X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=src%2FIntegration%2FTrapezoid.hs;h=807bbc5839cb70e303dbc47d1bbf986305780b19;hb=38b68b8c9b83fc7bc9c6a2c9535a50a904d20b08;hp=c358feffec5d536f913d8e3a1c080391b17762d4;hpb=29f7502f34bdd54dff446a3a886f0e24b7e44493;p=numerical-analysis.git

diff --git a/src/Integration/Trapezoid.hs b/src/Integration/Trapezoid.hs
index c358fef..807bbc5 100644
--- a/src/Integration/Trapezoid.hs
+++ b/src/Integration/Trapezoid.hs
@@ -1,17 +1,20 @@
+{-# LANGUAGE NoImplicitPrelude #-}
+{-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE RebindableSyntax #-}
 
-module Integration.Trapezoid
+module Integration.Trapezoid (
+  trapezoid,
+  trapezoid_1 )
 where
 
-import Misc (partition)
+import Misc ( partition )
+
+import NumericPrelude hiding ( abs )
+import qualified Algebra.Field as Field ( C )
+import qualified Algebra.RealField as RealField ( C )
+import qualified Algebra.ToInteger as ToInteger ( C )
+import qualified Algebra.ToRational as ToRational ( C )
 
-import NumericPrelude hiding (abs)
-import Algebra.Absolute (abs)
-import qualified Algebra.Field as Field
-import qualified Algebra.RealField as RealField
-import qualified Algebra.RealRing as RealRing
-import qualified Algebra.ToInteger as ToInteger
-import qualified Algebra.ToRational as ToRational
 
 -- | Use the trapezoid rule to numerically integrate @f@ over the
 --   interval [@a@, @b@].
@@ -34,25 +37,28 @@ import qualified Algebra.ToRational as ToRational
 --   >>> trapezoid_1 f (-1) 1
 --   2.0
 --
-trapezoid_1 :: (Field.C a, ToRational.C a, Field.C b)
+trapezoid_1 :: forall a b. (Field.C a, ToRational.C a, Field.C b)
             => (a -> b) -- ^ The function @f@
             -> a       -- ^ The \"left\" endpoint, @a@
             -> a       -- ^ The \"right\" endpoint, @b@
             -> b
-trapezoid_1 f a b =
-  (((f a) + (f b)) / 2) * (fromRational' $ toRational (b - a))
-
+trapezoid_1 f x y =
+  (((f x) + (f y)) / 2) * coerced_interval_length
+  where
+    coerced_interval_length = fromRational' $ toRational (y - x) :: b
 
 -- | Use the composite trapezoid rule to numerically integrate @f@
 --   over @n@ subintervals of [@a@, @b@].
 --
 --   Examples:
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let f x = x^2
 --   >>> let area = trapezoid 1000 f (-1) 1
 --   >>> abs (area - (2/3)) < 0.00001
 --   True
 --
+--   >>> import Algebra.Absolute (abs)
 --   >>> let area = trapezoid 1000 sin 0 pi
 --   >>> abs (area - 2) < 0.0001
 --   True