diff --git a/include/boost/histogram/axis/any.hpp b/include/boost/histogram/axis/any.hpp
index c10f338a..9552f26a 100644
--- a/include/boost/histogram/axis/any.hpp
+++ b/include/boost/histogram/axis/any.hpp
@@ -7,10 +7,10 @@
 #ifndef _BOOST_HISTOGRAM_AXIS_ANY_HPP_
 #define _BOOST_HISTOGRAM_AXIS_ANY_HPP_
 
+#include <boost/histogram/axis/interval.hpp>
 #include <boost/histogram/axis/iterator.hpp>
 #include <boost/histogram/detail/axis_visitor.hpp>
 #include <boost/histogram/detail/cat.hpp>
-#include <boost/histogram/interval.hpp>
 #include <boost/mpl/contains.hpp>
 #include <boost/utility/string_view.hpp>
 #include <boost/variant.hpp>
@@ -54,36 +54,47 @@ struct set_label : public static_visitor<void> {
   template <typename A> void operator()(A &a) const { a.label(label); }
 };
 
-template <typename T> struct index : public static_visitor<int> {
-  const T &t;
-  explicit index(const T &arg) : t(arg) {}
+struct index : public static_visitor<int> {
+  const double x;
+  explicit index(const double arg) : x(arg) {}
   template <typename Axis> int operator()(const Axis &a) const {
-    return impl(std::is_convertible<T, typename Axis::value_type>(), a);
+    return impl(std::is_convertible<double, typename Axis::value_type>(), a);
   }
   template <typename Axis> int impl(std::true_type, const Axis &a) const {
-    return a.index(t);
+    return a.index(x);
   }
   template <typename Axis> int impl(std::false_type, const Axis &) const {
     throw std::runtime_error(::boost::histogram::detail::cat(
-        "fill argument not convertible to axis value type: ",
-        boost::typeindex::type_id<Axis>().pretty_name(), ", ",
-        boost::typeindex::type_id<T>().pretty_name()));
+        "cannot convert value_type ",
+        boost::typeindex::type_id<typename Axis::value_type>().pretty_name(),
+        " of ",
+        boost::typeindex::type_id<Axis>().pretty_name(),
+        " to double")
+      );
   }
 };
 
-struct bin : public static_visitor<axis::interval<double>> {
-  using double_interval = axis::interval<double>;
-  const int i;
-  bin(const int v) : i(v) {}
-  template <typename A> double_interval operator()(const A &a) const {
-    return impl(is_convertible<typename A::bin_type, double_interval>(),
-                std::forward<typename A::bin_type>(a[i]));
+struct eval : public static_visitor<std::function<double(int)>> {
+  template <typename Axis> std::function<double(int)> operator()(const Axis &a) const {
+    return impl(std::integral_constant<bool,
+        (std::is_convertible<typename Axis::value_type, double>::value &&
+         std::is_same<
+           typename Axis::bin_type,
+           interval_view<typename Axis::value_type>
+         >::value)
+        >(), a);
   }
-  template <typename B> double_interval impl(true_type, B &&b) const {
-    return b;
+  template <typename Axis> std::function<double(int)> impl(std::true_type, const Axis &a) const {
+    return [&a](int i) -> double { return a[i].lower(); } ;
   }
-  template <typename B> double_interval impl(false_type, B &&) const {
-    throw std::runtime_error("cannot convert bin_type to interval<double>");
+  template <typename Axis> std::function<double(int)> impl(std::false_type, const Axis &) const {
+    throw std::runtime_error(::boost::histogram::detail::cat(
+        "cannot convert bin_type ",
+        boost::typeindex::type_id<typename Axis::bin_type>().pretty_name(),
+        " of ",
+        boost::typeindex::type_id<Axis>().pretty_name(),
+        " to interval_view<double>")
+      );
   }
 };
 } // namespace detail
@@ -95,7 +106,7 @@ template <typename Axes> class any : public make_variant_over<Axes>::type {
 public:
   using types = typename base_type::types;
   using value_type = double;
-  using bin_type = interval<double>;
+  using bin_type = interval_view<double>;
   using const_iterator = iterator_over<any>;
   using const_reverse_iterator = reverse_iterator_over<any>;
 
@@ -112,15 +123,15 @@ public:
   template <typename T, typename = typename std::enable_if<
                             mpl::contains<types, T>::value>::type>
   any &operator=(const T &t) {
-    // ugly workaround for compiler bug
-    return reinterpret_cast<any &>(base_type::operator=(t));
+    base_type::operator=(t);
+    return *this;
   }
 
   template <typename T, typename = typename std::enable_if<
                             mpl::contains<types, T>::value>::type>
   any &operator=(T &&t) {
-    // ugly workaround for compiler bug
-    return reinterpret_cast<any &>(base_type::operator=(std::move(t)));
+    base_type::operator=(std::move(t));
+    return *this;
   }
 
   int size() const { return apply_visitor(detail::size(), *this); }
@@ -131,7 +142,7 @@ public:
 
   // note: this only works for axes with compatible value type
   int index(const value_type x) const {
-    return apply_visitor(detail::index<value_type>(x), *this);
+    return apply_visitor(detail::index(x), *this);
   }
 
   string_view label() const {
@@ -143,9 +154,10 @@ public:
   }
 
   // this only works for axes with compatible bin type
-  // and will raise an error otherwise
+  // and will throw a runtime_error otherwise
   bin_type operator[](const int i) const {
-    return apply_visitor(detail::bin(i), *this);
+    auto eval = apply_visitor(detail::eval(), *this);
+    return bin_type(i, eval);
   }
 
   bool operator==(const any &rhs) const {
diff --git a/include/boost/histogram/axis/axis.hpp b/include/boost/histogram/axis/axis.hpp
index 583221d0..783bcf27 100644
--- a/include/boost/histogram/axis/axis.hpp
+++ b/include/boost/histogram/axis/axis.hpp
@@ -9,9 +9,9 @@
 
 #include <algorithm>
 #include <boost/bimap.hpp>
+#include <boost/histogram/axis/interval.hpp>
 #include <boost/histogram/axis/iterator.hpp>
 #include <boost/histogram/detail/meta.hpp>
-#include <boost/histogram/interval.hpp>
 #include <boost/math/constants/constants.hpp>
 #include <boost/utility/string_view.hpp>
 #include <cmath>
@@ -36,7 +36,7 @@ namespace axis {
 
 enum class uoflow { off = false, on = true };
 
-/// Base class for all axes, uses CRTP.
+/// Base class for all axes, uses CRTP to inject iterator logic.
 template <typename Derived> class axis_base {
 public:
   using const_iterator = iterator_over<Derived>;
@@ -102,7 +102,7 @@ private:
   template <class Archive> void serialize(Archive &, unsigned);
 };
 
-/// Base class for axes with overflow/underflow bins, uses CRTP.
+/// Base class for axes with optional under-/overflow bins, uses CRTP.
 template <typename Derived> class axis_base_uoflow : public axis_base<Derived> {
   using base_type = axis_base<Derived>;
 
@@ -114,7 +114,7 @@ public:
 
 protected:
   axis_base_uoflow(unsigned n, string_view label, enum uoflow uo)
-      : base_type(n, label), shape_(n + 2u * static_cast<unsigned>(uo)) {}
+      : base_type(n, label), shape_(n + 2 * static_cast<int>(uo)) {}
 
   axis_base_uoflow() = default;
   axis_base_uoflow(const axis_base_uoflow &) = default;
@@ -202,7 +202,7 @@ class regular : public axis_base_uoflow<regular<RealType, Transform>>,
 
 public:
   using value_type = RealType;
-  using bin_type = interval<value_type>;
+  using bin_type = interval_view<value_type>;
 
   /** Construct axis with n bins over real range [lower, upper).
    *
@@ -241,9 +241,9 @@ public:
                     : -1;
   }
 
-  /// Returns the starting edge of the bin.
+  /// Returns the bin interval.
   bin_type operator[](int idx) const noexcept {
-    auto eval = [this](int i) {
+    return bin_type(idx, [this](int i) {
       const auto n = base_type::size();
       if (i < 0)
         return this->inverse(-std::numeric_limits<value_type>::infinity());
@@ -251,8 +251,7 @@ public:
         return this->inverse(std::numeric_limits<value_type>::infinity());
       const auto z = value_type(i) / n;
       return this->inverse((1.0 - z) * min_ + z * (min_ + delta_ * n));
-    };
-    return {eval(idx), eval(idx + 1)};
+    });
   }
 
   bool operator==(const regular &o) const noexcept {
@@ -260,6 +259,7 @@ public:
            min_ == o.min_ && delta_ == o.delta_;
   }
 
+  /// Access properties of the transform.
   const Transform &transform() const noexcept {
     return static_cast<const Transform &>(*this);
   }
@@ -283,7 +283,7 @@ class circular : public axis_base<circular<RealType>> {
 
 public:
   using value_type = RealType;
-  using bin_type = interval<value_type>;
+  using bin_type = interval_view<value_type>;
 
   /** Constructor for n bins with an optional offset.
    *
@@ -313,11 +313,10 @@ public:
 
   /// Returns the starting edge of the bin.
   bin_type operator[](int idx) const {
-    auto eval = [this](int i) {
+    return bin_type(idx, [this](int i) {
       const value_type z = value_type(i) / base_type::size();
       return z * perimeter_ + phase_;
-    };
-    return {eval(idx), eval(idx + 1)};
+    });
   }
 
   bool operator==(const circular &o) const noexcept {
@@ -346,7 +345,7 @@ class variable : public axis_base_uoflow<variable<RealType>> {
 
 public:
   using value_type = RealType;
-  using bin_type = interval<value_type>;
+  using bin_type = interval_view<value_type>;
 
   /** Construct an axis from bin edges.
    *
@@ -397,7 +396,7 @@ public:
 
   /// Returns the starting edge of the bin.
   bin_type operator[](int idx) const {
-    auto eval = [this](int i) {
+    return bin_type(idx, [this](int i) {
       if (i < 0) {
         return -std::numeric_limits<value_type>::infinity();
       }
@@ -405,8 +404,7 @@ public:
         return std::numeric_limits<value_type>::infinity();
       }
       return x_[i];
-    };
-    return {eval(idx), eval(idx + 1)};
+    });
   }
 
   bool operator==(const variable &o) const noexcept {
@@ -434,7 +432,7 @@ class integer : public axis_base_uoflow<integer<IntType>> {
 
 public:
   using value_type = IntType;
-  using bin_type = interval<value_type>;
+  using bin_type = interval_view<value_type>;
 
   /** Construct axis over a semi-open integer interval [lower, upper).
    *
@@ -465,7 +463,7 @@ public:
 
   /// Returns the integer that is mapped to the bin index.
   bin_type operator[](int idx) const {
-    auto eval = [this](int i) {
+    return bin_type(idx, [this](int i) {
       if (i < 0) {
         return -std::numeric_limits<value_type>::max();
       }
@@ -473,8 +471,7 @@ public:
         return std::numeric_limits<value_type>::max();
       }
       return min_ + i;
-    };
-    return {eval(idx), eval(idx + 1)};
+    });
   }
 
   bool operator==(const integer &o) const noexcept {
diff --git a/include/boost/histogram/axis/interval.hpp b/include/boost/histogram/axis/interval.hpp
new file mode 100644
index 00000000..c5feed58
--- /dev/null
+++ b/include/boost/histogram/axis/interval.hpp
@@ -0,0 +1,46 @@
+// Copyright 2015-2017 Hans Dembinski
+//
+// Distributed under the Boost Software License, Version 1.0.
+// (See accompanying file LICENSE_1_0.txt
+// or copy at http://www.boost.org/LICENSE_1_0.txt)
+
+#ifndef _BOOST_HISTOGRAM_AXIS_INTERVAL_HPP_
+#define _BOOST_HISTOGRAM_AXIS_INTERVAL_HPP_
+
+#include <functional>
+#include <utility>
+
+namespace boost {
+namespace histogram {
+namespace axis {
+
+template <typename T> class interval_view {
+public:
+  interval_view(int idx, std::function<T(int)> eval) : idx_(idx), eval_(eval) {}
+
+  interval_view(const interval_view &) = default;
+  interval_view &operator=(const interval_view &) = default;
+  interval_view(interval_view &&) = default;
+  interval_view &operator=(interval_view &&) = default;
+
+  T lower() const noexcept { return eval_(idx_); }
+  T upper() const noexcept { return eval_(idx_ + 1); }
+  T width() const noexcept { return upper() - lower(); }
+
+  bool operator==(const interval_view &rhs) const noexcept {
+    return lower() == rhs.lower() && upper() == rhs.upper();
+  }
+  bool operator!=(const interval_view &rhs) const noexcept {
+    return !operator==(rhs);
+  }
+
+private:
+  const int idx_;
+  const std::function<T(int)> eval_;
+};
+
+} // namespace axis
+} // namespace histogram
+} // namespace boost
+
+#endif
diff --git a/include/boost/histogram/axis/ostream_operators.hpp b/include/boost/histogram/axis/ostream_operators.hpp
index cbd9df58..50a6152f 100644
--- a/include/boost/histogram/axis/ostream_operators.hpp
+++ b/include/boost/histogram/axis/ostream_operators.hpp
@@ -10,8 +10,8 @@
 #define _BOOST_HISTOGRAM_AXIS_OSTREAM_OPERATORS_HPP_
 
 #include <boost/histogram/axis/axis.hpp>
+#include <boost/histogram/axis/interval.hpp>
 #include <boost/histogram/detail/utility.hpp>
-#include <boost/histogram/interval.hpp>
 #include <boost/math/constants/constants.hpp>
 #include <ostream>
 
@@ -26,6 +26,12 @@ inline string_view to_string(const transform::sqrt &) { return {"_sqrt", 5}; }
 inline string_view to_string(const transform::cos &) { return {"_cos", 4}; }
 } // namespace detail
 
+template <typename T>
+inline std::ostream &operator<<(std::ostream &os, const interval_view<T> &i) {
+  os << "[" << i.lower() << ", " << i.upper() << ")";
+  return os;
+}
+
 template <typename RealType, typename Transform>
 inline std::ostream &operator<<(std::ostream &os,
                                 const regular<RealType, Transform> &a) {
diff --git a/include/boost/histogram/detail/axis_visitor.hpp b/include/boost/histogram/detail/axis_visitor.hpp
index 6618de12..38869368 100644
--- a/include/boost/histogram/detail/axis_visitor.hpp
+++ b/include/boost/histogram/detail/axis_visitor.hpp
@@ -13,7 +13,7 @@
 #include <boost/fusion/include/is_sequence.hpp>
 #include <boost/fusion/include/size.hpp>
 #include <boost/fusion/support/is_sequence.hpp>
-#include <boost/histogram/interval.hpp>
+#include <boost/histogram/axis/interval.hpp>
 #include <boost/mpl/bool.hpp>
 #include <boost/mpl/contains.hpp>
 #include <boost/variant/get.hpp>
diff --git a/include/boost/histogram/interval.hpp b/include/boost/histogram/interval.hpp
deleted file mode 100644
index c3113205..00000000
--- a/include/boost/histogram/interval.hpp
+++ /dev/null
@@ -1,46 +0,0 @@
-// Copyright 2015-2017 Hans Dembinski
-//
-// Distributed under the Boost Software License, Version 1.0.
-// (See accompanying file LICENSE_1_0.txt
-// or copy at http://www.boost.org/LICENSE_1_0.txt)
-
-#ifndef _BOOST_HISTOGRAM_INTERVAL_HPP_
-#define _BOOST_HISTOGRAM_INTERVAL_HPP_
-
-#include <utility>
-
-namespace boost {
-namespace histogram {
-namespace axis {
-
-template <typename T> class interval {
-public:
-  interval() = default;
-  interval(const interval &) = default;
-  interval &operator=(const interval &) = default;
-  interval(interval &&) = default;
-  interval &operator=(interval &&) = default;
-
-  interval(const T &x, const T &y) : a(x), b(y) {}
-  interval(T &&x, T &&y) : a(std::move(x)), b(std::move(y)) {}
-
-  template <typename U>
-  interval(const interval<U> &i) : a(i.lower()), b(i.upper()) {}
-
-  const T &lower() const noexcept { return a; }
-  const T &upper() const noexcept { return b; }
-
-  bool operator==(const interval &i) const noexcept {
-    return a == i.a && b == i.b;
-  }
-  bool operator!=(const interval &i) const noexcept { return !operator==(i); }
-
-private:
-  T a, b;
-};
-
-} // namespace axis
-} // namespace histogram
-} // namespace boost
-
-#endif
diff --git a/src/python/axis.cpp b/src/python/axis.cpp
index 450727a7..1467513b 100644
--- a/src/python/axis.cpp
+++ b/src/python/axis.cpp
@@ -55,25 +55,14 @@ generic_iterator make_generic_iterator(bp::object self) {
 }
 
 template <typename T>
-struct axis_interval_to_python
+struct axis_interval_view_to_python
 {
-  static PyObject* convert(const bha::interval<T> &i)
+  static PyObject* convert(const bha::interval_view<T> &i)
   {
     return bp::incref(bp::make_tuple(i.lower(), i.upper()).ptr());
   }
 };
 
-template <typename T>
-struct pair_int_axis_interval_to_python
-{
-  static PyObject* convert(const std::pair<int, bha::interval<T>> &p)
-  {
-    return bp::incref(bp::make_tuple(
-      p.first, bp::make_tuple(p.second.lower(), p.second.upper())
-    ).ptr());
-  }
-};
-
 bp::object variable_init(bp::tuple args, bp::dict kwargs) {
   bp::object self = args[0];
 
@@ -263,23 +252,13 @@ void register_axis_types() {
   docstring_options dopt(true, true, false);
 
   to_python_converter<
-    bha::interval<int>,
-    axis_interval_to_python<int>
+    bha::interval_view<int>,
+    axis_interval_view_to_python<int>
   >();
 
   to_python_converter<
-    bha::interval<double>,
-    axis_interval_to_python<double>
-  >();
-
-  to_python_converter<
-    std::pair<int, bha::interval<int>>,
-    pair_int_axis_interval_to_python<int>
-  >();
-
-  to_python_converter<
-    std::pair<int, bha::interval<double>>,
-    pair_int_axis_interval_to_python<double>
+    bha::interval_view<double>,
+    axis_interval_view_to_python<double>
   >();
 
   class_<generic_iterator>("generic_iterator", init<object>())
diff --git a/test/axis_test.cpp b/test/axis_test.cpp
index d34ca6c7..25513468 100644
--- a/test/axis_test.cpp
+++ b/test/axis_test.cpp
@@ -23,18 +23,6 @@
 #define BOOST_TEST_NOT(expr) BOOST_TEST(!(expr))
 #define BOOST_TEST_IS_CLOSE(a, b, eps) BOOST_TEST(std::abs(a - b) < eps)
 
-namespace boost {
-namespace histogram {
-namespace axis {
-template <typename T>
-std::ostream &operator<<(std::ostream &os, const interval<T> &i) {
-  os << "[" << i.lower() << ", " << i.upper() << ")";
-  return os;
-}
-} // namespace axis
-} // namespace histogram
-} // namespace boost
-
 template <typename Axis>
 void test_axis_iterator(const Axis &a, int begin, int end) {
   auto it = a.begin();
@@ -239,6 +227,7 @@ int main() {
     test_axis_iterator(axis::integer<>(0, 4, ""), 0, 4);
     test_axis_iterator(axis::category<>({A, B, C}, ""), 0, 3);
     test_axis_iterator(any_axis_type(axis::regular<>(5, 0, 1)), 0, 5);
+    BOOST_TEST_THROWS(any_axis_type(axis::category<>({A, B, C}))[0], std::runtime_error);
   }
 
   // any_axis_type_copyable
diff --git a/test/histogram_test.cpp b/test/histogram_test.cpp
index 517ba56b..02df5aac 100644
--- a/test/histogram_test.cpp
+++ b/test/histogram_test.cpp
@@ -882,8 +882,7 @@ int main() {
   {
     enum { A, B };
     auto c = make_dynamic_histogram(axis::category<>({A, B}));
-    BOOST_TEST_THROWS(c.axis()[0].lower(), std::runtime_error);
-    BOOST_TEST_THROWS(c.axis()[0].upper(), std::runtime_error);
+    BOOST_TEST_THROWS(c.axis()[0], std::runtime_error);
   }
 
   // reduce