From 9b04ac4c45a99dcfa21fb547af0770637b5fc90c Mon Sep 17 00:00:00 2001
From: "Glen K. Peterson" <glen@organicdesign.org>
Date: Mon, 23 Feb 2015 23:15:37 -0500
Subject: [PATCH] Added foldLeftViaFoldRight_1

I needed a lot more detail in order to understand the solution to foldLeftViaFoldRight, so I added foldLeftViaFoldRight_1 which is functionally the same, but with additional details (longer variable names, intermediate types and variables, comments, and a sample run).  There may be a better intermediate step in the sample run to illustrate how the delay functions are combined.  I also may have swapped Normal and Applicative order evaluation by mistake at some point in that comment, but it still helped me visualize how this might play out.  I thought I'd offer it here in case other people might find it helpful too.
---
 answerkey/datastructures/13.answer.scala | 103 ++++++++++++++++++++++-
 1 file changed, 102 insertions(+), 1 deletion(-)

diff --git a/answerkey/datastructures/13.answer.scala b/answerkey/datastructures/13.answer.scala
index 9f1406d4de..115c0e2c6f 100644
--- a/answerkey/datastructures/13.answer.scala
+++ b/answerkey/datastructures/13.answer.scala
@@ -10,4 +10,105 @@ def foldRightViaFoldLeft_1[A,B](l: List[A], z: B)(f: (A,B) => B): B =
   foldLeft(l, (b:B) => b)((g,a) => b => g(f(a,b)))(z)
 
 def foldLeftViaFoldRight[A,B](l: List[A], z: B)(f: (B,A) => B): B = 
-  foldRight(l, (b:B) => b)((a,g) => b => g(f(b,a)))(z)
\ No newline at end of file
+  foldRight(l, (b:B) => b)((a,g) => b => g(f(b,a)))(z)
+
+// Here is the same function with much more description
+def foldLeftViaFoldRight_1[A,B](as: List[A], outerIdent: B)(combiner: (B, A) => B): B = {
+
+  // foldLeft processes items in the reverse order from foldRight.  It's
+  // cheating to use reverse() here because that's implemented in terms of
+  // foldLeft!  Instead, wrap each operation in a simple identity function to
+  // delay evaluation until later and stack (nest) the functions so that the
+  // order of application can be reversed.  We'll call the type of this
+  // particular identity/delay function BtoB so we aren't writing B => B
+  // everywhere:
+  type BtoB = B => B
+
+  // Here we declare a simple instance of BtoB according to the above
+  // description.  This function will be the identity value for the inner
+  // foldRight.
+  def innerIdent:BtoB = (b:B) => b
+
+  // For each item in the 'as' list (the 'a' parameter below), make a new
+  // delay function which will use the combiner function (passed in above)
+  // when it is evaluated later.  Each new function becomes the input to the
+  // previous function (delayFunc).
+  //
+  //                        This much is just the type signature
+  //                  ,-------^-------.
+  def combinerDelayer:(A, BtoB) => BtoB =
+    (a: A, delayFunc: BtoB) => (b:B) => delayFunc(combiner(b, a))
+  // `----------v---------'    `----------------v---------------'
+  //         Paramaters                 The returned function
+
+  // Pass the original list 'as', plus the simple identity function and the
+  // new combinerDelayer to foldRight.  This will create the functions for
+  // delayed evaluation with an combiner inside each one, but will not
+  // apply any of those functions.
+  def go:BtoB = foldRight(as, innerIdent)(combinerDelayer)
+
+  // This forces all the evaluations to take place
+  go(outerIdent)
+}
+
+/*
+Here is a sample run for further illustration purposes
+foldLeftViaFoldRight_1(List(1,2,3), Nil:List[Int])((b:B, a:A) => Cons(a, b))
+
+Becomes:
+foldRight(List(1,2,3), innerIdent)(combinerDelayer)(Nil)
+
+Becomes:
+def delay3(b:B) = innerIdent(combiner(b,  3))
+def delay2(b:B) = delay3(combiner(b, 2))
+def delay1(b:B) = delay2(combiner(b,  1))
+delay1(Nil)
+
+Becomes:
+def delay3(b:B) = innerIdent(combiner(b,  3))
+def delay2(b:B) = delay3(combiner(b, 2))
+delay2(combiner(Nil,  1))
+
+Becomes:
+def delay3(b:B) = innerIdent(combiner(b,  3))
+delay3(combiner(combiner(Nil,  1), 2))
+
+Becomes:
+innerIdent(combiner(combiner(combiner(Nil,  1), 2),  3))
+
+Becomes:
+combiner(combiner(combiner(Nil,  1), 2),  3)
+
+Becomes:
+combiner(combiner(Cons(1,Nil), 2),  3)
+
+Becomes:
+combiner(Cons(2,Cons(1,Nil)),  3)
+
+Becomes:
+Cons(3,Cons(2,Cons(1,Nil)))
+Voila!
+
+
+
+Alternate Route:
+def delay3(b:B) = innerIdent(combiner(b,  3))
+def delay2(b:B) = delay3(combiner(b, 2))
+def delay1(b:B) = delay2(combiner(b,  1))
+delay1(Nil)
+
+Becomes:
+def delay2(b:B) = innerIdent(combiner(combiner(b, 2),  3))
+def delay1(b:B) = delay2(combiner(b,  1))
+delay1(Nil)
+
+Equivalent:
+def delay1(b:B) = innerIdent(combiner(combiner(combiner(b,  1), 2),  3))
+delay1(Nil)
+
+Equivalent:
+((b:B) => innerIdent(combiner(combiner(combiner(b,  1), 2),  3)))(Nil)
+
+Equivalent:
+innerIdent(combiner(combiner(combiner(Nil,  1), 2),  3))
+*/