wiType :: WiredIn -> NFType
 wiType WiType     = VType
@@ -193,7 +194,7 @@ ielim _line _left _right fn i =
     VSystem (Map.toList -> []) -> VSystem (Map.fromList [])
     _ -> error $ "can't ielim " ++ show fn
 
-outS :: NFSort -> NFEndp -> Value -> Value -> Value
+outS :: HasCallStack => NFSort -> NFEndp -> Value -> Value -> Value
 outS _ (force -> VI1) u _  = u @@ VItIsOne
 
 outS _ _phi _ (VInc _ _ x) = x
@@ -205,7 +206,7 @@ outS _ _ _ v             = error $ "can't outS " ++ show v
 -- Composition
 comp :: NFLine -> NFEndp -> Value -> Value -> Value
 comp _ VI1 u _ = u @@ VI1 @@ VItIsOne
-comp a psi@phi u (outS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
+comp a psi@phi u (compOutS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
   case force $ a @@ VVar (Bound (T.pack "neutral composition") 0) of
     VPi{} ->
       let
@@ -285,6 +286,10 @@ comp a psi@phi u (outS (a @@ VI1) phi (u @@ VI1 @@ VItIsOne) -> a0) =
        in b1
     _ -> VComp a phi u a0
 
+compOutS :: NFSort -> NFEndp -> Value -> Value -> Value
+compOutS _ _hi _0 vl@VComp{} = vl
+compOutS a phi u0 x = outS a phi u0 x
+
 system :: (Value -> Value -> Value) -> Value
 system k = fun \i -> fun \isone -> k i isone
 
diff --git a/src/Elab/WiredIn.hs-boot b/src/Elab/WiredIn.hs-boot
index b3b6545..38ce758 100644
--- a/src/Elab/WiredIn.hs-boot
+++ b/src/Elab/WiredIn.hs-boot
@@ -1,6 +1,7 @@
 module Elab.WiredIn where
 
 import Syntax
+import GHC.Stack
 
 wiType  :: WiredIn -> NFType
 wiValue :: WiredIn -> NFType
@@ -9,7 +10,7 @@ iand, ior :: NFEndp -> NFEndp -> NFEndp
 inot      :: NFEndp -> NFEndp
 ielim     :: NFSort -> Value -> Value -> Value -> NFEndp -> Value
 
-outS :: NFSort -> NFEndp -> Value -> Value -> Value
+outS :: HasCallStack => NFSort -> NFEndp -> Value -> Value -> Value
 comp :: NFLine -> NFEndp -> Value -> Value -> Value
 
 glueType :: NFSort -> NFEndp -> NFPartial -> NFPartial -> Value
diff --git a/src/Main.hs b/src/Main.hs
index 9140b90..9c835fd 100644
--- a/src/Main.hs
+++ b/src/Main.hs
@@ -1,6 +1,8 @@
+{-# LANGUAGE LambdaCase #-}
 {-# LANGUAGE BlockArguments #-}
 {-# LANGUAGE OverloadedStrings #-}
 {-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE DeriveAnyClass #-}
 module Main where
 
 import Control.Monad.IO.Class
@@ -34,6 +36,8 @@ import Syntax
 
 import System.Console.Haskeline
 import System.Exit
+import qualified Data.Set as Set
+import Data.Maybe
 
 main :: IO ()
 main = do
@@ -44,7 +48,7 @@ main = do
       enterReplIn env
     Check files verbose -> do
       env <- checkFiles files
-      when verbose $ dumpEnv (getEnv env)
+      when verbose $ dumpEnv env
     Repl -> enterReplIn emptyEnv
 
 enterReplIn :: ElabEnv -> IO ()
@@ -71,18 +75,28 @@ enterReplIn env = runInputT defaultSettings (loop env') where
 
 checkFiles :: [String] -> IO ElabEnv
 checkFiles files = runElab (go files ask) emptyEnv where
-  go [] k = k
+  go [] k = do
+    env <- ask
+    for_ (Map.toList (nameMap env)) \case
+      (_, v@Defined{})
+        | Set.member v (definedNames env) -> pure ()
+        | otherwise ->
+          let
+            pos = fromJust (Map.lookup v (whereBound env))
+           in withSpan (fst pos) (snd pos) $ throwElab $ DeclaredUndefined v
+      _ -> pure ()
+    k
   go (x:xs) k = do
     code <- liftIO $ Bsl.readFile x
     case runAlex code parseProg of
       Left e -> liftIO $ print e *> error (show e)
-      Right prog -> do
-        env <- ask
-        liftIO $ runElab (checkProgram prog (go xs k)) env
-                  `catch` \e -> displayAndDie (T.decodeUtf8 (Bsl.toStrict code)) (e :: SomeException)
+      Right prog ->
+        checkProgram prog (go xs k)
+          `catchElab` \e -> liftIO $ displayAndDie (T.decodeUtf8 (Bsl.toStrict code)) (e :: SomeException)
 
-dumpEnv :: Map.Map Name (NFType, Value) -> IO ()
-dumpEnv env = for_ (Map.toList env) $ \(name, (nft, _)) ->
+dumpEnv :: ElabEnv -> IO ()
+dumpEnv env = for_ (Map.toList (nameMap env)) $ \(_, name) ->
+  let nft = fst $ getEnv env Map.! name in
   T.putStrLn $ render (pretty name <+> align (nest (negate 1) (colon <+> prettyTm (quote (zonk nft)))))
 
 parser :: ParserInfo Opts
@@ -109,7 +123,7 @@ displayAndDie lines e = do
   exitFailure
 
 displayExceptions :: Text -> [Handler ()]
-displayExceptions lines =
+displayExceptions lines = 
   [ Handler \(WhileChecking a b e) -> do
       T.putStrLn $ squiggleUnder a b lines
       displayExceptions' lines e
@@ -140,7 +154,9 @@ displayExceptions lines =
   , Handler \(NoSuchPrimitive x) -> do
       putStrLn $ "Unknown primitive: " ++ T.unpack x
   , Handler \(NotInScope x) -> do
-      putStrLn $ "Variable not in scope: " ++ show x
+      putStrLn $ "Variable not in scope: " ++ show (pretty x)
+  , Handler \(DeclaredUndefined n) -> do
+      putStrLn $ "Name declared but not defined: " ++ show (pretty n)
   ]
 
 displayExceptions' :: Exception e => Text -> e -> IO ()
@@ -155,4 +171,7 @@ squiggleUnder (Posn l c) (Posn l' c') file
       squiggle = T.replicate c " " <> T.pack "\x1b[1;31m" <> T.replicate (c' - c) "~" <> T.pack "\x1b[0m"
 
      in T.unlines [ padding, line, padding <> squiggle ]
-  | otherwise = T.pack (show (Posn l c, Posn l' c'))
+  | otherwise = T.unlines (take (l' - l) (drop l (T.lines file)))
+
+newtype DeclaredUndefined = DeclaredUndefined { declaredUndefName :: Name }
+  deriving (Eq, Show, Exception)
\ No newline at end of file
diff --git a/src/Presyntax/Lexer.x b/src/Presyntax/Lexer.x
index 71de049..f911153 100644
--- a/src/Presyntax/Lexer.x
+++ b/src/Presyntax/Lexer.x
@@ -6,6 +6,8 @@ import qualified Data.Text.Encoding as T
 import qualified Data.Text as T
 
 import Presyntax.Tokens
+
+import Debug.Trace
 }
 
 %wrapper "monadUserState-bytestring"
@@ -18,7 +20,7 @@ tokens :-
   $white_nol+                   ;
   "--" .* \n                    ;
   
-<0,prtext> $alpha [$alpha $digit \_ \']* { yield tokVar }
+<0,prtext> $alpha [$alpha $digit \_ \']* { variableOrKeyword }
 
 -- zero state: normal lexing
 <0> \=                            { always TokEqual }
@@ -47,11 +49,11 @@ tokens :-
 <0> "&&"                          { always TokAnd }
 <0> "||"                          { always TokOr }
 
-<0> "{-"                  { just $ pushStartCode comment }
+<0> "{-"                          { just $ pushStartCode comment }
 
 <comment> {
-  "-}"                    { \i l -> popStartCode *> skip i l }
-  .                       ;
+  "-}"   { \i l -> popStartCode *> skip i l }
+  .      ;
 }
 
 <0> "{-#"                         { \i l -> pushStartCode prkw *> always TokOPragma i l }
@@ -67,6 +69,14 @@ tokens :-
   () { offsideRule }
 }
 
+-- layout: indentation of the next token is context for offside rule
+<layout> {
+  \n ;
+  () { startLayout }
+}
+
+<empty_layout> () { emptyLayout }
+
 {
 alexEOF :: Alex Token
 alexEOF = do
@@ -78,8 +88,8 @@ yield k (AlexPn _ l c, _, s, _) i = pure (Token (k $! (T.decodeUtf8 (Lbs.toStric
 always :: TokenClass -> AlexInput -> Int64 -> Alex Token
 always k x i = yield (const k) x i
 
-data AlexUserState = AlexUserState { layoutColumns :: [Int], startCodes :: [Int] }
-alexInitUserState = AlexUserState [1] []
+data AlexUserState = AlexUserState { layoutColumns :: [Int], startCodes :: [Int], leastColumn :: Int }
+alexInitUserState = AlexUserState [1] [] 0
 
 just :: Alex a -> AlexAction Token
 just k _ _ = k *> alexMonadScan
@@ -109,19 +119,40 @@ offsideRule :: AlexInput -> Int64 -> Alex Token
 offsideRule (AlexPn _ line col, _, s, _) _
   | Lbs.null s = pure (Token TokEof line col)
   | otherwise = do
-    ~(col':_) <- layoutColumns <$> getUserState
+    popStartCode
+    ~(col':ctx) <- layoutColumns <$> getUserState
     case col `compare` col' of
-      EQ -> do
-        popStartCode
-        pure (Token TokSemi line col)
-      GT -> do
-        popStartCode
-        alexMonadScan
-      LT -> alexError "wrong ass indentation"
-
-tokVar :: T.Text -> TokenClass
-tokVar text =
+      EQ -> pure (Token TokSemi line col)
+      GT -> alexMonadScan
+      LT -> do
+        mapUserState $ \s -> s { layoutColumns = ctx }
+        pure (Token TokLEnd line col)
+
+emptyLayout :: AlexInput -> Int64 -> Alex Token
+emptyLayout (AlexPn _ line col, _, _, _) _ = do
+  popStartCode
+  pushStartCode newline
+  pure (Token TokLEnd line col)
+
+startLayout :: AlexInput -> Int64 -> Alex Token
+startLayout (AlexPn _ line col, _, s, _) size = do
+  popStartCode
+  least <- leastColumn <$> getUserState
+  ~(col':_) <- layoutColumns <$> getUserState
+  if (col' >= col) || col <= least
+    then pushStartCode empty_layout
+    else mapUserState $ \s -> s { layoutColumns = col:layoutColumns s }
+  pure (Token TokLStart line col)
+
+variableOrKeyword :: AlexAction Token
+variableOrKeyword (AlexPn _ l c, _, s, _) size =
+  let text = T.decodeUtf8 (Lbs.toStrict (Lbs.take size s)) in
   case T.unpack text of
-    "as" -> TokAs
-    _ -> TokVar text
+    "as" -> pure (Token TokAs l c)
+    "in" -> pure (Token TokIn l c)
+    "let" -> do
+      pushStartCode layout
+      mapUserState $ \s -> s { leastColumn = c }
+      pure (Token TokLet l c)
+    _ -> pure (Token (TokVar text) l c)
 }
\ No newline at end of file
diff --git a/src/Presyntax/Parser.y b/src/Presyntax/Parser.y
index ed477fb..e617f19 100644
--- a/src/Presyntax/Parser.y
+++ b/src/Presyntax/Parser.y
@@ -36,6 +36,9 @@ import Prelude hiding (span)
   '{'         { Token TokOBrace _ _ }
   '}'         { Token TokCBrace _ _ }
 
+  START       { Token TokLStart _ _ }
+  END         { Token TokLEnd   _ _ }
+
   '['         { Token TokOSquare _ _ }
   ']'         { Token TokCSquare _ _ }
 
@@ -52,6 +55,9 @@ import Prelude hiding (span)
   '*'         { Token TokStar _ _ }
   'as'        { Token TokAs _ _ }
 
+  'let'       { Token TokLet _ _ }
+  'in'        { Token TokIn _ _ }
+
   '&&'        { Token TokAnd _ _ }
   '||'        { Token TokOr _ _ }
 
@@ -76,6 +82,9 @@ Exp
   | '(' var ':' Exp ')' '*'  Exp         { span $1 $7 $ Sigma (getVar $2) $4 $7 }
   | ExpApp '*' Exp                       { span $1 $3 $ Sigma (T.singleton '_') $1 $3 }
 
+  | 'let' START LetList END 'in' Exp     { span $1 $6 $ Let $3 $6 }
+  | 'let' START LetList END Exp          { span $1 $5 $ Let $3 $5 }
+
   | ExpApp                               { $1 }
 
 ExpApp :: { Expr }
@@ -125,6 +134,15 @@ Statement :: { Statement }
   | var LhsList '=' Exp { spanSt $1 $4 $ Defn (getVar $1) (makeLams $2 $4) }
   | '{-#' Pragma '#-}'  { spanSt $1 $3 $ $2 }
 
+LetItem :: { LetItem }
+  : var ':' Exp         { LetDecl (getVar $1) $3 }
+  | var LhsList '=' Exp { LetBind (getVar $1) (makeLams $2 $4) }
+
+LetList :: { [LetItem] }
+  :                     { [] }
+  | LetItem             { [$1] }
+  | LetItem ';' LetList { $1:$3 }
+
 ReplStatement :: { Statement }
   : Exp                        { spanSt $1 $1 $ ReplNf $1 }
   | ':t' Exp                   { spanSt $1 $2 $ ReplTy $2 }
diff --git a/src/Presyntax/Presyntax.hs b/src/Presyntax/Presyntax.hs
index 39b20fc..2141de3 100644
--- a/src/Presyntax/Presyntax.hs
+++ b/src/Presyntax/Presyntax.hs
@@ -20,12 +20,17 @@ data Expr
   | Proj1 Expr
   | Proj2 Expr
 
-  -- System
   | LamSystem [(Condition, Expr)]
+  | Let [LetItem] Expr
 
   | Span Expr Posn Posn
   deriving (Eq, Show, Ord)
 
+data LetItem
+  = LetDecl { leIName :: Text, leIVal :: Expr }
+  | LetBind { leIName :: Text, leIVal :: Expr }
+  deriving (Eq, Show, Ord)
+
 data Condition
   = Condition { condF :: Formula, condV :: Maybe Text }
   deriving (Eq, Show, Ord)
diff --git a/src/Presyntax/Tokens.hs b/src/Presyntax/Tokens.hs
index 2f32aa4..0a24eb5 100644
--- a/src/Presyntax/Tokens.hs
+++ b/src/Presyntax/Tokens.hs
@@ -34,6 +34,10 @@ data TokenClass
 
   | TokPi1
   | TokPi2
+  | TokLet
+  | TokIn
+  | TokLStart
+  | TokLEnd
 
   | TokAnd
   | TokOr
@@ -69,6 +73,10 @@ tokSize TokAnd = 2
 tokSize TokOr = 2
 tokSize TokAs = 2
 tokSize (TokReplT s) = T.length s
+tokSize TokLet = 3
+tokSize TokIn = 2
+tokSize TokLStart = 0
+tokSize TokLEnd = 0
 
 data Token
   = Token { tokenClass   :: TokenClass
diff --git a/src/Syntax.hs b/src/Syntax.hs
index 899c0bb..13df6dc 100644
--- a/src/Syntax.hs
+++ b/src/Syntax.hs
@@ -53,6 +53,7 @@ data Term
   | App  Plicity Term Term
   | Lam  Plicity Name Term
   | Pi   Plicity Name Term Term
+  | Let  [(Name, Term, Term)] Term
   | Meta MV
   | Type
   | Typeω