diff --git a/common/constants.h b/common/constants.h
index 23a504f5..5569eec9 100644
--- a/common/constants.h
+++ b/common/constants.h
@@ -112,7 +112,6 @@ struct PointerType : Type {
 
  private:
   friend Type;
-  friend struct TypeSystem;
   friend PointerType Ptr(Type t);
 
   explicit PointerType() = default;
@@ -131,7 +130,6 @@ struct BufferPointerType : Type {
 
  private:
   friend Type;
-  friend struct TypeSystem;
   friend BufferPointerType BufPtr(Type t);
 
   explicit BufferPointerType() = default;
@@ -151,7 +149,6 @@ struct SliceType : Type {
 
  private:
   friend Type;
-  friend struct TypeSystem;
   friend SliceType Slice(Type t);
 
   explicit SliceType() = default;
@@ -222,7 +219,6 @@ struct ParametersType : Type {
  private:
   friend Type;
   friend struct FunctionType;
-  friend struct TypeSystem;
   friend ParametersType Parameters(std::span<Parameter const>);
   explicit constexpr ParametersType(uint32_t n)
       : Type(Type::Kind::Parameters, n) {}
@@ -266,7 +262,6 @@ struct FunctionType : Type {
 
  private:
   friend Type;
-  friend struct TypeSystem;
   friend FunctionType Function(ParametersType, std::span<Type const>,
                                Evaluation);
 
diff --git a/ir/deserialize.h b/ir/deserialize.h
index 6b96ed6b..2f063404 100644
--- a/ir/deserialize.h
+++ b/ir/deserialize.h
@@ -52,7 +52,6 @@ struct ModuleDeserializer : R {
     type::Type t;
     co_await nth::io::deserialize(d, t);
     std::vector<jasmin::Value> values;
-    t = d.reindexing_(t);
     switch (t.kind()) {
       case type::Type::Kind::Primitive: {
         auto p = t.AsPrimitive();
@@ -197,13 +196,11 @@ struct ModuleDeserializer : R {
     StringLiteral name;
     type::Type t;
     co_await nth::io::deserialize(d, name, t);
-    f = ForeignFunction(name, d.reindexing_(t).AsFunction());
+    f = ForeignFunction(name, t.AsFunction());
     co_return Result::success();
   }
 
   friend Result NthDeserialize(ModuleDeserializer& d, Module& m) {
-    d.reindexing_.clear();
-
     co_await nth::io::deserialize(d, GlobalConstantTable());
     co_await nth::io::deserialize(d, d.context_.foreign);
     co_await nth::io::deserialize(d, m.program());
@@ -217,7 +214,6 @@ struct ModuleDeserializer : R {
     return context_.registry;
   }
  private:
-  type::TypeSystem::ReindexTable reindexing_;
   SharedContext& context_;
 
   Result read_as_string(std::string& content) {
diff --git a/ir/emit.h b/ir/emit.h
index c1bd6971..44f746ad 100644
--- a/ir/emit.h
+++ b/ir/emit.h
@@ -9,6 +9,7 @@
 #include "absl/container/flat_hash_map.h"
 #include "common/identifier.h"
 #include "common/module_id.h"
+#include "common/type.h"
 #include "ir/dependent_modules.h"
 #include "ir/lexical_scope.h"
 #include "ir/local_storage.h"
@@ -20,7 +21,6 @@
 #include "parse/declaration.h"
 #include "parse/node_index.h"
 #include "parse/tree.h"
-#include "type/type.h"
 
 namespace ic {
 
diff --git a/ir/ir.cc b/ir/ir.cc
index 34a0a535..a433cb46 100644
--- a/ir/ir.cc
+++ b/ir/ir.cc
@@ -10,6 +10,7 @@
 #include "common/module_id.h"
 #include "common/resources.h"
 #include "common/string.h"
+#include "common/type.h"
 #include "ir/lexical_scope.h"
 #include "ir/type_stack.h"
 #include "jasmin/core/function.h"
@@ -19,7 +20,6 @@
 #include "parse/node_index.h"
 #include "parse/tree.h"
 #include "type/cast.h"
-#include "type/type.h"
 
 namespace ic {
 namespace {
diff --git a/ir/lexical_scope.h b/ir/lexical_scope.h
index c0992d71..93accb4c 100644
--- a/ir/lexical_scope.h
+++ b/ir/lexical_scope.h
@@ -9,7 +9,6 @@
 #include "nth/debug/debug.h"
 #include "nth/utility/iterator_range.h"
 #include "parse/node_index.h"
-#include "type/type.h"
 
 namespace ic {
 
diff --git a/ir/local_storage.h b/ir/local_storage.h
index ec44e298..411606f6 100644
--- a/ir/local_storage.h
+++ b/ir/local_storage.h
@@ -2,11 +2,11 @@
 #define ICARUS_IR_LOCAL_STORAGE_H
 
 #include "absl/container/flat_hash_map.h"
+#include "common/type.h"
 #include "nth/container/interval.h"
 #include "nth/debug/debug.h"
 #include "parse/node_index.h"
 #include "type/byte_width.h"
-#include "type/type.h"
 
 namespace ic {
 
diff --git a/ir/module.h b/ir/module.h
index bd96b73a..1bf6fd37 100644
--- a/ir/module.h
+++ b/ir/module.h
@@ -11,7 +11,6 @@
 #include "ir/function.h"
 #include "ir/scope.h"
 #include "jasmin/core/value.h"
-#include "type/type.h"
 
 namespace ic {
 
diff --git a/ir/type_stack.h b/ir/type_stack.h
index 59216c9b..d02b1289 100644
--- a/ir/type_stack.h
+++ b/ir/type_stack.h
@@ -6,7 +6,8 @@
 #include <span>
 #include <vector>
 
-#include "type/type.h"
+#include "common/type.h"
+#include "type/basic.h"
 
 namespace ic {
 
diff --git a/toolchain/builtin/module.cc b/toolchain/builtin/module.cc
index bf32ab6d..8f0ce861 100644
--- a/toolchain/builtin/module.cc
+++ b/toolchain/builtin/module.cc
@@ -5,7 +5,7 @@
 #include "common/any_value.h"
 #include "common/identifier.h"
 #include "common/pattern.h"
-#include "type/type.h"
+#include "common/type.h"
 
 namespace ic::builtin {
 namespace {
diff --git a/type/BUILD b/type/BUILD
index c08b99d4..438e846e 100644
--- a/type/BUILD
+++ b/type/BUILD
@@ -173,10 +173,10 @@ cc_library(
 
 cc_library(
     name = "type",
-    hdrs = ["type.h"],
     srcs = ["type.cc"],
     deps = [
-        ":type_system",
+        ":dependent",
+        ":type_contour",
         "//common:constants",
         "@nth_cc//nth/container:flyweight_set",
         "@nth_cc//nth/debug",
@@ -201,28 +201,3 @@ cc_test(
         "@nth_cc//nth/test:main",
     ]
 )
-
-cc_library(
-    name = "type_system",
-    hdrs = ["type_system.h"],
-    srcs = ["type_system.cc"],
-    deps = [
-        ":alignment",
-        ":basic",
-        ":byte_width",
-        ":dependent",
-        ":function",
-        ":opaque",
-        ":parameters",
-        ":pattern",
-        ":pointer",
-        ":primitive",
-        ":refinement",
-        ":type_contour",
-        "//common/language:type_kind",
-        "//common:pattern",
-        "@nth_cc//nth/container:flyweight_set",
-        "@nth_cc//nth/debug",
-        "@nth_cc//nth/utility:no_destructor",
-    ],
-)
diff --git a/type/cast.h b/type/cast.h
index 5858d8a1..baa00a07 100644
--- a/type/cast.h
+++ b/type/cast.h
@@ -1,8 +1,8 @@
 #ifndef ICARUS_TYPE_CAST_H
 #define ICARUS_TYPE_CAST_H
 
-#include "type/type.h"
 #include "common/any_value.h"
+#include "common/type.h"
 
 namespace ic::type {
 
diff --git a/type/dependent_test.cc b/type/dependent_test.cc
index fb1c9272..35fe6977 100644
--- a/type/dependent_test.cc
+++ b/type/dependent_test.cc
@@ -1,13 +1,14 @@
 #include "type/dependent.h"
 
 #include "common/any_value.h"
+#include "common/type.h"
 #include "jasmin/instructions/arithmetic.h"
 #include "jasmin/instructions/common.h"
 #include "nth/test/test.h"
+#include "type/basic.h"
 #include "type/function.h"
 #include "type/parameters.h"
 #include "type/primitive.h"
-#include "type/type.h"
 
 namespace ic::type {
 namespace {
diff --git a/type/type.cc b/type/type.cc
index 19554a73..9514da3b 100644
--- a/type/type.cc
+++ b/type/type.cc
@@ -1,4 +1,4 @@
-#include "type/type.h"
+#include "common/type.h"
 
 #include <cstring>
 #include <utility>
@@ -9,12 +9,12 @@
 #include "common/pattern.h"
 #include "nth/debug/debug.h"
 #include "nth/utility/no_destructor.h"
+#include "type/dependent.h"
+#include "type/type_contour.h"
 
 namespace ic::type {
 namespace {
 
-nth::NoDestructor<TypeSystem> type_system;
-
 uint64_t opaque_count = 0;
 
 }  // namespace
diff --git a/type/type.h b/type/type.h
deleted file mode 100644
index eb4eeeb5..00000000
--- a/type/type.h
+++ /dev/null
@@ -1,11 +0,0 @@
-#ifndef ICARUS_TYPE_TYPE_H
-#define ICARUS_TYPE_TYPE_H
-
-#include <cstdint>
-#include <tuple>
-#include <utility>
-#include <vector>
-
-#include "type/type_system.h"
-
-#endif  // ICARUS_TYPE_TYPE_H
diff --git a/type/type_system.cc b/type/type_system.cc
deleted file mode 100644
index a4a8c988..00000000
--- a/type/type_system.cc
+++ /dev/null
@@ -1,32 +0,0 @@
-#include "type/type_system.h"
-
-#include "common/identifier.h"
-#include "nth/debug/debug.h"
-
-namespace ic::type {
-
-ParametersType TypeSystem::parameter_type(
-    std::vector<ParametersType::Parameter>&& p) {
-  return ParametersType(
-      parameters.index(parameters.insert(std::move(p)).first));
-}
-
-ParametersType TypeSystem::parameter_type(
-    std::vector<ParametersType::Parameter> const& p) {
-  return ParametersType(parameters.index(parameters.insert(p).first));
-}
-
-FunctionType TypeSystem::function(ParametersType p, std::vector<Type> r,
-                                  Evaluation e) {
-  uint64_t rt = returns.index(returns.insert(std::move(r)).first);
-  return FunctionType(functions.index(functions.insert({p, rt, e}).first));
-}
-
-Type TypeSystem::ReindexTable::operator()(Type t) const {
-  if (t.kind() == Type::Kind::Primitive) { return t; }
-  auto iter = mapping_.find(t);
-  NTH_REQUIRE((v.debug), iter != mapping_.end());
-  return iter->second;
-}
-
-}  // namespace ic::type
diff --git a/type/type_system.h b/type/type_system.h
deleted file mode 100644
index ad71b9cf..00000000
--- a/type/type_system.h
+++ /dev/null
@@ -1,57 +0,0 @@
-#ifndef ICARUS_TYPE_TYPE_SYSTEM_H
-#define ICARUS_TYPE_TYPE_SYSTEM_H
-
-#include <cstdint>
-#include <tuple>
-#include <utility>
-#include <vector>
-
-#include "common/pattern.h"
-#include "nth/container/flyweight_set.h"
-#include "type/basic.h"
-#include "type/dependent.h"
-#include "type/function.h"
-#include "type/opaque.h"
-#include "type/parameters.h"
-#include "type/pattern.h"
-#include "type/pointer.h"
-#include "type/primitive.h"
-#include "type/refinement.h"
-#include "type/type_contour.h"
-
-namespace ic::type {
-
-struct TypeSystem {
-  ParametersType parameter_type(
-      std::vector<ParametersType::Parameter> const& p);
-  ParametersType parameter_type(std::vector<ParametersType::Parameter>&& p);
-  FunctionType function(ParametersType p, std::vector<Type> r, Evaluation e);
-
-  nth::flyweight_set<std::vector<ParametersType::Parameter>> parameters;
-  nth::flyweight_set<std::vector<Type>> returns;
-
-  nth::flyweight_set<std::tuple<ParametersType, uint64_t, Evaluation>>
-      functions;
-  nth::flyweight_set<DependentTerm> dependent_terms;
-  nth::flyweight_set<DependentParameterMapping> dependent_mapping;
-  nth::flyweight_set<std::pair<size_t, size_t>> dependent_term_mapping_pairs;
-  nth::flyweight_set<std::pair<Type, ::ic::Pattern>> refinements;
-  nth::flyweight_set<Type> pattern_match_types;
-
-  struct ReindexTable {
-    Type operator()(Type t) const;
-    void clear() {
-      returns_.clear();
-      mapping_.clear();
-    }
-
-   private:
-    friend TypeSystem;
-    std::vector<uint64_t> returns_;
-    absl::flat_hash_map<Type, Type> mapping_;
-  };
-};
-
-}  // namespace ic::type
-
-#endif  // ICARUS_TYPE_TYPE_SYSTEM_H
diff --git a/type/type_test.cc b/type/type_test.cc
deleted file mode 100644
index 9d76bfc3..00000000
--- a/type/type_test.cc
+++ /dev/null
@@ -1,97 +0,0 @@
-#include "type/type.h"
-
-#include "nth/test/test.h"
-
-namespace ic::type {
-namespace {
-
-NTH_TEST("type/construction") {
-  Type t = PrimitiveType(PrimitiveType::Kind::Bool);
-  NTH_EXPECT(t == Bool);
-  NTH_EXPECT(t.kind() == Type::Kind::Primitive);
-
-  t = PrimitiveType(PrimitiveType::Kind::Module);
-  NTH_EXPECT(t == Module);
-  NTH_EXPECT(t.kind() == Type::Kind::Primitive);
-
-  t = PrimitiveType(PrimitiveType::Kind::Type);
-  NTH_EXPECT(t == Type_);
-  NTH_EXPECT(t.kind() == Type::Kind::Primitive);
-}
-
-NTH_TEST("type/parameters/construction") {
-  Type t0 = Parameters({});
-  Type t1 = Parameters(
-      {ParametersType::Parameter{.name = Identifier("a"), .type = Bool}});
-  Type t2 = Parameters(
-      {ParametersType::Parameter{.name = Identifier("b"), .type = Bool}});
-  Type t3 = Parameters(
-      {ParametersType::Parameter{.name = Identifier("b"), .type = Char}});
-
-  NTH_EXPECT(t0 == t0);
-  NTH_EXPECT(t0 != t1);
-  NTH_EXPECT(t0 != t2);
-  NTH_EXPECT(t0 != t3);
-  NTH_EXPECT(t1 != t0);
-  NTH_EXPECT(t1 == t1);
-  NTH_EXPECT(t1 != t2);
-  NTH_EXPECT(t1 != t3);
-  NTH_EXPECT(t2 != t1);
-  NTH_EXPECT(t2 != t0);
-  NTH_EXPECT(t2 == t2);
-  NTH_EXPECT(t2 != t3);
-  NTH_EXPECT(t3 != t0);
-  NTH_EXPECT(t3 != t1);
-  NTH_EXPECT(t3 != t2);
-  NTH_EXPECT(t3 == t3);
-
-  NTH_EXPECT(t0.kind() == Type::Kind::Parameters);
-  NTH_EXPECT(t1.kind() == Type::Kind::Parameters);
-  NTH_EXPECT(t2.kind() == Type::Kind::Parameters);
-  NTH_EXPECT(t3.kind() == Type::Kind::Parameters);
-
-  NTH_EXPECT(t0 != Error);
-  NTH_EXPECT(t0 != Bool);
-
-  NTH_EXPECT(t3 == Parameters({ParametersType::Parameter{
-                       .name = Identifier("b"), .type = Char}}));
-}
-
-NTH_TEST("type/pointer") {
-  NTH_EXPECT(Ptr(Char) == Ptr(Char));
-  NTH_EXPECT(Ptr(Ptr(Char)) != Ptr(Char));
-  NTH_EXPECT(Ptr(Ptr(Char)).pointee() == Ptr(Char));
-  NTH_EXPECT(Ptr(Ptr(Char)).pointee().AsPointer().pointee() == Char);
-}
-
-NTH_TEST("type/buffer-pointer") {
-  NTH_EXPECT(BufPtr(Char) == BufPtr(Char));
-  NTH_EXPECT(BufPtr(Ptr(Char)) != Ptr(Char));
-  NTH_EXPECT(BufPtr(Ptr(Char)).pointee() == Ptr(Char));
-  NTH_EXPECT(BufPtr(Ptr(Char)).pointee().AsPointer().pointee() == Char);
-  NTH_EXPECT(BufPtr(BufPtr(Char)) != BufPtr(Char));
-  NTH_EXPECT(BufPtr(BufPtr(Char)).pointee() == BufPtr(Char));
-  NTH_EXPECT(BufPtr(BufPtr(Char)).pointee().AsBufferPointer().pointee() ==
-             Char);
-}
-
-NTH_TEST("type/slice") {
-  NTH_EXPECT(Slice(Char) == Slice(Char));
-  NTH_EXPECT(Slice(Slice(Char)) != Slice(Char));
-  NTH_EXPECT(Slice(Slice(Char)).element_type() == Slice(Char));
-  NTH_EXPECT(Slice(Slice(Char)).element_type().AsSlice().element_type() ==
-             Char);
-}
-
-NTH_TEST("qualified-type/construction") {
-  NTH_EXPECT(QualifiedType(Qualifier::Constant(), Bool).type() == Bool);
-  NTH_EXPECT(QualifiedType(Qualifier::Constant(), Bool).qualifier() ==
-             Qualifier::Constant());
-
-  NTH_EXPECT(QualifiedType(Qualifier::Constant(), Bool).type() == Bool);
-  NTH_EXPECT(QualifiedType(Qualifier::Unqualified(), Bool).qualifier() ==
-             Qualifier::Unqualified());
-}
-
-}  // namespace
-}  // namespace ic::type