X-Git-Url: http://gitweb.michael.orlitzky.com/?p=numerical-analysis.git;a=blobdiff_plain;f=src%2FIntegration%2FSimpson.hs;h=afa932b672cee04075a43c52ccacba1e9f56be2c;hp=f0f57f29245db1a7db7bd10bd05a39a87c2347df;hb=e529722143189fe05de5a054784e22cc2a27a522;hpb=b32831b5dde3440b85cbef62f4c47fcce0ee974f

diff --git a/src/Integration/Simpson.hs b/src/Integration/Simpson.hs
index f0f57f2..afa932b 100644
--- a/src/Integration/Simpson.hs
+++ b/src/Integration/Simpson.hs
@@ -1,4 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE RebindableSyntax #-}
 
 module Integration.Simpson (
@@ -40,16 +41,16 @@ import qualified Algebra.ToRational as ToRational ( C )
 --   >>> simpson_1 f 0 1
 --   0.25
 --
-simpson_1 :: (RealField.C a, ToRational.C a, RealField.C b)
+simpson_1 :: forall a b. (RealField.C a, ToRational.C a, RealField.C b)
             => (a -> b) -- ^ The function @f@
             -> a       -- ^ The \"left\" endpoint, @a@
             -> a       -- ^ The \"right\" endpoint, @b@
             -> b
-simpson_1 f a b =
-  coefficient * ((f a) + 4*(f midpoint) + (f b))
+simpson_1 f x y =
+  coefficient * ((f x) + 4*(f midpoint) + (f y))
   where
-    coefficient = fromRational' $ (toRational (b - a)) / 6
-    midpoint = (a + b) / 2
+    coefficient = fromRational' $ (toRational (y - x)) / 6 :: b
+    midpoint = (x + y) / 2
 
 
 -- | Use the composite Simpson's rule to numerically integrate @f@