diff --git a/src/Elara/AST/Generic/Instances/StripLocation.hs b/src/Elara/AST/Generic/Instances/StripLocation.hs
index dac67b9..3cecd78 100644
--- a/src/Elara/AST/Generic/Instances/StripLocation.hs
+++ b/src/Elara/AST/Generic/Instances/StripLocation.hs
@@ -200,8 +200,7 @@ instance
     forall (ast1 :: LocatedAST) (ast2 :: UnlocatedAST).
     ( ASTLocate' ast1 ~ Located
     , ASTLocate' ast2 ~ Unlocated
-    , ( StripLocation (Select "Infixed" ast1) (Select "Infixed" ast2)
-      )
+    , (StripLocation (Select "Infixed" ast1) (Select "Infixed" ast2))
     , ( StripLocation
             (CleanupLocated (Located (Select "SymOp" ast1)))
             (Select "SymOp" ast2)
diff --git a/src/Elara/AST/Pretty.hs b/src/Elara/AST/Pretty.hs
index e4556d3..b517d98 100644
--- a/src/Elara/AST/Pretty.hs
+++ b/src/Elara/AST/Pretty.hs
@@ -45,8 +45,7 @@ prettyLambdaExpr args body = parens (if ?contextFree then prettyCTFLambdaExpr el
 
         long =
             align
-                ( "\\" <+> hsep (pretty <$> args) <+> "->" <> hardline <> nest indentDepth (pretty body)
-                )
+                ("\\" <+> hsep (pretty <$> args) <+> "->" <> hardline <> nest indentDepth (pretty body))
 
 prettyFunctionCall :: (?contextFree :: Bool, Pretty a, Pretty b) => a -> b -> Doc AnsiStyle
 prettyFunctionCall e1' e2' = parens (if ?contextFree then short else group (flatAlt long short))
diff --git a/src/Elara/Parse/Declaration.hs b/src/Elara/Parse/Declaration.hs
index b4e5cb1..c981773 100644
--- a/src/Elara/Parse/Declaration.hs
+++ b/src/Elara/Parse/Declaration.hs
@@ -42,8 +42,7 @@ defDec modName = fmapLocated Declaration $ do
         ( Declaration'
             modName
             name
-            ( DeclarationBody declBody
-            )
+            (DeclarationBody declBody)
         )
 
 letDec :: Located ModuleName -> Parser FrontendDeclaration
diff --git a/src/Elara/TypeInfer/ConstraintGeneration.hs b/src/Elara/TypeInfer/ConstraintGeneration.hs
index a61ad15..f6aa874 100644
--- a/src/Elara/TypeInfer/ConstraintGeneration.hs
+++ b/src/Elara/TypeInfer/ConstraintGeneration.hs
@@ -11,7 +11,8 @@ import Elara.AST.Typed (TypedExpr, TypedExpr')
 import Elara.AST.VarRef
 import Elara.Data.Unique (UniqueGen)
 import Elara.TypeInfer.Environment (InferError, LocalTypeEnvironment, TypeEnvKey (TermVarKey), TypeEnvironment, addType, lookupLocalVar, lookupLocalVarType, lookupType, withLocalType)
-import Elara.TypeInfer.Type (AxiomScheme, Constraint (..), Monotype (..), Scalar (..), Substitutable (..), Substitution, Type (Forall))
+import Elara.TypeInfer.Ftv (occurs)
+import Elara.TypeInfer.Type (AxiomScheme, Constraint (..), Monotype (..), Scalar (..), Substitutable (..), Substitution (..), Type (Forall))
 import Elara.TypeInfer.Unique (makeUniqueTyVar)
 import Polysemy
 import Polysemy.Error
@@ -95,9 +96,61 @@ tidyConstraint (Conjunction x (Conjunction y z)) | x == y = Conjunction (tidyCon
 tidyConstraint (Conjunction c1 c2) = Conjunction (tidyConstraint c1) (tidyConstraint c2)
 tidyConstraint (Equality x y) = Equality x y
 
--- unifyConstraints :: [Constraint loc] ->
-
--- simplifyConstraints :: AxiomScheme loc -> Constraint loc -> Constraint loc -> (Constraint loc, Substitution loc)
--- simplifyConstraints axioms given wanted = (residual, subst)
---   where
---     (residual, subst) = todo
+solveConstraints :: AxiomScheme loc -> Constraint loc -> Constraint loc -> Sem '[Error UnifyError] (Constraint loc, Substitution loc)
+solveConstraints axioms given wanted = do
+    (substitution, simplifiedWanted) <- unifyEquality wanted
+
+    -- let simplifiedGiven = substitute substitution given
+
+    -- let simplifiedWanted' = substitute substitution simplifiedWanted
+
+    -- let (entailable, residualWanted) = entail axioms simplifiedGiven simplifiedWanted'
+
+    pure (todo, substitution)
+
+unifyEquality :: Constraint loc -> Sem '[Error UnifyError] (Substitution loc, Constraint loc)
+unifyEquality (Equality a b) = unify a b
+unifyEquality c = pure (mempty, c)
+
+unify :: HasCallStack => Monotype loc -> Monotype loc -> Sem '[Error UnifyError] (Substitution loc, Constraint loc)
+unify (TypeVar a) (TypeVar b) | a == b = pure (mempty, EmptyConstraint)
+unify (TypeVar a) b =
+    if occurs a b
+        then throw OccursCheckFailed
+        else pure (Substitution [(a, b)], EmptyConstraint)
+unify a (TypeVar b) = unify (TypeVar b) a -- swap to avoid duplication
+unify (Scalar a) (Scalar b) =
+    if a == b
+        then pure (mempty, EmptyConstraint)
+        else throw ScalarMismatch
+unify (TypeConstructor a as) (TypeConstructor b bs)
+    | a /= b = throw TypeConstructorMismatch
+    | length as /= length bs = throw ArityMismatch
+    | otherwise = unifyMany as bs
+unify (Function a b) (Function c d) = do
+    (s1, c1) <- unify a c
+    (s2, c2) <- unify (substituteAll s1 b) (substituteAll s1 d)
+    pure (s1 <> s2, c1 <> c2)
+unify a b = throw $ UnificationFailed $ "Unification failed: " <> show a <> " and " <> show b
+
+unifyMany ::
+    HasCallStack =>
+    [Monotype loc] ->
+    [Monotype loc] ->
+    Sem
+        '[Error UnifyError]
+        (Substitution loc, Constraint loc)
+unifyMany [] _ = pure (mempty, EmptyConstraint)
+unifyMany _ [] = pure (mempty, EmptyConstraint)
+unifyMany (a : as) (b : bs) = do
+    (s1, c1) <- unify a b
+    (s2, c2) <- unifyMany (fmap (substituteAll s1) as) (fmap (substituteAll s1) bs)
+    pure (s1 <> s2, c1 <> c2)
+
+data UnifyError
+    = OccursCheckFailed
+    | ScalarMismatch
+    | TypeConstructorMismatch
+    | ArityMismatch
+    | UnificationFailed String
+    deriving (Eq, Show)
diff --git a/src/Elara/TypeInfer/Ftv.hs b/src/Elara/TypeInfer/Ftv.hs
new file mode 100644
index 0000000..3879475
--- /dev/null
+++ b/src/Elara/TypeInfer/Ftv.hs
@@ -0,0 +1,20 @@
+module Elara.TypeInfer.Ftv where
+
+import Data.Set (difference, member)
+import Elara.TypeInfer.Type (Monotype (..), Type (..))
+import Elara.TypeInfer.Unique
+
+class Ftv a where
+    ftv :: a -> Set UniqueTyVar
+
+instance Ftv (Monotype loc) where
+    ftv (TypeVar tv) = one tv
+    ftv (Scalar _) = mempty
+    ftv (TypeConstructor _ ts) = foldMap ftv ts
+    ftv (Function t1 t2) = ftv t1 <> ftv t2
+
+instance Ftv (Type loc) where
+    ftv (Forall tv _ t) = ftv t `difference` one tv
+
+occurs :: Ftv a => UniqueTyVar -> a -> Bool
+occurs tv a = tv `member` ftv a
diff --git a/src/Elara/TypeInfer/Type.hs b/src/Elara/TypeInfer/Type.hs
index 53efe26..f0a6a15 100644
--- a/src/Elara/TypeInfer/Type.hs
+++ b/src/Elara/TypeInfer/Type.hs
@@ -3,9 +3,7 @@ module Elara.TypeInfer.Type where
 
 import Data.Kind qualified as Kind
 import Elara.AST.Name
-import Elara.AST.VarRef (UnlocatedVarRef, VarRef)
 import Elara.TypeInfer.Unique
-import Prelude hiding (Constraint)
 
 -- | A type scheme σ
 data Type loc
@@ -67,11 +65,13 @@ data Scalar
     | ScalarString
     | ScalarChar
     | ScalarUnit
-    deriving (Generic, Show, Eq, Ord)
+    deriving (Generic, Show, Eq, Ord, Enum, Bounded)
 
 type DataCon = Qualified TypeName
 
-data Substitution loc = Substitution [(UniqueTyVar, Monotype loc)]
+newtype Substitution loc = Substitution [(UniqueTyVar, Monotype loc)]
+    deriving newtype (Semigroup, Monoid)
+    deriving stock (Eq, Show)
 
 class Substitutable (a :: k -> Kind.Type) where
     substitute :: UniqueTyVar -> Monotype loc -> a loc -> a loc
diff --git a/test/Arbitrary/Type.hs b/test/Arbitrary/Type.hs
new file mode 100644
index 0000000..faf06b9
--- /dev/null
+++ b/test/Arbitrary/Type.hs
@@ -0,0 +1,28 @@
+module Arbitrary.Type where
+
+import Elara.AST.Name
+import Elara.Data.Unique (unsafeMkUnique)
+import Elara.TypeInfer.Type
+import Elara.TypeInfer.Unique
+import Hedgehog (Gen)
+import Hedgehog.Gen qualified as Gen
+import Hedgehog.Range qualified as Range
+import Region (qualifiedTest)
+
+-- | contrary to what the name suggests, this will NOT be unique :)
+genUniqueTypeVar :: Gen UniqueTyVar
+genUniqueTypeVar = unsafeMkUnique Nothing <$> Gen.integral (Range.linear 0 100)
+
+typeConstructorNames :: [TypeName]
+typeConstructorNames = ["List", "Maybe", "Pair", "Box", "IO"]
+
+genMonotype :: Gen (Monotype loc)
+genMonotype =
+    Gen.recursive
+        Gen.choice
+        [ TypeVar <$> genUniqueTypeVar
+        , Scalar <$> Gen.enumBounded
+        ]
+        [ TypeConstructor <$> Gen.element (qualifiedTest <$> typeConstructorNames) <*> Gen.list (Range.linear 0 2) genMonotype
+        , Function <$> genMonotype <*> genMonotype
+        ]
diff --git a/test/Infer.hs b/test/Infer.hs
index 3d6f2ab..67ef51f 100644
--- a/test/Infer.hs
+++ b/test/Infer.hs
@@ -16,6 +16,7 @@ import Elara.TypeInfer.Type
 import Hedgehog (Property, assert, evalEither, evalEitherM, evalIO, failure, forAll, property)
 import Hedgehog.Gen qualified as Gen
 import Hedgehog.Range qualified as Range
+import Infer.Unify qualified as Unify
 import Optics.Operators.Unsafe ((^?!))
 import Polysemy (Sem, run, runM, subsume, subsume_)
 import Polysemy.Error (runError)
@@ -30,11 +31,12 @@ import Test.Syd.Hedgehog ()
 import Prelude hiding (fail)
 
 spec :: Spec
-spec = describe "Infers types correctly" $ parallel $ do
+spec = describe "Infers types correctly" $ do
     literalTests
     lambdaTests
 
     it "infers literals" prop_literalTypesInvariants
+    Unify.spec
 
 -- Literal Type Inference Tests
 literalTests :: Spec
diff --git a/test/Infer/Unify.hs b/test/Infer/Unify.hs
new file mode 100644
index 0000000..ae6c0bc
--- /dev/null
+++ b/test/Infer/Unify.hs
@@ -0,0 +1,62 @@
+module Infer.Unify where
+
+import Arbitrary.Type (genMonotype, genUniqueTypeVar)
+import Elara.TypeInfer.ConstraintGeneration
+import Elara.TypeInfer.Type
+import Hedgehog (Gen, Property, evalEither, forAll, property, (===))
+import Hedgehog.Gen qualified as Gen
+import Hedgehog.Range qualified as Range
+import Polysemy
+import Polysemy.Error
+import Test.Syd
+import Test.Syd.Hedgehog ()
+
+spec :: Spec
+spec = describe "Type unification" $ do
+    it "unifies type variables" prop_unify_type_vars
+    it "unifies scalars" prop_unify_scalars
+    it "unifies functions" prop_unify_functions
+    it "unifies self" prop_unify_self
+    it "fails to unify mismatched types" prop_unify_failure
+
+runUnify ::
+    Sem '[Error UnifyError] (Substitution loc, Constraint loc) ->
+    Either UnifyError (Substitution loc, Constraint loc)
+runUnify = run . runError
+
+prop_unify_type_vars :: Property
+prop_unify_type_vars = property $ do
+    a <- forAll $ genUniqueTypeVar
+    let typeVar = TypeVar a
+    (sub, _) <- evalEither $ runUnify $ unify typeVar typeVar
+    sub === Substitution []
+
+prop_unify_scalars :: Property
+prop_unify_scalars = property $ do
+    a <- forAll $ Gen.enumBounded
+    let scalarType = Scalar a
+    (sub, _) <- evalEither $ runUnify $ unify scalarType scalarType
+    sub === Substitution []
+
+prop_unify_self :: Property
+prop_unify_self = property $ do
+    a <- forAll genMonotype
+    (sub, _) <- evalEither $ runUnify $ unify a a
+    sub === Substitution []
+
+prop_unify_functions :: Property
+prop_unify_functions = property $ do
+    a <- forAll genMonotype
+    b <- forAll genMonotype
+    (sub, _) <- evalEither $ runUnify $ unify (Function a b) (Function a b)
+    sub === Substitution []
+
+-- Hedgehog property: Check unification failure for mismatched types
+prop_unify_failure :: Property
+prop_unify_failure = property $ do
+    a <- forAll genMonotype
+    b <- forAll genMonotype
+    -- let's come back to this later
+    -- let result = runUnify $ unify a b
+    -- result === Left (UnificationFailed $ "Unification failed: " <> show a <> " and " <> show b)
+    guard $ a /= b