replace instance == with isEqualBy to ensure consistency in using a single...

replace instance == with isEqualBy to ensure consistency in using a single ordering function to determine equivalence

src/libraries/OS-Independent/Data/SetBy.dcl

@@ -12,7 +12,7 @@ definition module Data.SetBy
  * For all documentation, please consult Data.Set.
  *
  * The `morally equivalent` function from Data.Set is added in the comment. This is not
- * strictly equivalent function because of the different types.
+ * a strictly equivalent function because of the different types.
  *
  * When using the functions in Data.SetBy, make sure to use the same higher-order
  * function parameter for the same data structure to ensure internal integrity. 
@@ -37,7 +37,14 @@ from Data.Foldable import class Foldable
 :: SetBy a = TipBy
            | BinBy !Int !a !(SetBy a) !(SetBy a)
 
-instance == (SetBy a) | == a
+/**
+ * True iff the two sets have the same number of elements, and these elements
+ * are pairwise 'equal' as described above, so the higher-order function 
+ * parameter represents < on a, *not* == on a(!)
+ *
+ * Morally equivalent function: instance == (Set a) | == a
+ */
+isEqualBy :: !(a a -> Bool) !(SetBy a) !(SetBy a) -> Bool
 
 /**
  * True iff first set is `smaller` than second set, according to 

src/libraries/OS-Independent/Data/SetBy.icl

@@ -23,8 +23,16 @@ mapSetByMonotonic f (BinBy n x l r) = BinBy n (f x) (mapSetByMonotonic f l) (map
 :: SetBy a = TipBy
            | BinBy !Int !a !(SetBy a) !(SetBy a)
 
-instance  == (SetBy a) | == a 
-   where (==) t1 t2  = size t1 == size t2 && toAscList t1 == toAscList t2
+isEqualBy :: !(a a -> Bool) !(SetBy a) !(SetBy a) -> Bool
+isEqualBy comp s1 s2 = size s1 == size s2 && equalEltsBy comp (toAscList s1) (toAscList s2)
+where
+	equalEltsBy :: !(a a -> Bool) ![a] ![a] -> Bool
+	equalEltsBy _ [] [] = True
+	equalEltsBy _ [] _  = False
+	equalEltsBy _ [_:_] [] = False
+	equalEltsBy comp [a:as] [b:bs]
+		| comp a b || comp b a = False
+		| otherwise            = equalEltsBy comp as bs
 
 isOrderedBy :: !(a a -> Bool) !(SetBy a) !(SetBy a) -> Bool
 isOrderedBy comp s1 s2 = compare comp (toAscList s1) (toAscList s2)