diff --git a/test_syntax.cpp b/test_syntax.cpp
new file mode 100644
index 000000000..41e738cef
--- /dev/null
+++ b/test_syntax.cpp
@@ -0,0 +1,99 @@
+#if HAVE_DYNAMIC_BOOST_TEST
+#define BOOST_TEST_DYN_LINK
+#endif
+
+#define BOOST_TEST_MODULE SyntaxTest
+
+#include "AutoDiff.hpp"
+
+#include <boost/test/unit_test.hpp>
+
+BOOST_AUTO_TEST_CASE(Initialisation)
+{
+    typedef AutoDiff::Forward<double> AdFW;
+
+    const double atol = 1.0e-14;
+
+    AdFW a(0.0), b(1.0);
+
+    BOOST_CHECK_CLOSE(a.val(), 0.0, atol);
+    BOOST_CHECK_CLOSE(b.val(), 1.0, atol);
+
+    BOOST_CHECK_CLOSE(a.der(), b.der(), atol);
+
+    a = b;
+    BOOST_CHECK_EQUAL(a.val(), b.val());
+    BOOST_CHECK_EQUAL(a.der(), b.der());
+}
+
+
+BOOST_AUTO_TEST_CASE(Addition)
+{
+    typedef AutoDiff::Forward<double> AdFW;
+
+    const double atol = 1.0e-14;
+
+    AdFW a(0.0), b(1.0);
+
+    AdFW two_a = a + a;
+    BOOST_CHECK_CLOSE(two_a.val(), 2*a.val(), atol);
+    BOOST_CHECK_CLOSE(two_a.der(), 2*a.der(), atol);
+
+    double av = a.val();
+    double ad = a.der();
+    a += b;
+    BOOST_CHECK_CLOSE(a.val(), av + b.val(), atol);
+    BOOST_CHECK_CLOSE(a.der(), ad + b.der(), atol);
+
+    av = a.val();
+    ad = a.der();
+    a += 1;
+    BOOST_CHECK_CLOSE(a.val(), av + 1, atol);
+    BOOST_CHECK_CLOSE(a.der(), ad    , atol);
+
+    AdFW bpo = b + 1;           // b plus one
+    BOOST_CHECK_CLOSE(bpo.val(), b.val() + 1, atol);
+    BOOST_CHECK_CLOSE(bpo.der(), b.der()    , atol);
+
+    AdFW opb = 1 + b;           // one plus b
+    BOOST_CHECK_CLOSE(opb.val(), b.val() + 1, atol);
+    BOOST_CHECK_CLOSE(opb.der(), b.der()    , atol);
+}
+
+
+BOOST_AUTO_TEST_CASE(Subtraction)
+{
+    typedef AutoDiff::Forward<double> AdFW;
+
+    const double atol = 1.0e-14;
+
+    AdFW a(0.0), b(1.0);
+
+    AdFW no_a = a - a;
+    BOOST_CHECK_CLOSE(no_a.val(), 0.0, atol);
+    BOOST_CHECK_CLOSE(no_a.der(), 0.0, atol);
+
+    AdFW amb = a - b;
+    BOOST_CHECK_CLOSE(amb.val(), a.val() - b.val(), atol);
+    BOOST_CHECK_CLOSE(amb.der(), a.der() - b.der(), atol);
+
+    double av = a.val();
+    double ad = a.der();
+    a -= b;
+    BOOST_CHECK_CLOSE(a.val(), av - b.val(), atol);
+    BOOST_CHECK_CLOSE(a.der(), ad - b.der(), atol);
+
+    av = a.val();
+    ad = a.der();
+    a -= 1;
+    BOOST_CHECK_CLOSE(a.val(), av - 1, atol);
+    BOOST_CHECK_CLOSE(a.der(), ad    , atol);
+
+    AdFW bmo = b - 1;           // b minus one
+    BOOST_CHECK_CLOSE(bmo.val(), b.val() - 1, atol);
+    BOOST_CHECK_CLOSE(bmo.der(), b.der()    , atol);
+
+    AdFW omb = 1 - b;           // one minus b
+    BOOST_CHECK_CLOSE(omb.val(), 1 - b.val(), atol);
+    BOOST_CHECK_CLOSE(omb.der(),   - b.der(), atol);
+}