From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 7 Dec 2018 15:33:43 +0000 (-0500)
Subject: src/Roots/Fast.hs: fix monomorphism restriction warnings.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=numerical-analysis.git;a=commitdiff_plain;h=d2222aa1c04ba9c0eb80a03149abdf7d86eca032

src/Roots/Fast.hs: fix monomorphism restriction warnings.
---

diff --git a/src/Roots/Fast.hs b/src/Roots/Fast.hs
index e5321c9..a879950 100644
--- a/src/Roots/Fast.hs
+++ b/src/Roots/Fast.hs
@@ -1,4 +1,5 @@
 {-# LANGUAGE RebindableSyntax #-}
+{-# LANGUAGE ScopedTypeVariables #-}
 
 -- | The Roots.Fast module contains faster implementations of the
 --   'Roots.Simple' algorithms. Generally, we will pass precomputed
@@ -148,7 +149,7 @@ fixed_point_iterations =
 --
 --   We also return the number of iterations required.
 --
-fixed_point_with_iterations :: (Normed a,
+fixed_point_with_iterations :: forall a b. (Normed a,
                                 Additive.C a,
                                 RealField.C b,
                                 Algebraic.C b)
@@ -165,12 +166,13 @@ fixed_point_with_iterations f epsilon x0 =
     abs_diff v w = norm (v - w)
 
     -- The nth entry in this list is the absolute value of x_{n} -
-    -- x_{n+1}.
-    differences = zipWith abs_diff xn xn_plus_one
+    -- x_{n+1}. They're of type "b" because we're going to compare
+    -- them against epsilon.
+    differences = zipWith abs_diff xn xn_plus_one :: [b]
 
     -- This produces the list [(n, xn)] so that we can determine
     -- the number of iterations required.
-    numbered_xn = zip [0..] xn
+    numbered_xn = zip [0..] xn :: [(Int,a)]
 
     -- A list of pairs, (xn, |x_{n} - x_{n+1}|).
     pairs = zip numbered_xn differences