diff --git a/src/Datalog.hs b/src/Datalog.hs
index ca155dc..416efa9 100644
--- a/src/Datalog.hs
+++ b/src/Datalog.hs
@@ -1,8 +1,12 @@
 module Datalog
     ( module Datalog.Syntax
     , module Datalog.Parser
+    , module Datalog.Eval
+    , module Datalog.IO
     )
   where
 
 import Datalog.Syntax
 import Datalog.Parser
+import Datalog.Eval
+import Datalog.IO
diff --git a/src/Datalog/Eval.hs b/src/Datalog/Eval.hs
new file mode 100644
index 0000000..9b26770
--- /dev/null
+++ b/src/Datalog/Eval.hs
@@ -0,0 +1,173 @@
+module Datalog.Eval where
+
+import Data.Bifunctor (Bifunctor(..))
+import Data.Foldable
+import Data.Map (Map)
+import Data.Map qualified as Map
+import Data.Map.Merge.Lazy qualified as Map
+import Data.Maybe
+import Data.Set (Set)
+import Data.Set qualified as Set
+
+import Datalog.Syntax
+
+data Relation = Relation
+  { _relation_arity :: Int
+  , _relation_members :: Set [ConId]
+      -- all the tuples in the relation
+  , _relation_indices :: Map (Int, ConId) (Set [ConId])
+      -- map from (position, value) pairs to the subset of the member tuples of the relation that have that value at the given position
+  }
+  deriving (Eq, Ord, Show)
+
+emptyRelation :: Int -> Relation
+emptyRelation arity = Relation arity Set.empty Map.empty
+
+insertInRelation :: [ConId] -> Relation -> Relation
+insertInRelation tuple rel = rel
+  { _relation_members = Set.insert tuple (_relation_members rel)
+  , _relation_indices = foldl (\ixs p -> Map.insertWith Set.union p (Set.singleton tuple) ixs) (_relation_indices rel) (zip [0..] tuple)
+  }
+
+insertManyInRelation :: Set [ConId] -> Relation -> Relation
+insertManyInRelation tuples rel = foldl (\r x -> insertInRelation x r) rel tuples
+
+data Database = Database
+  { _database_universe :: Set ConId -- Herbrand universe, set of constants
+  , _database_relations :: Map RelId Relation -- relations indexed by name
+  , _database_rules :: Map RelId [Rule] -- rules indexed by head relation name
+  }
+  deriving (Eq, Ord, Show)
+
+emptyDatabase :: Database
+emptyDatabase = Database Set.empty Map.empty Map.empty
+
+insertManyInRelationDb :: RelId -> Set [ConId] -> Database -> Database
+insertManyInRelationDb relName tuples db = db
+  { _database_relations =
+      Map.insert
+        relName
+        (insertManyInRelation tuples
+          (Map.findWithDefault (error "insertManyInRelationDb: shouldn't happen")
+            relName
+            rels
+          ))
+        rels
+  }
+  where
+    rels = _database_relations db
+
+data EvalError =
+    EvalError_RuleWrongArity Rule WrongArity
+  | EvalError_AtomWrongArity Atom WrongArity
+  deriving (Eq, Ord, Show)
+
+data WrongArity = WrongArity
+  { _wrongArity_relation :: RelId
+  , _wrongArity_expected :: Int
+  , _wrongArity_got :: Int
+  }
+  deriving (Eq, Ord, Show)
+
+addRelation :: RelId -> Relation -> Database -> Database
+addRelation relName rel db = db
+  { _database_relations = Map.insert relName rel (_database_relations db)
+  }
+
+arityCheck :: Database -> Atom -> Either WrongArity (Database, Relation)
+arityCheck db (Atom relName args) = case Map.lookup relName (_database_relations db) of
+  Nothing ->
+    let n = length args
+        rel = emptyRelation n
+    in Right (addRelation relName rel db, rel)
+  Just rel ->
+    let n = length args
+    in if n == _relation_arity rel
+         then Right (db, rel)
+         else Left $ WrongArity
+           { _wrongArity_relation = relName
+           , _wrongArity_expected = _relation_arity rel
+           , _wrongArity_got = n
+           }
+
+addRule :: Rule -> Database -> Either EvalError Database
+addRule r@(ruleHead@(Atom relName _) :- ruleBody) db = do
+  let ruleConstants = constants r
+  db' <- first (EvalError_RuleWrongArity r) $ foldlM (\d a -> fmap fst $ arityCheck d a) db (ruleHead : ruleBody)
+
+  return $ db'
+      { _database_universe = Set.union ruleConstants (_database_universe db)
+      , _database_rules = Map.insertWith (<>) relName [r] (_database_rules db)
+      }
+
+addProgram :: Program -> Database -> Either EvalError Database
+addProgram (Program rs) db = foldlM (\d r -> addRule r d) db rs
+
+evalAtomDb :: Database -> Atom -> Either EvalError (Set (Map VarId ConId))
+evalAtomDb db a =
+  case arityCheck db a of
+    Left w -> Left (EvalError_AtomWrongArity a w)
+    Right (_, rel) -> Right (unsafeEvalAtomRel rel a)
+
+-- NB: Assumes the atom has appropriate arity and that provided relation is the right one for the atom
+unsafeEvalAtomRel :: Relation -> Atom -> Set (Map VarId ConId)
+unsafeEvalAtomRel rel (Atom _ args) = Set.fromList [b | m <- Set.toList matches, b <- maybeToList (mkBinding args m Map.empty)]
+  where
+    keys = [(k, v) | (k, Con v) <- zip [0..] args]
+    sets = map (\k -> Map.findWithDefault Set.empty k (_relation_indices rel)) keys
+    matches = case sets of
+      [] -> _relation_members rel
+      (s:ss) -> foldl Set.intersection s ss
+
+    mkBinding :: [Term] -> [ConId] -> Map VarId ConId -> Maybe (Map VarId ConId)
+    mkBinding [] [] m = Just m
+    mkBinding (Con _ : ts) (_ : cs) m = mkBinding ts cs m
+    mkBinding (Var v : ts) (c : cs) m =
+      case Map.lookup v m of
+        Nothing -> mkBinding ts cs (Map.insert v c m)
+        Just c'
+          | c == c'   -> mkBinding ts cs m
+          | otherwise -> Nothing
+    mkBinding _ _ _ = error "mkBinding: arity mismatch"
+
+joinBindings :: Map VarId ConId -> Map VarId ConId -> Maybe (Map VarId ConId)
+joinBindings = Map.mergeA
+  (Map.traverseMissing (\_ v -> Just v))
+  (Map.traverseMissing (\_ v -> Just v))
+  (Map.zipWithAMatched (\_ v1 v2 -> if v1 == v2 then Just v1 else Nothing))
+
+(><) :: Set (Map VarId ConId) -> Set (Map VarId ConId) -> Set (Map VarId ConId)
+s1 >< s2 = Set.fromList (catMaybes [joinBindings b1 b2 | b1 <- Set.toList s1, b2 <- Set.toList s2])
+
+evalConjunction :: Database -> [Atom] -> Either EvalError (Set (Map VarId ConId))
+evalConjunction db atoms = do
+  rs <- mapM (evalAtomDb db) atoms
+  return (foldr (><) (Set.singleton Map.empty) rs)
+
+projectTuple :: Set ConId -> Map VarId ConId -> [Term] -> Set [ConId]
+projectTuple univ m = Set.fromList . mapM proj
+  where
+    proj (Con c) = [c]
+    proj (Var v) = Map.findWithDefault (Set.toList univ) v (fmap (:[]) m)
+
+immediateConsequences :: Database -> Rule -> Either EvalError (Set [ConId])
+immediateConsequences db (Atom _ ts :- bodyAtoms) = do
+  rs <- evalConjunction db bodyAtoms
+  return $ Set.unions [projectTuple (_database_universe db) binding ts | binding <- Set.toList rs]
+
+allImmediateConsequences :: Database -> RelId -> Either EvalError (Set [ConId])
+allImmediateConsequences db relName = do
+  cs <- sequence [immediateConsequences db r | r <- Map.findWithDefault [] relName (_database_rules db)]
+  return (Set.unions cs)
+
+extendDb :: Database -> Either EvalError Database
+extendDb db = do
+  consequences <- mapM (\relName -> fmap ((,) relName) (allImmediateConsequences db relName)) (Map.keys (_database_relations db))
+  return $ foldl (\d (relName, tuples) -> insertManyInRelationDb relName tuples d) db consequences
+
+extendFixedpointDb :: Database -> Either EvalError Database
+extendFixedpointDb db = do
+  db' <- extendDb db
+  if fmap _relation_members (_database_relations db) == fmap _relation_members (_database_relations db')
+    then return db'
+    else extendFixedpointDb db'
diff --git a/src/Datalog/IO.hs b/src/Datalog/IO.hs
new file mode 100644
index 0000000..d7f7dd4
--- /dev/null
+++ b/src/Datalog/IO.hs
@@ -0,0 +1,26 @@
+module Datalog.IO where
+
+import Data.Bifunctor (first)
+import Data.Text (Text)
+import Data.Void (Void)
+import Data.Text.IO qualified as T
+import Text.Megaparsec qualified as P
+
+import Datalog.Syntax
+import Datalog.Parser
+import Datalog.Eval
+
+data ReadFailure = ParseFailure (P.ParseErrorBundle Text Void) | EvalFailure EvalError
+  deriving (Eq, Show)
+
+readProgram :: FilePath -> IO (Either ReadFailure Program)
+readProgram fp = do
+  inp <- T.readFile fp
+  return $ first ParseFailure (P.parse parseProgram fp inp)
+
+readDatabase :: FilePath -> IO (Either ReadFailure Database)
+readDatabase fp = do
+  progE <- readProgram fp
+  return $ case progE of
+    Left e -> Left e
+    Right prog -> first EvalFailure (addProgram prog emptyDatabase)
diff --git a/src/Datalog/Parser.hs b/src/Datalog/Parser.hs
index 4215ae7..571ab39 100644
--- a/src/Datalog/Parser.hs
+++ b/src/Datalog/Parser.hs
@@ -35,36 +35,21 @@ comma, period :: (MonadParsec e Text m) => m ()
 comma = () <$ symbol ","
 period = () <$ symbol "."
 
-{-
-data Term = Con Ident | Var Ident
-  deriving (Eq, Ord, Show)
--}
-
 parseCon :: (MonadParsec e Text m) => m Term
-parseCon = Con . T.pack <$> lexeme (liftA2 (:) lowerChar (many alphaNumChar))
+parseCon = Con . ConId . T.pack <$> lexeme (many alphaNumChar)
 
 parseVar :: (MonadParsec e Text m) => m Term
-parseVar = Var . T.pack <$> lexeme (liftA2 (:) upperChar (many alphaNumChar))
+parseVar = Var . VarId . T.pack <$> lexeme (liftA2 (:) upperChar (many alphaNumChar))
 
 parseTerm :: Parser Term
-parseTerm = parseCon <|> parseVar
-
-{-
-data Atom = Atom Ident [Term]
-  deriving (Eq, Ord, Show)
--}
+parseTerm = parseVar <|> parseCon
 
 parseAtom :: Parser Atom
 parseAtom = do
-  rel <- T.pack <$> lexeme (liftA2 (:) lowerChar (many alphaNumChar))
+  rel <- RelId . T.pack <$> lexeme (liftA2 (:) lowerChar (many alphaNumChar))
   args <- parens (parseTerm `sepBy` comma)
   return (Atom rel args)
 
-{-
-data Rule = Atom :- [Atom]
-  deriving (Eq, Ord, Show)
--}
-
 parseFact :: Parser Rule
 parseFact = do
   headAtom <- parseAtom
@@ -78,9 +63,5 @@ parseRule = try parseFact <|> do
   period
   return (headAtom :- bodyAtoms)
 
-{-
-data Program = Program [Rule]
--}
-
 parseProgram :: Parser Program
 parseProgram = Program <$> many parseRule
diff --git a/src/Datalog/Syntax.hs b/src/Datalog/Syntax.hs
index 956bbfc..5982e7a 100644
--- a/src/Datalog/Syntax.hs
+++ b/src/Datalog/Syntax.hs
@@ -1,17 +1,60 @@
 module Datalog.Syntax where
 
+import Data.Char (isUpper)
 import Data.Text (Text)
+import Data.Text qualified as T
+import Data.Set qualified as Set
+import Data.Set (Set)
 
-type Ident = Text
-
-data Term = Con Ident | Var Ident
+newtype ConId = ConId Text
   deriving (Eq, Ord, Show)
 
-data Atom = Atom Ident [Term]
+newtype VarId = VarId Text
   deriving (Eq, Ord, Show)
 
+newtype RelId = RelId Text
+  deriving (Eq, Ord, Show)
+
+data Term = Con ConId | Var VarId
+  deriving (Eq, Ord, Show)
+
+con :: Text -> Term
+con = Con . ConId
+
+var :: Text -> Term
+var = Var . VarId
+
+term :: Text -> Term
+term t = if not (T.null t) && isUpper (T.head t) then var t else con t
+
+data Atom = Atom RelId [Term]
+  deriving (Eq, Ord, Show)
+
+atom :: Text -> [Text] -> Atom
+atom relName args = Atom (RelId relName) (map term args)
+
 data Rule = Atom :- [Atom]
   deriving (Eq, Ord, Show)
 
 data Program = Program [Rule]
   deriving (Eq, Ord, Show)
+
+class HasConstants a where
+  constants :: a -> Set ConId
+
+instance HasConstants Term where
+  constants t = case t of
+    Con x -> Set.singleton x
+    Var _ -> Set.empty
+
+instance HasConstants a => HasConstants [a] where
+  constants xs = Set.unions (map constants xs)
+
+instance HasConstants Atom where
+  constants (Atom _ ts) = constants ts
+
+instance HasConstants Rule where
+  constants (h :- b) = Set.union (constants h) (constants b)
+
+instance HasConstants Program where
+  constants (Program rs) = constants rs
diff --git a/test/Main.hs b/test/Main.hs
index e8f19aa..da6f7a0 100644
--- a/test/Main.hs
+++ b/test/Main.hs
@@ -1,27 +1,40 @@
 module Main (main) where
 
 import Datalog
+
 import Data.Text qualified as T
 import Data.Text.IO qualified as T
-import Text.Megaparsec qualified as M
 
-parserGoldenTest :: String -> IO Bool
-parserGoldenTest prefix = do
+import Test.Tasty
+import Test.Tasty.HUnit
+
+golden :: (Show err, Show val) => String -> String -> (FilePath -> IO (Either err val)) -> IO ()
+golden outExt prefix run = do
   let inFile = "test/golden/" <> prefix <> ".dl"
-      outFile = "test/golden/" <> prefix <> ".show"
-  inp <- T.readFile inFile
+      outFile = "test/golden/" <> prefix <> outExt
+  res <- run inFile
   out <- T.readFile outFile
-  result <- case M.parse parseProgram inFile inp of
-    Left e -> do
-      print e
-      return False
-    Right out' -> do
-      return (T.strip out == T.pack (show out'))
-  let resultS = if result then "passed" else "failed"
-  putStrLn $ unwords ["Parser test", prefix, resultS]
-  return result
+  case res of
+    Left e -> assertFailure (show e)
+    Right out' -> assertEqual "" (T.strip out) (T.pack (show out'))
+
+parserGoldenTest :: String -> TestTree
+parserGoldenTest prefix = testCase ("Parser test: " <> prefix) $ golden ".show" prefix readProgram
+
+{-
+databaseGoldenTest :: String -> TestTree
+databaseGoldenTest prefix = testCase ("Database test: " <> prefix) $ golden ".db0" prefix readDatabase
+
+fixedpointGoldenTest :: String -> TestTree
+fixedpointGoldenTest prefix = testCase ("Fixedpoint test: " <> prefix) $ golden ".dbF" prefix $ \fp -> do
+  fmap (fmap extendFixedpointDb) (readDatabase fp)
+-}
 
 main :: IO ()
-main = do
-  True <- parserGoldenTest "ancestor"
-  return ()
+main = defaultMain $
+  testGroup "all"
+    [ testGroup "parser"
+      [ parserGoldenTest "ancestor"
+      , parserGoldenTest "graph"
+      ]
+    ]
diff --git a/test/golden/ancestor.show b/test/golden/ancestor.show
index f2673d7..c2405e2 100644
--- a/test/golden/ancestor.show
+++ b/test/golden/ancestor.show
@@ -1 +1 @@
-Program [Atom "parent" [Con "xerces",Con "brooke"] :- [],Atom "parent" [Con "brooke",Con "damocles"] :- [],Atom "ancestor" [Var "X",Var "Y"] :- [Atom "parent" [Var "X",Var "Y"]],Atom "ancestor" [Var "X",Var "Y"] :- [Atom "parent" [Var "X",Var "Z"],Atom "ancestor" [Var "Z",Var "Y"]]]
+Program [Atom (RelId "parent") [Con (ConId "xerces"),Con (ConId "brooke")] :- [],Atom (RelId "parent") [Con (ConId "brooke"),Con (ConId "damocles")] :- [],Atom (RelId "ancestor") [Var (VarId "X"),Var (VarId "Y")] :- [Atom (RelId "parent") [Var (VarId "X"),Var (VarId "Y")]],Atom (RelId "ancestor") [Var (VarId "X"),Var (VarId "Y")] :- [Atom (RelId "parent") [Var (VarId "X"),Var (VarId "Z")],Atom (RelId "ancestor") [Var (VarId "Z"),Var (VarId "Y")]]]
diff --git a/test/golden/graph.dl b/test/golden/graph.dl
new file mode 100644
index 0000000..01879ed
--- /dev/null
+++ b/test/golden/graph.dl
@@ -0,0 +1,11 @@
+odd(X,Y) :- r(X,Y).
+odd(X,Y) :- even(X,Z), r(Z,Y).
+even(X,Y) :- odd(X,Z), r(Z,Y).
+
+r(0,1).
+r(1,2).
+r(2,3).
+r(3,4).
+r(4,5).
+
+r(X,Y) :- r(Y,X).
diff --git a/test/golden/graph.show b/test/golden/graph.show
new file mode 100644
index 0000000..0668ac0
--- /dev/null
+++ b/test/golden/graph.show
@@ -0,0 +1 @@
+Program [Atom (RelId "odd") [Var (VarId "X"),Var (VarId "Y")] :- [Atom (RelId "r") [Var (VarId "X"),Var (VarId "Y")]],Atom (RelId "odd") [Var (VarId "X"),Var (VarId "Y")] :- [Atom (RelId "even") [Var (VarId "X"),Var (VarId "Z")],Atom (RelId "r") [Var (VarId "Z"),Var (VarId "Y")]],Atom (RelId "even") [Var (VarId "X"),Var (VarId "Y")] :- [Atom (RelId "odd") [Var (VarId "X"),Var (VarId "Z")],Atom (RelId "r") [Var (VarId "Z"),Var (VarId "Y")]],Atom (RelId "r") [Con (ConId "0"),Con (ConId "1")] :- [],Atom (RelId "r") [Con (ConId "1"),Con (ConId "2")] :- [],Atom (RelId "r") [Con (ConId "2"),Con (ConId "3")] :- [],Atom (RelId "r") [Con (ConId "3"),Con (ConId "4")] :- [],Atom (RelId "r") [Con (ConId "4"),Con (ConId "5")] :- [],Atom (RelId "r") [Var (VarId "X"),Var (VarId "Y")] :- [Atom (RelId "r") [Var (VarId "Y"),Var (VarId "X")]]]
diff --git a/toy-datalog.cabal b/toy-datalog.cabal
index d4e7fa3..9151344 100644
--- a/toy-datalog.cabal
+++ b/toy-datalog.cabal
@@ -24,10 +24,13 @@ library
         Datalog
         Datalog.Parser
         Datalog.Syntax
+        Datalog.Eval
+        Datalog.IO
     build-depends:
         base,
         text,
-        megaparsec
+        megaparsec,
+        containers
     hs-source-dirs:   src
     default-language: Haskell2010
 
@@ -51,4 +54,6 @@ test-suite toy-datalog-test
         base,
         toy-datalog,
         megaparsec,
-        text
+        text,
+        tasty,
+        tasty-hunit