diff --git a/crates/ide/src/lib.rs b/crates/ide/src/lib.rs
index 301380d..296a0d6 100644
--- a/crates/ide/src/lib.rs
+++ b/crates/ide/src/lib.rs
@@ -3,7 +3,7 @@ mod def;
 mod diagnostic;
 mod ide;
 mod text_edit;
-mod ty;
+pub(crate) mod ty;
 
 #[cfg(test)]
 mod tests;
diff --git a/crates/ide/src/ty/infer.rs b/crates/ide/src/ty/infer.rs
index 02ba830..dded443 100644
--- a/crates/ide/src/ty/infer.rs
+++ b/crates/ide/src/ty/infer.rs
@@ -38,6 +38,8 @@ enum Ty {
     List(TyVar),
     Lambda(TyVar, TyVar),
     Attrset(Attrset),
+
+    External(super::Ty),
 }
 
 impl Ty {
@@ -66,6 +68,14 @@ impl InferenceResult {
 }
 
 pub(crate) fn infer_query(db: &dyn TyDatabase, file: FileId) -> Arc<InferenceResult> {
+    infer_with(db, file, None)
+}
+
+pub(crate) fn infer_with(
+    db: &dyn TyDatabase,
+    file: FileId,
+    expect_ty: Option<super::Ty>,
+) -> Arc<InferenceResult> {
     let module = db.module(file);
     let nameres = db.name_resolution(file);
     let table = UnionFind::new(module.names().len() + module.exprs().len(), |_| Ty::Unknown);
@@ -74,7 +84,10 @@ pub(crate) fn infer_query(db: &dyn TyDatabase, file: FileId) -> Arc<InferenceRes
         nameres: &nameres,
         table,
     };
-    ctx.infer_expr(module.entry_expr());
+    let ty = ctx.infer_expr(module.entry_expr());
+    if let Some(expect_ty) = expect_ty {
+        ctx.unify_var_ty(ty, Ty::External(expect_ty));
+    }
     Arc::new(ctx.finish())
 }
 
@@ -101,10 +114,23 @@ impl<'db> InferCtx<'db> {
         TyVar(self.module.names().len() as u32 + u32::from(i.into_raw()))
     }
 
+    fn import_external(&mut self, ty: super::Ty) -> TyVar {
+        let ty = match ty {
+            super::Ty::Unknown => Ty::Unknown,
+            super::Ty::Bool => Ty::Bool,
+            super::Ty::Int => Ty::Int,
+            super::Ty::Float => Ty::Float,
+            super::Ty::String => Ty::String,
+            super::Ty::Path => Ty::Path,
+            super::Ty::List(_) | super::Ty::Lambda(..) | super::Ty::Attrset(_) => Ty::External(ty),
+        };
+        TyVar(self.table.push(ty))
+    }
+
     fn infer_expr(&mut self, e: ExprId) -> TyVar {
         let ty = self.infer_expr_inner(e);
         let placeholder_ty = self.ty_for_expr(e);
-        self.unify(placeholder_ty, ty);
+        self.unify_var(placeholder_ty, ty);
         ty
     }
 
@@ -134,11 +160,11 @@ impl<'db> InferCtx<'db> {
                 let param_ty = self.new_ty_var();
 
                 if let Some(name) = *name {
-                    self.unify(param_ty, self.ty_for_name(name));
+                    self.unify_var(param_ty, self.ty_for_name(name));
                 }
 
                 if let Some(pat) = pat {
-                    self.unify_kind(param_ty, Ty::Attrset(Attrset::default()));
+                    self.unify_var_ty(param_ty, Ty::Attrset(Attrset::default()));
                     for &(name, default_expr) in pat.fields.iter() {
                         // Always infer default_expr.
                         let default_ty = default_expr.map(|e| self.infer_expr(e));
@@ -148,12 +174,12 @@ impl<'db> InferCtx<'db> {
                         };
                         let name_ty = self.ty_for_name(name);
                         if let Some(default_ty) = default_ty {
-                            self.unify(name_ty, default_ty);
+                            self.unify_var(name_ty, default_ty);
                         }
                         let field_text = self.module[name].text.clone();
                         let param_field_ty =
                             self.infer_set_field(param_ty, field_text, AttrSource::Name(name));
-                        self.unify(param_field_ty, name_ty);
+                        self.unify_var(param_field_ty, name_ty);
                     }
                 }
 
@@ -170,10 +196,10 @@ impl<'db> InferCtx<'db> {
             }
             &Expr::IfThenElse(cond, then, else_) => {
                 let cond_ty = self.infer_expr(cond);
-                self.unify_kind(cond_ty, Ty::Bool);
+                self.unify_var_ty(cond_ty, Ty::Bool);
                 let then_ty = self.infer_expr(then);
                 let else_ty = self.infer_expr(else_);
-                self.unify(then_ty, else_ty);
+                self.unify_var(then_ty, else_ty);
                 then_ty
             }
             &Expr::Binary(op, lhs, rhs) => {
@@ -188,15 +214,15 @@ impl<'db> InferCtx<'db> {
                 match op {
                     BinaryOpKind::Equal | BinaryOpKind::NotEqual => Ty::Bool.intern(self),
                     BinaryOpKind::Imply | BinaryOpKind::Or | BinaryOpKind::And => {
-                        self.unify_kind(lhs_ty, Ty::Bool);
-                        self.unify_kind(rhs_ty, Ty::Bool);
+                        self.unify_var_ty(lhs_ty, Ty::Bool);
+                        self.unify_var_ty(rhs_ty, Ty::Bool);
                         Ty::Bool.intern(self)
                     }
                     BinaryOpKind::Less
                     | BinaryOpKind::Greater
                     | BinaryOpKind::LessEqual
                     | BinaryOpKind::GreaterEqual => {
-                        self.unify(lhs_ty, rhs_ty);
+                        self.unify_var(lhs_ty, rhs_ty);
                         Ty::Bool.intern(self)
                     }
                     // TODO: Polymorphism.
@@ -205,19 +231,19 @@ impl<'db> InferCtx<'db> {
                     | BinaryOpKind::Mul
                     | BinaryOpKind::Div => {
                         // TODO: Arguments have type: int | float.
-                        self.unify(lhs_ty, rhs_ty);
+                        self.unify_var(lhs_ty, rhs_ty);
                         lhs_ty
                     }
                     BinaryOpKind::Update => {
-                        self.unify_kind(lhs_ty, Ty::Attrset(Attrset::default()));
-                        self.unify_kind(rhs_ty, Ty::Attrset(Attrset::default()));
-                        self.unify(lhs_ty, rhs_ty);
+                        self.unify_var_ty(lhs_ty, Ty::Attrset(Attrset::default()));
+                        self.unify_var_ty(rhs_ty, Ty::Attrset(Attrset::default()));
+                        self.unify_var(lhs_ty, rhs_ty);
                         lhs_ty
                     }
                     BinaryOpKind::Concat => {
                         let ret_ty = Ty::List(self.new_ty_var()).intern(self);
-                        self.unify(lhs_ty, ret_ty);
-                        self.unify(rhs_ty, ret_ty);
+                        self.unify_var(lhs_ty, ret_ty);
+                        self.unify_var(rhs_ty, ret_ty);
                         ret_ty
                     }
                 }
@@ -227,7 +253,7 @@ impl<'db> InferCtx<'db> {
                 match op {
                     None => self.new_ty_var(),
                     Some(UnaryOpKind::Not) => {
-                        self.unify_kind(arg_ty, Ty::Bool);
+                        self.unify_var_ty(arg_ty, Ty::Bool);
                         Ty::Bool.intern(self)
                     }
                     // TODO: The argument is int | bool.
@@ -238,9 +264,9 @@ impl<'db> InferCtx<'db> {
                 let param_ty = self.new_ty_var();
                 let ret_ty = self.new_ty_var();
                 let lam_ty = self.infer_expr(lam);
-                self.unify_kind(lam_ty, Ty::Lambda(param_ty, ret_ty));
+                self.unify_var_ty(lam_ty, Ty::Lambda(param_ty, ret_ty));
                 let arg_ty = self.infer_expr(arg);
-                self.unify(arg_ty, param_ty);
+                self.unify_var(arg_ty, param_ty);
                 ret_ty
             }
             Expr::HasAttr(set_expr, path) => {
@@ -248,7 +274,7 @@ impl<'db> InferCtx<'db> {
                 self.infer_expr(*set_expr);
                 for &attr in path.iter() {
                     let attr_ty = self.infer_expr(attr);
-                    self.unify_kind(attr_ty, Ty::String);
+                    self.unify_var_ty(attr_ty, Ty::String);
                 }
                 Ty::Bool.intern(self)
             }
@@ -256,20 +282,20 @@ impl<'db> InferCtx<'db> {
                 let set_ty = self.infer_expr(*set_expr);
                 let ret_ty = path.iter().fold(set_ty, |set_ty, &attr| {
                     let attr_ty = self.infer_expr(attr);
-                    self.unify_kind(attr_ty, Ty::String);
+                    self.unify_var_ty(attr_ty, Ty::String);
                     match &self.module[attr] {
                         Expr::Literal(Literal::String(key)) => {
                             self.infer_set_field(set_ty, key.clone(), AttrSource::Unknown)
                         }
                         _ => {
-                            self.unify_kind(set_ty, Ty::Attrset(Attrset::default()));
+                            self.unify_var_ty(set_ty, Ty::Attrset(Attrset::default()));
                             self.new_ty_var()
                         }
                     }
                 });
                 if let Some(default_expr) = *default_expr {
                     let default_ty = self.infer_expr(default_expr);
-                    self.unify(ret_ty, default_ty);
+                    self.unify_var(ret_ty, default_ty);
                 }
                 ret_ty
             }
@@ -277,7 +303,7 @@ impl<'db> InferCtx<'db> {
                 for &part in parts.iter() {
                     let ty = self.infer_expr(part);
                     // FIXME: Parts are coerce-able to string.
-                    self.unify_kind(ty, Ty::String);
+                    self.unify_var_ty(ty, Ty::String);
                 }
                 Ty::Path.intern(self)
             }
@@ -285,7 +311,7 @@ impl<'db> InferCtx<'db> {
                 for &part in parts.iter() {
                     let ty = self.infer_expr(part);
                     // FIXME: Parts are coerce-able to string.
-                    self.unify_kind(ty, Ty::String);
+                    self.unify_var_ty(ty, Ty::String);
                 }
                 Ty::String.intern(self)
             }
@@ -294,7 +320,7 @@ impl<'db> InferCtx<'db> {
                 let ret_ty = Ty::List(expect_elem_ty).intern(self);
                 for &elem in elems.iter() {
                     let elem_ty = self.infer_expr(elem);
-                    self.unify(elem_ty, expect_elem_ty);
+                    self.unify_var(elem_ty, expect_elem_ty);
                 }
                 ret_ty
             }
@@ -330,14 +356,14 @@ impl<'db> InferCtx<'db> {
                     self.infer_set_field(from_ty, name_text.clone(), AttrSource::Name(name))
                 }
             };
-            self.unify(name_ty, value_ty);
+            self.unify_var(name_ty, value_ty);
             let src = AttrSource::Name(name);
             fields.insert(name_text, (value_ty, src));
         }
 
         for &(k, v) in bindings.dynamics.iter() {
             let name_ty = self.infer_expr(k);
-            self.unify_kind(name_ty, Ty::String);
+            self.unify_var_ty(name_ty, Ty::String);
             self.infer_expr(v);
         }
 
@@ -357,53 +383,44 @@ impl<'db> InferCtx<'db> {
                     ent.insert((next_ty, src));
                 }
             },
+            Ty::External(super::Ty::Attrset(set)) => {
+                if let Some(ty) = set.get(&field).cloned() {
+                    return self.import_external(ty);
+                }
+            }
             k @ Ty::Unknown => {
                 *k = Ty::Attrset(Attrset([(field, (next_ty, src))].into_iter().collect()));
             }
-            Ty::Bool
-            | Ty::Int
-            | Ty::Float
-            | Ty::String
-            | Ty::Path
-            | Ty::List(_)
-            | Ty::Lambda(_, _) => {}
+            _ => {}
         }
         self.new_ty_var()
     }
 
-    /// Unify a type in table with an expected kind.
-    fn unify_kind(&mut self, a: TyVar, b: Ty) {
-        match (self.table.get_mut(a.0), b) {
-            (a @ Ty::Unknown, b) => *a = b,
-            (&mut Ty::List(a), Ty::List(b)) => self.unify(a, b),
-            (&mut Ty::Lambda(a1, a2), Ty::Lambda(b1, b2)) => {
-                self.unify(a1, b1);
-                self.unify(a2, b2);
-            }
-            (Ty::Attrset(_), Ty::Attrset(b)) => {
-                assert!(b.0.is_empty(), "Never unify_kind an non-empty set");
-            }
-            _ => {}
-        }
+    fn unify_var_ty(&mut self, var: TyVar, rhs: Ty) {
+        let lhs = mem::replace(self.table.get_mut(var.0), Ty::Unknown);
+        let ret = self.unify(lhs, rhs);
+        *self.table.get_mut(var.0) = ret;
     }
 
-    fn unify(&mut self, a: TyVar, b: TyVar) {
-        let (i, other) = self.table.unify(a.0, b.0);
-        let other = match other {
-            Some(other) => other,
-            None => return,
-        };
-        let mut a = mem::replace(self.table.get_mut(i), Ty::Unknown);
-        match (&mut a, other) {
-            (a @ Ty::Unknown, b) => *a = b,
-            (&mut Ty::List(a), Ty::List(b)) => {
-                self.unify(a, b);
+    fn unify_var(&mut self, lhs: TyVar, rhs: TyVar) {
+        let (var, rhs) = self.table.unify(lhs.0, rhs.0);
+        let Some(rhs) = rhs else { return };
+        self.unify_var_ty(TyVar(var), rhs);
+    }
+
+    fn unify(&mut self, lhs: Ty, rhs: Ty) -> Ty {
+        match (lhs, rhs) {
+            (Ty::Unknown, other) | (other, Ty::Unknown) => other,
+            (Ty::List(a), Ty::List(b)) => {
+                self.unify_var(a, b);
+                Ty::List(a)
             }
-            (&mut Ty::Lambda(a1, a2), Ty::Lambda(b1, b2)) => {
-                self.unify(a1, b1);
-                self.unify(a2, b2);
+            (Ty::Lambda(arg1, ret1), Ty::Lambda(arg2, ret2)) => {
+                self.unify_var(arg1, arg2);
+                self.unify_var(ret1, ret2);
+                Ty::Lambda(arg1, ret1)
             }
-            (Ty::Attrset(a), Ty::Attrset(b)) => {
+            (Ty::Attrset(mut a), Ty::Attrset(b)) => {
                 for (field, (ty2, src2)) in b.0 {
                     match a.0.entry(field) {
                         Entry::Vacant(ent) => {
@@ -412,14 +429,34 @@ impl<'db> InferCtx<'db> {
                         Entry::Occupied(mut ent) => {
                             let (ty1, src1) = ent.get_mut();
                             src1.unify(src2);
-                            self.unify(*ty1, ty2);
+                            self.unify_var(*ty1, ty2);
                         }
                     }
                 }
+                Ty::Attrset(a)
             }
-            _ => {}
+            (Ty::External(external), local) | (local, Ty::External(external)) => {
+                match (local, &external) {
+                    (Ty::Lambda(arg1, ret1), super::Ty::Lambda(arg2, ret2)) => {
+                        let arg2 = self.import_external(super::Ty::clone(arg2));
+                        let ret2 = self.import_external(super::Ty::clone(ret2));
+                        self.unify_var(arg1, arg2);
+                        self.unify_var(ret1, ret2);
+                    }
+                    (Ty::Attrset(a), super::Ty::Attrset(b)) => {
+                        for (field, (ty, _)) in &a.0 {
+                            if let Some(field_ty) = b.get(field) {
+                                let var = self.import_external(field_ty.clone());
+                                self.unify_var(*ty, var);
+                            }
+                        }
+                    }
+                    _ => {}
+                }
+                Ty::External(external)
+            }
+            (lhs, _) => lhs,
         }
-        *self.table.get_mut(i) = a;
     }
 
     fn finish(mut self) -> InferenceResult {
@@ -494,6 +531,7 @@ impl<'a> Collector<'a> {
                     .collect();
                 super::Ty::Attrset(super::Attrset(set).into())
             }
+            Ty::External(ty) => ty,
         }
     }
 }
diff --git a/crates/ide/src/ty/mod.rs b/crates/ide/src/ty/mod.rs
index bef879a..94e578d 100644
--- a/crates/ide/src/ty/mod.rs
+++ b/crates/ide/src/ty/mod.rs
@@ -1,3 +1,31 @@
+#[rustfmt::skip]
+#[macro_export]
+macro_rules! ty {
+    (?) => { $crate::ty::Ty::Unknown };
+    (bool) => { $crate::ty::Ty::Int };
+    (int) => { $crate::ty::Ty::Int };
+    (float) => { $crate::ty::Ty::Float };
+    (string) => { $crate::ty::Ty::String };
+    (path) => { $crate::ty::Ty::Path };
+    // TODO: More precise type for derivations.
+    (derivation) => {
+        $crate::ty::Ty::Attrset(::std::sync::Arc::new($crate::ty::Attrset::default()))
+    };
+    (($($inner:tt)*)) => {{ ty!($($inner)*) }};
+    ([$($inner:tt)*]) => { $crate::ty::Ty::List(::std::arc::Arc::new($ty!($($inner)*)))};
+    ({ $($key:literal : $ty:tt),* $(,)? }) => {{
+        $crate::ty::Ty::Attrset(::std::sync::Arc::new($crate::ty::Attrset::from_internal([
+            $(($key, ty!($ty)),)*
+        ])))
+    }};
+    ($arg:tt -> $($ret:tt)*) => {
+        $crate::ty::Ty::Lambda(
+            ::std::sync::Arc::new(ty!($arg)),
+            ::std::sync::Arc::new(ty!($($ret)*)),
+        )
+    };
+}
+
 mod fmt;
 mod infer;
 mod union_find;
@@ -65,6 +93,26 @@ impl std::fmt::Debug for Ty {
 pub struct Attrset(Box<[(SmolStr, Ty, AttrSource)]>);
 
 impl Attrset {
+    /// Build an Attrset for internal type schemas.
+    ///
+    /// # Panics
+    /// The given iterator must have no duplicated fields, or it'll panic.
+    #[track_caller]
+    // FIXME: Currently this is only used in tests.
+    #[cfg_attr(not(test), allow(dead_code))]
+    fn from_internal(iter: impl IntoIterator<Item = (&'static str, Ty)>) -> Self {
+        let mut set = iter
+            .into_iter()
+            .map(|(name, ty)| (SmolStr::from(name), ty, AttrSource::Unknown))
+            .collect::<Box<[_]>>();
+        set.sort_by(|(lhs, ..), (rhs, ..)| lhs.cmp(rhs));
+        assert!(
+            set.windows(2).all(|w| w[0].0 != w[1].0),
+            "Duplicated fields",
+        );
+        Self(set)
+    }
+
     pub fn is_empty(&self) -> bool {
         self.0.is_empty()
     }
diff --git a/crates/ide/src/ty/tests.rs b/crates/ide/src/ty/tests.rs
index a1ae488..aa995b3 100644
--- a/crates/ide/src/ty/tests.rs
+++ b/crates/ide/src/ty/tests.rs
@@ -2,6 +2,9 @@ use crate::tests::TestDB;
 use crate::{DefDatabase, TyDatabase};
 use expect_test::{expect, Expect};
 
+use super::Ty;
+
+#[track_caller]
 fn check(src: &str, expect: Expect) {
     let (db, file) = TestDB::single_file(src).unwrap();
     let module = db.module(file);
@@ -11,10 +14,16 @@ fn check(src: &str, expect: Expect) {
     expect.assert_eq(&got);
 }
 
+#[track_caller]
 fn check_all(src: &str, expect: Expect) {
+    check_all_expect(src, None, expect);
+}
+
+#[track_caller]
+fn check_all_expect(src: &str, expect_ty: impl Into<Option<Ty>>, expect: Expect) {
     let (db, file) = TestDB::single_file(src).unwrap();
     let module = db.module(file);
-    let infer = db.infer(file);
+    let infer = super::infer::infer_with(&db, file, expect_ty.into());
     let got = module
         .names()
         .map(|(i, name)| format!("{}: {}\n", name.text, infer.ty_for_name(i).debug()))
@@ -140,3 +149,31 @@ fn select() {
         "#]],
     );
 }
+
+#[test]
+fn external() {
+    check_all_expect(
+        "let a = a; in a",
+        ty!(int),
+        expect![[r#"
+            a: int
+            : int
+        "#]],
+    );
+
+    check_all_expect(
+        "{ stdenv }: stdenv.mkDerivation {
+            name = undefined;
+        }",
+        ty!({
+            "stdenv": {
+                "mkDerivation": ({ "name": string } -> derivation),
+            },
+        } -> derivation),
+        expect![[r#"
+            stdenv: { mkDerivation: { name: string } → { } }
+            name: string
+            : { stdenv: { mkDerivation: { name: string } → { } } } → { }
+        "#]],
+    );
+}