From da1a02298e0fd91006ccf49ace7218efcfb7fedb Mon Sep 17 00:00:00 2001
From: Unknown <sciencegeek1999@gmail.com>
Date: Wed, 4 Jul 2018 11:13:17 -0500
Subject: [PATCH 1/6] Added Forward Euler in Haskell

---
 .../euler/code/haskell/euler.hs                     | 13 +++++++++++++
 chapters/differential_equations/euler/euler.md      |  4 +++-
 2 files changed, 16 insertions(+), 1 deletion(-)
 create mode 100644 chapters/differential_equations/euler/code/haskell/euler.hs

diff --git a/chapters/differential_equations/euler/code/haskell/euler.hs b/chapters/differential_equations/euler/code/haskell/euler.hs
new file mode 100644
index 000000000..c82e33776
--- /dev/null
+++ b/chapters/differential_equations/euler/code/haskell/euler.hs
@@ -0,0 +1,13 @@
+solve_euler timestep n = take n $ iterate f 1
+    where f x = x - 3 * x * timestep
+
+check_result results threshold timestep =
+    and $ zipWith check' results [exp $ -3 * i * timestep | i <- [0..]]
+    where check' result solution = abs (result - solution) < threshold
+
+main = let timestep = 0.01;
+           n = 1;
+           threshold = 0.01;
+        in putStrLn $ if check_result (solve_euler timestep n) threshold timestep
+                      then "All values within threshold"
+                      else "Value(s) not in threshold"
diff --git a/chapters/differential_equations/euler/euler.md b/chapters/differential_equations/euler/euler.md
index bc766cab7..8cf7732b7 100644
--- a/chapters/differential_equations/euler/euler.md
+++ b/chapters/differential_equations/euler/euler.md
@@ -121,6 +121,9 @@ Full code for the visualization follows:
 {% sample lang="py" %}
 ### Python
 [import, lang:"python"](code/python/euler.py)
+{% sample lang="hs" %}
+### Haskell
+[import, lang:"haskell"](code/haskell/euler.hs)
 {% endmethod %}
 
 <script>
@@ -145,4 +148,3 @@ $$
 \newcommand{\bfomega}{\boldsymbol{\omega}}
 \newcommand{\bftau}{\boldsymbol{\tau}}
 $$
-

From eb1cd8d0902b67a30fecc25cefc3553077912abf Mon Sep 17 00:00:00 2001
From: Unknown <sciencegeek1999@gmail.com>
Date: Wed, 4 Jul 2018 16:20:56 -0500
Subject: [PATCH 2/6] Add explicit types and apply hindent

---
 .../euler/code/haskell/euler.hs               | 29 ++++++++++++-------
 1 file changed, 18 insertions(+), 11 deletions(-)

diff --git a/chapters/differential_equations/euler/code/haskell/euler.hs b/chapters/differential_equations/euler/code/haskell/euler.hs
index c82e33776..b428b0316 100644
--- a/chapters/differential_equations/euler/code/haskell/euler.hs
+++ b/chapters/differential_equations/euler/code/haskell/euler.hs
@@ -1,13 +1,20 @@
-solve_euler timestep n = take n $ iterate f 1
-    where f x = x - 3 * x * timestep
+solveEuler :: Double -> Int -> [Double]
+solveEuler timestep n = take n $ iterate f 1
+    where
+        f x = x - 3 * x * timestep
 
-check_result results threshold timestep =
-    and $ zipWith check' results [exp $ -3 * i * timestep | i <- [0..]]
-    where check' result solution = abs (result - solution) < threshold
+checkResult :: [Double] -> Double -> Double -> Bool
+checkResult results threshold timestep =
+    and $ zipWith check' results [exp $ -3 * i * timestep | i <- [0 ..]]
+    where
+        check' result solution = abs (result - solution) < threshold
 
-main = let timestep = 0.01;
-           n = 1;
-           threshold = 0.01;
-        in putStrLn $ if check_result (solve_euler timestep n) threshold timestep
-                      then "All values within threshold"
-                      else "Value(s) not in threshold"
+main :: IO ()
+main =
+    let timestep = 0.01
+        n = 1
+        threshold = 0.01
+    in  putStrLn $
+        if checkResult (solveEuler timestep n) threshold timestep
+        then "All values within threshold"
+        else "Value(s) not in threshold"

From 537be2c43df8f95a94950f7060b8c9e847fe5c51 Mon Sep 17 00:00:00 2001
From: Unknown <sciencegeek1999@gmail.com>
Date: Thu, 5 Jul 2018 13:40:54 -0500
Subject: [PATCH 3/6] Generalize solveEuler and checkResults

---
 .../euler/code/haskell/euler.hs               | 21 +++++++++++--------
 1 file changed, 12 insertions(+), 9 deletions(-)

diff --git a/chapters/differential_equations/euler/code/haskell/euler.hs b/chapters/differential_equations/euler/code/haskell/euler.hs
index b428b0316..660915604 100644
--- a/chapters/differential_equations/euler/code/haskell/euler.hs
+++ b/chapters/differential_equations/euler/code/haskell/euler.hs
@@ -1,20 +1,23 @@
-solveEuler :: Double -> Int -> [Double]
-solveEuler timestep n = take n $ iterate f 1
-    where
-        f x = x - 3 * x * timestep
+solveEuler :: Num a => (a -> a) -> a -> Int -> [a]
+solveEuler func initVal n = take n $ iterate func initVal
 
-checkResult :: [Double] -> Double -> Double -> Bool
-checkResult results threshold timestep =
-    and $ zipWith check' results [exp $ -3 * i * timestep | i <- [0 ..]]
+checkResult :: (Num a, Ord a, Enum a) => [a] -> (a -> a) -> a -> Bool
+checkResult results checkFunc threshold =
+    and $ zipWith check' results (fmap checkFunc [0 ..])
     where
         check' result solution = abs (result - solution) < threshold
 
+kinematics :: Double -> Double -> Double
+kinematics timestep x = x - 3 * x * timestep
+
 main :: IO ()
 main =
     let timestep = 0.01
-        n = 1
+        n = 100
         threshold = 0.01
+        kinematics' = kinematics timestep
+        checkFunc'  = exp . kinematics'
     in  putStrLn $
-        if checkResult (solveEuler timestep n) threshold timestep
+        if checkResult (solveEuler kinematics' 1 n) checkFunc' threshold
         then "All values within threshold"
         else "Value(s) not in threshold"

From 78ed76a24b2a523aea75c9594d0c01f082eb8829 Mon Sep 17 00:00:00 2001
From: Unknown <sciencegeek1999@gmail.com>
Date: Fri, 6 Jul 2018 11:42:28 -0500
Subject: [PATCH 4/6] Further generalize checkResult and slim down solveEuler

---
 .../euler/code/haskell/euler.hs                  | 16 +++++++---------
 1 file changed, 7 insertions(+), 9 deletions(-)

diff --git a/chapters/differential_equations/euler/code/haskell/euler.hs b/chapters/differential_equations/euler/code/haskell/euler.hs
index 660915604..dc85a60f1 100644
--- a/chapters/differential_equations/euler/code/haskell/euler.hs
+++ b/chapters/differential_equations/euler/code/haskell/euler.hs
@@ -1,11 +1,9 @@
-solveEuler :: Num a => (a -> a) -> a -> Int -> [a]
-solveEuler func initVal n = take n $ iterate func initVal
+solveEuler :: Num a => (a -> a) -> a -> [a]
+solveEuler = iterate
 
-checkResult :: (Num a, Ord a, Enum a) => [a] -> (a -> a) -> a -> Bool
-checkResult results checkFunc threshold =
-    and $ zipWith check' results (fmap checkFunc [0 ..])
-    where
-        check' result solution = abs (result - solution) < threshold
+checkResult :: (Ord a, Num a, Num t, Enum t) => a -> (t -> a) -> [a] -> Bool
+checkResult thresh check =
+    and . zipWith (\i k -> abs (check i - k) < thresh) [0..]
 
 kinematics :: Double -> Double -> Double
 kinematics timestep x = x - 3 * x * timestep
@@ -16,8 +14,8 @@ main =
         n = 100
         threshold = 0.01
         kinematics' = kinematics timestep
-        checkFunc'  = exp . kinematics'
+        checkResult' = checkResult threshold $ exp . kinematics'
     in  putStrLn $
-        if checkResult (solveEuler kinematics' 1 n) checkFunc' threshold
+        if checkResult' (take n $ solveEuler kinematics' 1)
         then "All values within threshold"
         else "Value(s) not in threshold"

From 0dd8148ed9148debdc6ee2857df598933ab6cfd1 Mon Sep 17 00:00:00 2001
From: Unknown <sciencegeek1999@gmail.com>
Date: Sat, 7 Jul 2018 11:12:39 -0500
Subject: [PATCH 5/6] Move timestep over to solveEuler

---
 .../euler/code/haskell/euler.hs                     | 13 ++++++-------
 1 file changed, 6 insertions(+), 7 deletions(-)

diff --git a/chapters/differential_equations/euler/code/haskell/euler.hs b/chapters/differential_equations/euler/code/haskell/euler.hs
index dc85a60f1..72cfad847 100644
--- a/chapters/differential_equations/euler/code/haskell/euler.hs
+++ b/chapters/differential_equations/euler/code/haskell/euler.hs
@@ -1,21 +1,20 @@
-solveEuler :: Num a => (a -> a) -> a -> [a]
-solveEuler = iterate
+solveEuler :: Num a => (a -> a) -> a -> a -> [a]
+solveEuler f ts = iterate (\x -> x + f x * ts)
 
 checkResult :: (Ord a, Num a, Num t, Enum t) => a -> (t -> a) -> [a] -> Bool
 checkResult thresh check =
     and . zipWith (\i k -> abs (check i - k) < thresh) [0..]
 
-kinematics :: Double -> Double -> Double
-kinematics timestep x = x - 3 * x * timestep
+kinematics :: Double -> Double
+kinematics x = -3 * x
 
 main :: IO ()
 main =
     let timestep = 0.01
         n = 100
         threshold = 0.01
-        kinematics' = kinematics timestep
-        checkResult' = checkResult threshold $ exp . kinematics'
+        checkResult' = checkResult threshold $ exp . (\x -> x - 3 * x * timestep)
     in  putStrLn $
-        if checkResult' (take n $ solveEuler kinematics' 1)
+        if checkResult' (take n $ solveEuler kinematics timestep 1)
         then "All values within threshold"
         else "Value(s) not in threshold"

From 1a391128f9625040aa5b24c4f64b41e918c374ad Mon Sep 17 00:00:00 2001
From: Unknown <sciencegeek1999@gmail.com>
Date: Sat, 7 Jul 2018 20:58:58 -0500
Subject: [PATCH 6/6] Fix Typo

---
 chapters/differential_equations/euler/code/haskell/euler.hs | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/chapters/differential_equations/euler/code/haskell/euler.hs b/chapters/differential_equations/euler/code/haskell/euler.hs
index 72cfad847..6ca9bf479 100644
--- a/chapters/differential_equations/euler/code/haskell/euler.hs
+++ b/chapters/differential_equations/euler/code/haskell/euler.hs
@@ -13,7 +13,7 @@ main =
     let timestep = 0.01
         n = 100
         threshold = 0.01
-        checkResult' = checkResult threshold $ exp . (\x -> x - 3 * x * timestep)
+        checkResult' = checkResult threshold $ exp . (\x -> -3 * x * timestep)
     in  putStrLn $
         if checkResult' (take n $ solveEuler kinematics timestep 1)
         then "All values within threshold"