diff --git a/include/npcomp/Typing/CPASupport.h b/include/npcomp/Typing/CPASupport.h
new file mode 100644
index 000000000..fb01fb8e4
--- /dev/null
+++ b/include/npcomp/Typing/CPASupport.h
@@ -0,0 +1,357 @@
+//===- CPASupport.h - Support types and utilities for CPA -----------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+// Support types and utilities for the Cartesian Product Algorithm for
+// Type Inference.
+//
+// See:
+//   http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.30.8177
+//   http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.129.2756
+//===----------------------------------------------------------------------===//
+
+#include "mlir/IR/Types.h"
+#include "llvm/ADT/DenseMap.h"
+#include "llvm/ADT/ilist.h"
+#include "llvm/Support/Allocator.h"
+#include "llvm/Support/Casting.h"
+
+#ifndef NPCOMP_TYPING_CPASUPPORT_H
+#define NPCOMP_TYPING_CPASUPPORT_H
+
+namespace mlir {
+namespace npcomp {
+namespace typing {
+namespace CPA {
+
+class Context;
+
+/// A uniqued string identifier.
+class Identifier {
+public:
+  StringRef getValue() const { return value; }
+
+private:
+  Identifier(StringRef value) : value(value) {}
+  StringRef value;
+  friend class Context;
+};
+
+/// Base class for the CPA type hierarchy.
+class ObjectBase {
+public:
+  enum class Kind {
+    // Type
+    FIRST_TYPE,
+    TypeBase = FIRST_TYPE,
+    TypeVar,
+    CastType,
+    ReadType,
+    WriteType,
+
+    // ValueType
+    FIRST_VALUE_TYPE,
+    ValueType = FIRST_VALUE_TYPE,
+    IRValueType,
+    ObjectValueType,
+    LAST_VALUE_TYPE = ObjectValueType,
+
+    LAST_TYPE = TypeVar,
+
+    // Constraint
+    Constraint,
+    ConstraintSet,
+    TypeVarSet,
+  };
+  ObjectBase(Kind kind) : kind(kind) {}
+
+  Kind getKind() const { return kind; }
+
+private:
+  const Kind kind;
+};
+
+/// Base class for types.
+/// This type hierarchy is adapted from section 2.1 of:
+///   Precise Constraint-Based Type Inference for Java
+///
+/// Referred to as: 'τ' (tau)
+class TypeBase : public ObjectBase {
+public:
+  using ObjectBase::ObjectBase;
+  bool classof(const ObjectBase *tb) {
+    return tb->getKind() >= Kind::FIRST_TYPE &&
+           tb->getKind() <= Kind::LAST_TYPE;
+  }
+};
+
+/// A unique type variable.
+/// Both the pointer and the ordinal will be unique within a context.
+/// Referred to as 't'
+class TypeVar : public TypeBase {
+public:
+  TypeVar(int ordinal) : TypeBase(Kind::TypeVar), ordinal(ordinal) {}
+  bool classof(const ObjectBase *tb) { return tb->getKind() == Kind::TypeVar; }
+
+  int getOrdinal() { return ordinal; }
+
+private:
+  int ordinal;
+};
+
+/// A type-cast type.
+/// Referred to as: 'cast(δ, t)'
+class CastType : public TypeBase {
+public:
+  bool classof(const ObjectBase *tb) { return tb->getKind() == Kind::CastType; }
+
+  Identifier *getTypeIdentifier() { return typeIdentifier; }
+  TypeVar *getTypeVar() { return typeVar; }
+
+private:
+  CastType(Identifier *typeIdentifier, TypeVar *typeVar)
+      : TypeBase(Kind::CastType), typeIdentifier(typeIdentifier),
+        typeVar(typeVar) {}
+  Identifier *typeIdentifier;
+  TypeVar *typeVar;
+  friend class Context;
+};
+
+/// Type representing a read-field operation.
+/// Referred to as: 'read τ'
+class ReadType : public TypeBase {
+public:
+  bool classof(const ObjectBase *tb) { return tb->getKind() == Kind::ReadType; }
+
+  TypeBase *getType() { return type; }
+
+private:
+  ReadType(TypeBase *type) : TypeBase(Kind::ReadType), type(type) {}
+  TypeBase *type;
+  friend class Context;
+};
+
+/// Type representing a read-field operation.
+/// Referred to as: 'read τ'
+class WriteType : public TypeBase {
+public:
+  bool classof(const ObjectBase *tb) {
+    return tb->getKind() == Kind::WriteType;
+  }
+
+  TypeBase *getType() { return type; }
+
+private:
+  WriteType(TypeBase *type) : TypeBase(Kind::WriteType), type(type) {}
+  TypeBase *type;
+  friend class Context;
+};
+
+/// A legal value type in the language. We represent this as one of:
+///   IRValueType: Wraps a primitive MLIR type
+///   ObjectValueType: Defines an object.
+/// Referred to as 'τv' (tau-v)
+class ValueType : public TypeBase {
+public:
+  using TypeBase::TypeBase;
+  bool classof(ObjectBase *ob) {
+    return ob->getKind() >= Kind::FIRST_VALUE_TYPE &&
+           ob->getKind() <= Kind::LAST_VALUE_TYPE;
+  }
+};
+
+/// Concrete ValueType that wraps an MLIR Type.
+class IRValueType : public ValueType {
+public:
+  IRValueType(mlir::Type irType)
+      : ValueType(Kind::IRValueType), irType(irType) {}
+  bool classof(ObjectBase *ob) { return ob->getKind() == Kind::IRValueType; }
+
+  mlir::Type getIrType() { return irType; }
+
+private:
+  const mlir::Type irType;
+};
+
+/// ValueType for an object.
+/// Referred to as 'obj(δ, [ li : τi ])'
+class ObjectValueType : public ValueType {
+public:
+  bool classof(ObjectBase *ob) {
+    return ob->getKind() == Kind::ObjectValueType;
+  }
+
+  Identifier *getTypeIdentifier() { return typeIdentifier; }
+  size_t getFieldCount() { return fieldCount; }
+  llvm::ArrayRef<Identifier *> getFieldIdentifiers() {
+    return llvm::ArrayRef<Identifier *>(fieldIdentifiers, fieldCount);
+  }
+  llvm::ArrayRef<TypeBase *> getFieldTypes() {
+    return llvm::ArrayRef<TypeBase *>(fieldTypes, fieldCount);
+  }
+
+private:
+  ObjectValueType(Identifier *typeIdentifier, size_t fieldCount,
+                  Identifier **fieldIdentifiers, TypeBase **fieldTypes)
+      : ValueType(Kind::ObjectValueType), typeIdentifier(typeIdentifier),
+        fieldCount(fieldCount), fieldIdentifiers(fieldIdentifiers),
+        fieldTypes(fieldTypes) {}
+  Identifier *typeIdentifier;
+  size_t fieldCount;
+  Identifier **fieldIdentifiers;
+  TypeBase **fieldTypes;
+  friend class Context;
+};
+
+/// A Constraint between two types.
+/// Referred to as: 'τ1 <: τ2'
+class Constraint : public ObjectBase, public llvm::ilist_node<Constraint> {
+public:
+  bool classof(ObjectBase *ob) { return ob->getKind() == Kind::Constraint; }
+
+  TypeBase *getT1() { return t1; }
+  TypeBase *getT2() { return t2; }
+
+private:
+  Constraint(TypeBase *t1, TypeBase *t2)
+      : ObjectBase(Kind::Constraint), t1(t1), t2(t2) {}
+  TypeBase *t1;
+  TypeBase *t2;
+  friend class Context;
+};
+
+/// A set of constraints.
+/// Referred to as: 'C'
+class ConstraintSet : public ObjectBase {
+public:
+  bool classof(ObjectBase *ob) { return ob->getKind() == Kind::ConstraintSet; }
+
+  llvm::simple_ilist<Constraint> &getConstraints() { return constraints; }
+
+private:
+  ConstraintSet() : ObjectBase(Kind::ConstraintSet){};
+  llvm::simple_ilist<Constraint> constraints;
+  friend class Context;
+};
+
+/// A set of TypeVar.
+/// Referred to as 't_bar'
+class TypeVarSet : public ObjectBase {
+public:
+  bool classof(ObjectBase *ob) { return ob->getKind() == Kind::TypeVarSet; }
+
+  llvm::simple_ilist<TypeVar> &getTypeVars() { return typeVars; }
+
+private:
+  TypeVarSet() : ObjectBase(Kind::TypeVarSet) {}
+  llvm::simple_ilist<TypeVar> typeVars;
+  friend class Context;
+};
+
+/// Manages instances and containers needed for the lifetime of a CPA
+/// analysis.
+class Context {
+public:
+  TypeVar *newTypeVar() {
+    return allocator.Allocate<TypeVar>(++typeVarCounter);
+  }
+
+  /// Gets a uniqued IRValueType for the IR Type.
+  IRValueType *getIRValueType(Type irType) {
+    auto it = irValueTypeMap.find(irType);
+    if (it != irValueTypeMap.end())
+      return it->second;
+    auto *irv = allocator.Allocate<IRValueType>(1);
+    new (irv) IRValueType(irType);
+    irValueTypeMap[irType] = irv;
+    return irv;
+  }
+
+  /// Creates a new ObjectValueType.
+  /// Object value types are not uniqued.
+  ObjectValueType *
+  newObjectValueType(Identifier *typeIdentifier,
+                     llvm::ArrayRef<Identifier *> fieldIdentifiers) {
+    size_t n = fieldIdentifiers.size();
+    Identifier **allocFieldIdentifiers = allocator.Allocate<Identifier *>(n);
+    std::copy_n(fieldIdentifiers.begin(), n, allocFieldIdentifiers);
+    TypeBase **allocFieldTypes = allocator.Allocate<TypeBase *>(n);
+    std::fill_n(allocFieldTypes, n, nullptr);
+    auto *ovt = allocator.Allocate<ObjectValueType>(1);
+    new (ovt) ObjectValueType(typeIdentifier, n, allocFieldIdentifiers,
+                              allocFieldTypes);
+    return ovt;
+  }
+
+  /// Gets a uniqued Identifier for the given value.
+  Identifier *getIdentifier(StringRef value) {
+    auto it = identifierMap.find(value);
+    if (it != identifierMap.end())
+      return it->second;
+    auto *chars = allocator.Allocate<char>(value.size());
+    std::memcpy(chars, value.data(), value.size());
+    StringRef uniquedValue(chars, value.size());
+    Identifier *id = allocator.Allocate<Identifier>(1);
+    new (id) Identifier(uniquedValue);
+    identifierMap[uniquedValue] = id;
+    return id;
+  }
+
+  /// Gets a CastType.
+  CastType *getCastType(Identifier *typeIdentifier, TypeVar *typeVar) {
+    auto *ct = allocator.Allocate<CastType>(1);
+    new (ct) CastType(typeIdentifier, typeVar);
+    return ct;
+  }
+
+  /// Gets a ReadType.
+  ReadType *getReadType(TypeBase *type) {
+    auto *rt = allocator.Allocate<ReadType>(1);
+    new (rt) ReadType(type);
+    return rt;
+  }
+
+  /// Gets a WriteType.
+  WriteType *getWriteType(TypeBase *type) {
+    auto *wt = allocator.Allocate<WriteType>(1);
+    new (wt) WriteType(type);
+    return wt;
+  }
+
+  /// Gets a Constraint.
+  Constraint *getConstraint(TypeBase *t1, TypeBase *t2) {
+    auto *c = allocator.Allocate<Constraint>(1);
+    new (c) Constraint(t1, t2);
+    return c;
+  }
+
+  /// Creates a new ConstraintSet.
+  ConstraintSet *newConstraintSet() {
+    auto *cs = allocator.Allocate<ConstraintSet>(1);
+    new (cs) ConstraintSet();
+    return cs;
+  }
+
+  /// Creates a new TypeVarSet.
+  TypeVarSet *newTypeVarSet() {
+    auto *tvs = allocator.Allocate<TypeVarSet>(1);
+    new (tvs) TypeVarSet();
+    return tvs;
+  }
+
+private:
+  llvm::BumpPtrAllocator allocator;
+  llvm::DenseMap<mlir::Type, IRValueType *> irValueTypeMap;
+  llvm::DenseMap<StringRef, Identifier *> identifierMap;
+  int typeVarCounter = 0;
+};
+
+} // namespace CPA
+} // namespace typing
+} // namespace npcomp
+} // namespace mlir
+
+#endif
diff --git a/lib/CMakeLists.txt b/lib/CMakeLists.txt
index 8d5d98996..04d78208d 100644
--- a/lib/CMakeLists.txt
+++ b/lib/CMakeLists.txt
@@ -2,6 +2,7 @@ add_subdirectory(Conversion)
 add_subdirectory(Dialect)
 add_subdirectory(E2E)
 add_subdirectory(Python)
+add_subdirectory(Typing)
 
 if(NPCOMP_ENABLE_IREE)
   add_subdirectory(Backend/IREE)
diff --git a/lib/Typing/CMakeLists.txt b/lib/Typing/CMakeLists.txt
new file mode 100644
index 000000000..60f2ae62d
--- /dev/null
+++ b/lib/Typing/CMakeLists.txt
@@ -0,0 +1,7 @@
+add_library(NPCOMPTyping
+  CPASupport.cpp
+)
+
+target_link_libraries(NPCOMPTyping
+  MLIRIR
+)
diff --git a/lib/Typing/CPASupport.cpp b/lib/Typing/CPASupport.cpp
new file mode 100644
index 000000000..71d430da6
--- /dev/null
+++ b/lib/Typing/CPASupport.cpp
@@ -0,0 +1,9 @@
+//===- CPASupport.h - Support types and utilities for CPA -----------------===//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+
+#include "npcomp/Typing/CPASupport.h"