diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
--- a/CHANGELOG.markdown
+++ b/CHANGELOG.markdown
@@ -1,3 +1,7 @@
+
+# 1.4
+* Changed the behavior of the $(1) template haskell splices for Exp to use a Proxy rather than value-level numbers. This is more consistent with the role of this libraary and the other could always be generated via sa splice anyways.
+
 # 1.3.1
 * Added a workaround for changes in the behavior of the internal 'Magic' datatype under the current GHC PolyKinds implementation.
 
diff --git a/fast/Data/Reflection.hs b/fast/Data/Reflection.hs
--- a/fast/Data/Reflection.hs
+++ b/fast/Data/Reflection.hs
@@ -1,3 +1,4 @@
+{-# LANGUAGE PatternGuards #-}
 {-# LANGUAGE CPP #-}
 {-# LANGUAGE FlexibleContexts #-}
 {-# LANGUAGE FunctionalDependencies #-}
@@ -155,6 +156,11 @@
 --
 -- This does not use GHC TypeLits, instead it generates a numeric type by hand similar to the ones used
 -- in the \"Functional Pearl: Implicit Configurations\" paper by Oleg Kiselyov and Chung-Chieh Shan.
+--
+-- @instance Num (Q Exp)@ provided in this package allows writing @$(3)@
+-- instead of @$(int 3)@. Sometimes the two will produce the same
+-- representation (if compiled without the @-DUSE_TYPE_LITS@ preprocessor
+-- directive).
 int :: Int -> TypeQ
 int n = case quotRem n 2 of
   (0, 0) -> conT ''Z
@@ -192,7 +198,10 @@
 -- | This permits the use of $(5) as a type splice.
 instance Num Type where
 #ifdef USE_TYPE_LITS
+  LitT (NumTyLit a) + LitT (NumTyLit b) = LitT (NumTyLit (a+b))
   a + b = AppT (AppT (VarT ''(+)) a) b
+
+  LitT (NumTyLit a) * LitT (NumTyLit b) = LitT (NumTyLit (a*b))
   a * b = AppT (AppT (VarT ''(*)) a) b
 #if MIN_VERSION_base(4,8,0)
   a - b = AppT (AppT (VarT ''(-)) a) b
@@ -214,24 +223,56 @@
   abs = error "Type.abs"
   signum = error "Type.signum"
 
-plus, times, minus :: Num a => a -> a -> a
-plus = (+)
-times = (*)
-minus = (-)
-fract :: Fractional a => a -> a -> a
-fract = (/)
 
--- | This permits the use of $(5) as an expression splice.
+onProxyType1 :: (Type -> Type) -> (Exp -> Exp)
+onProxyType1 f
+    (SigE _ ta@(AppT (ConT proxyName)  (VarT _)))
+    | proxyName == ''Proxy = ConE 'Proxy `SigE` (ConT ''Proxy `AppT` f ta)
+onProxyType1 f a =
+        LamE [SigP WildP na] body `AppE` a
+    where 
+          body = ConE 'Proxy `SigE` (ConT ''Proxy `AppT` f na)
+          na = VarT (mkName "na")
+
+onProxyType2 :: Name -> (Type -> Type -> Type) -> (Exp -> Exp -> Exp)
+onProxyType2 _fName f
+    (SigE _ (AppT (ConT proxyName)  ta))
+    (SigE _ (AppT (ConT proxyName') tb))
+    | proxyName == ''Proxy,
+      proxyName' == ''Proxy = ConE 'Proxy `SigE`
+                                        (ConT ''Proxy `AppT` f ta tb)
+-- the above case should only match for things like $(2 + 2)
+onProxyType2 fName _f a b = VarE fName `AppE` a `AppE` b
+
+-- | This permits the use of $(5) as an expression splice,
+-- which stands for @Proxy :: Proxy $(5)@
 instance Num Exp where
-  a + b = AppE (AppE (VarE 'plus) a) b
-  a * b = AppE (AppE (VarE 'times) a) b
-  a - b = AppE (AppE (VarE 'minus) a) b
-  negate = AppE (VarE 'negate)
-  signum = AppE (VarE 'signum)
-  abs = AppE (VarE 'abs)
-  fromInteger = LitE . IntegerL
+  (+) = onProxyType2 'addProxy (+)
+  (*) = onProxyType2 'mulProxy (*)
+  (-) = onProxyType2 'subProxy (-)
+  negate = onProxyType1 negate
+  abs = onProxyType1 abs
+  signum = onProxyType1 signum
+  fromInteger n = ConE 'Proxy `SigE` (ConT ''Proxy `AppT` fromInteger n)
 
-instance Fractional Exp where
-  a / b = AppE (AppE (VarE 'fract) a) b
-  recip = AppE (VarE 'recip)
-  fromRational = LitE . RationalL
+#ifdef USE_TYPE_LITS
+addProxy :: Proxy a -> Proxy b -> Proxy (a + b)
+addProxy _ _ = Proxy
+mulProxy :: Proxy a -> Proxy b -> Proxy (a * b)
+mulProxy _ _ = Proxy
+#if MIN_VERSION_base(4,8,0)
+subProxy :: Proxy a -> Proxy b -> Proxy (a - b)
+subProxy _ _ = Proxy
+#else
+subProxy :: Proxy a -> Proxy b -> Proxy c
+subProxy _ _ = error "Exp.(-): undefined"
+#endif
+--  fromInteger = LitT . NumTyLit
+#else
+addProxy :: Proxy a -> Proxy b -> Proxy c
+addProxy _ _ = error "Exp.(+): undefined"
+mulProxy :: Proxy a -> Proxy b -> Proxy c
+mulProxy _ _ = error "Exp.(*): undefined"
+subProxy :: Proxy a -> Proxy b -> Proxy c
+subProxy _ _ = error "Exp.(-): undefined"
+#endif
diff --git a/reflection.cabal b/reflection.cabal
--- a/reflection.cabal
+++ b/reflection.cabal
@@ -1,5 +1,5 @@
 name:           reflection
-version:        1.3.2
+version:        1.4
 license:        BSD3
 license-file:   LICENSE
 author:         Edward A. Kmett, Elliott Hird, Oleg Kiselyov and Chung-chieh Shan
@@ -21,6 +21,10 @@
   .
   The original paper can be obtained from
   <http://www.cs.rutgers.edu/~ccshan/prepose/prepose.pdf>.
+  .
+  For a summary of the approach taken by this library, along with more motivating
+  examples, see Austin Seipp's tutorial at
+  <https://www.fpcomplete.com/user/thoughtpolice/using-reflection>.
 
 extra-source-files:
   examples/Monoid.hs