diff --git a/example/misc/infinite_set.cpp b/example/misc/infinite_set.cpp
index 6bccfd535c..925a0bc822 100644
--- a/example/misc/infinite_set.cpp
+++ b/example/misc/infinite_set.cpp
@@ -8,9 +8,12 @@
 #include <boost/hana/functional/compose.hpp>
 #include <boost/hana/functional/partial.hpp>
 #include <boost/hana/fwd/ap.hpp>
+#include <boost/hana/fwd/difference.hpp>
 #include <boost/hana/fwd/equal.hpp>
 #include <boost/hana/fwd/find_if.hpp>
+#include <boost/hana/fwd/intersection.hpp>
 #include <boost/hana/fwd/lift.hpp>
+#include <boost/hana/fwd/set.hpp>
 #include <boost/hana/fwd/union.hpp>
 #include <boost/hana/if.hpp>
 #include <boost/hana/is_subset.hpp>
@@ -48,6 +51,9 @@ constexpr auto doubleton(X x, Y y) {
 }
 
 namespace boost { namespace hana {
+    //////////////////////////////////////////////////////////////////////////
+    // SetTheoretic
+    //////////////////////////////////////////////////////////////////////////
     template <>
     struct union_impl<infinite_set_tag> {
         template <typename Xs, typename Ys>
@@ -56,6 +62,22 @@ namespace boost { namespace hana {
         }
     };
 
+    template <>
+    struct difference_impl<infinite_set_tag> {
+        template <typename Xs, typename Ys>
+        static constexpr auto apply(Xs xs, Ys ys) {
+            return difference_impl<set_tag>(xs, ys);
+        }
+    };
+
+    template <>
+    struct intersection_impl<infinite_set_tag> {
+        template <typename Xs, typename Ys>
+        static constexpr auto apply(Xs xs, Ys ys) {
+            return intersection_impl<set_tag>(xs, ys);
+        }
+    };
+
     //////////////////////////////////////////////////////////////////////////
     // Comparable
     //////////////////////////////////////////////////////////////////////////
diff --git a/include/boost/hana/concept.hpp b/include/boost/hana/concept.hpp
index 6046b0a4ef..d26835a533 100644
--- a/include/boost/hana/concept.hpp
+++ b/include/boost/hana/concept.hpp
@@ -31,6 +31,7 @@ Distributed under the Boost Software License, Version 1.0.
 #include <boost/hana/concept/ring.hpp>
 #include <boost/hana/concept/searchable.hpp>
 #include <boost/hana/concept/sequence.hpp>
+#include <boost/hana/concept/set_theoretic.hpp>
 #include <boost/hana/concept/struct.hpp>
 
 #endif // !BOOST_HANA_CONCEPT_HPP
diff --git a/include/boost/hana/concept/set_theoretic.hpp b/include/boost/hana/concept/set_theoretic.hpp
new file mode 100644
index 0000000000..8c2dc9820e
--- /dev/null
+++ b/include/boost/hana/concept/set_theoretic.hpp
@@ -0,0 +1,36 @@
+/*!
+@file
+Defines `boost::hana::SetTheoretic`.
+
+@copyright Shreyans Doshi 2017
+Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_HANA_CONCEPT_SET_THEORETIC_HPP
+#define BOOST_HANA_CONCEPT_SET_THEORETIC_HPP
+
+#include <boost/hana/fwd/concept/set_theoretic.hpp>
+
+#include <boost/hana/config.hpp>
+#include <boost/hana/core/default.hpp>
+#include <boost/hana/core/tag_of.hpp>
+#include <boost/hana/detail/integral_constant.hpp>
+#include <boost/hana/difference.hpp>
+#include <boost/hana/intersection.hpp>
+#include <boost/hana/symmetric_difference.hpp>
+#include <boost/hana/union.hpp>
+
+
+BOOST_HANA_NAMESPACE_BEGIN
+    template <typename STh>
+    struct SetTheoretic
+        : hana::integral_constant<bool,
+            !is_default<difference_impl<typename tag_of<STh>::type>>::value &&
+            !is_default<intersection_impl<typename tag_of<STh>::type>>::value &&
+            !is_default<union_impl<typename tag_of<STh>::type>>::value
+        >
+    { };
+BOOST_HANA_NAMESPACE_END
+
+#endif // !BOOST_HANA_CONCEPT_SET_THEORETIC_HPP
diff --git a/include/boost/hana/difference.hpp b/include/boost/hana/difference.hpp
index d2e2897d6e..4f63b8a39f 100644
--- a/include/boost/hana/difference.hpp
+++ b/include/boost/hana/difference.hpp
@@ -12,6 +12,7 @@ Distributed under the Boost Software License, Version 1.0.
 
 #include <boost/hana/fwd/difference.hpp>
 
+#include <boost/hana/concept/set_theoretic.hpp>
 #include <boost/hana/config.hpp>
 #include <boost/hana/core/dispatch.hpp>
 #include <boost/hana/erase_key.hpp>
@@ -21,11 +22,21 @@ BOOST_HANA_NAMESPACE_BEGIN
     //! @cond
     template <typename Xs, typename Ys>
     constexpr auto difference_t::operator()(Xs&& xs, Ys&& ys) const {
-        using S = typename hana::tag_of<Xs>::type;
-        using Difference = BOOST_HANA_DISPATCH_IF(difference_impl<S>,
-            true
+        using TX = typename hana::tag_of<Xs>::type;
+        using TY = typename hana::tag_of<Ys>::type;
+        using Difference = BOOST_HANA_DISPATCH_IF(difference_impl<TX>,
+            hana::SetTheoretic<TX>::value &&
+            std::is_same<TX, TY>::value
         );
 
+    #ifndef BOOST_HANA_CONFIG_DISABLE_CONCEPT_CHECKS
+        static_assert(hana::SetTheoretic<TX>::value,
+        "hana::difference(xs, ys) requires 'xs' to be SetTheoretic");
+
+        static_assert(std::is_same<TX, TY>::value,
+        "hana::difference(xs, ys) requires 'xs' and 'ys' to be of the same type");
+    #endif
+
         return Difference::apply(static_cast<Xs&&>(xs), static_cast<Ys&&>(ys));
     }
     //! @endcond
diff --git a/include/boost/hana/fwd/concept/set_theoretic.hpp b/include/boost/hana/fwd/concept/set_theoretic.hpp
new file mode 100644
index 0000000000..e239a65543
--- /dev/null
+++ b/include/boost/hana/fwd/concept/set_theoretic.hpp
@@ -0,0 +1,35 @@
+/*!
+@file
+Forward declares `boost::hana::SetTheoretic`.
+
+@copyright Shreyans Doshi 2017
+Distributed under the Boost Software License, Version 1.0.
+(See accompanying file LICENSE.md or copy at http://boost.org/LICENSE_1_0.txt)
+ */
+
+#ifndef BOOST_HANA_FWD_CONCEPT_SET_THEORETIC_HPP
+#define BOOST_HANA_FWD_CONCEPT_SET_THEORETIC_HPP
+
+#include <boost/hana/config.hpp>
+
+
+BOOST_HANA_NAMESPACE_BEGIN
+    //! @ingroup group-concepts
+    //! @defgroup group-SetTheoretic SetTheoretic
+    //! The `SetTheoretic` concept represents data structures supporting
+    //! algebra of sets.
+    //!
+    //! Minimal complete definition
+    //! ---------------------------
+    //! `union_`, `intersection`, `difference` and `symmetric_difference`
+    //!
+    //! Concrete models
+    //! ---------------
+    //! `hana::set`, `hana::map`
+    //!
+    //!
+    template <typename STh>
+    struct SetTheoretic;
+BOOST_HANA_NAMESPACE_END
+
+#endif // !BOOST_HANA_FWD_CONCEPT_SET_THEORETIC_HPP
diff --git a/include/boost/hana/intersection.hpp b/include/boost/hana/intersection.hpp
index a9859d8f42..1b6ecc8878 100644
--- a/include/boost/hana/intersection.hpp
+++ b/include/boost/hana/intersection.hpp
@@ -12,6 +12,7 @@ Distributed under the Boost Software License, Version 1.0.
 
 #include <boost/hana/fwd/intersection.hpp>
 
+#include <boost/hana/concept/set_theoretic.hpp>
 #include <boost/hana/config.hpp>
 #include <boost/hana/core/dispatch.hpp>
 
@@ -20,11 +21,21 @@ BOOST_HANA_NAMESPACE_BEGIN
     //! @cond
     template <typename Xs, typename Ys>
     constexpr auto intersection_t::operator()(Xs&& xs, Ys&& ys) const {
-        using S = typename hana::tag_of<Xs>::type;
-        using Intersection = BOOST_HANA_DISPATCH_IF(intersection_impl<S>,
-            true
+        using TX = typename hana::tag_of<Xs>::type;
+        using TY = typename hana::tag_of<Ys>::type;
+        using Intersection = BOOST_HANA_DISPATCH_IF(intersection_impl<TX>,
+            hana::SetTheoretic<TX>::value &&
+            std::is_same<TX, TY>::value
         );
 
+    #ifndef BOOST_HANA_CONFIG_DISABLE_CONCEPT_CHECKS
+        static_assert(hana::SetTheoretic<TX>::value,
+        "hana::intersection(xs, ys) requires 'xs' to be SetTheoretic");
+
+        static_assert(std::is_same<TX, TY>::value,
+        "hana::intersection(xs, ys) requires 'xs' and 'ys' to be of the same type");
+    #endif
+
         return Intersection::apply(static_cast<Xs&&>(xs), static_cast<Ys&&>(ys));
     }
     //! @endcond
diff --git a/include/boost/hana/union.hpp b/include/boost/hana/union.hpp
index d7bb4403bf..da672a53e0 100644
--- a/include/boost/hana/union.hpp
+++ b/include/boost/hana/union.hpp
@@ -12,6 +12,7 @@ Distributed under the Boost Software License, Version 1.0.
 
 #include <boost/hana/fwd/union.hpp>
 
+#include <boost/hana/concept/set_theoretic.hpp>
 #include <boost/hana/config.hpp>
 #include <boost/hana/core/dispatch.hpp>
 
@@ -20,11 +21,21 @@ BOOST_HANA_NAMESPACE_BEGIN
     //! @cond
     template <typename Xs, typename Ys>
     constexpr auto union_t::operator()(Xs&& xs, Ys&& ys) const {
-        using S = typename hana::tag_of<Xs>::type;
-        using Union = BOOST_HANA_DISPATCH_IF(union_impl<S>,
-            true
+        using TX = typename hana::tag_of<Xs>::type;
+        using TY = typename hana::tag_of<Ys>::type;
+        using Union = BOOST_HANA_DISPATCH_IF(union_impl<TX>,
+            hana::SetTheoretic<TX>::value &&
+            std::is_same<TX, TY>::value
         );
 
+    #ifndef BOOST_HANA_CONFIG_DISABLE_CONCEPT_CHECKS
+        static_assert(hana::SetTheoretic<TX>::value,
+        "hana::union_(xs, ys) requires 'xs' to be SetTheoretic");
+
+        static_assert(std::is_same<TX, TY>::value,
+        "hana::union_(xs, ys) requires 'xs' and 'ys' to be of the same type");
+    #endif
+
         return Union::apply(static_cast<Xs&&>(xs), static_cast<Ys&&>(ys));
     }
     //! @endcond