remove instances of 'local ... in ... end', replacing it with opauque structures with signatures, because I like the lower indentation level and additional whitespace in the latter

functional-core/app-init.sml

@@ -1,9 +1,14 @@
-structure AppInit =
+signature APP_INIT = 
+sig
+  val fromWidthAndHeight : int * int -> AppType.app_type
+end
+
+structure AppInit :> APP_INIT =
 struct
   open AppType
 
-  local
+  fun helpFromWidthAndHeight
-    fun init (windowWidth, windowHeight, wStart, wFinish, hStart, hFinish) =
+    (windowWidth, windowHeight, wStart, wFinish, hStart, hFinish) =
     let
       val xClickPoints = ClickPoints.generate (wStart, wFinish)
       val yClickPoints = ClickPoints.generate (hStart, hFinish)
@@ -20,17 +25,19 @@ struct
       , graphLines = graphLines
       }
     end
-  in
+
   fun fromWidthAndHeight (windowWidth, windowHeight) =
     if windowWidth = windowHeight then
-        init (windowWidth, windowHeight, 0, windowWidth, 0, windowHeight)
+      helpFromWidthAndHeight
+        (windowWidth, windowHeight, 0, windowWidth, 0, windowHeight)
     else if windowWidth > windowHeight then
       let
         val difference = windowWidth - windowHeight
         val wStart = difference div 2
         val wFinish = wStart + windowHeight
       in
-          init (windowWidth, windowHeight, wStart, wFinish, 0, windowHeight)
+        helpFromWidthAndHeight
+          (windowWidth, windowHeight, wStart, wFinish, 0, windowHeight)
       end
     else
       let
@@ -38,7 +45,7 @@ struct
         val hStart = difference div 2
         val hFinish = hStart + windowWidth
       in
-          init (windowWidth, windowHeight, 0, windowWidth, hStart, hFinish)
+        helpFromWidthAndHeight
-        end
+          (windowWidth, windowHeight, 0, windowWidth, hStart, hFinish)
       end
 end

functional-core/app-with.sml

@@ -1,4 +1,20 @@
-structure AppWith =
+signature APP_WITH =
+sig
+  val windowResize: AppType.app_type * int * int -> AppType.app_type
+  val triangleStage: AppType.app_type * AppType.triangle_stage
+                     -> AppType.app_type
+  val newTriangle:
+    AppType.app_type
+    * Real32.real
+    * Real32.real
+    * Real32.real
+    * Real32.real
+    * Real32.real
+    * Real32.real
+    -> AppType.app_type
+end
+
+structure AppWith :> APP_WITH =
 struct
   open AppType
 
@@ -49,16 +65,9 @@ struct
       }
     end
 
-  local
+  fun helpWindowResize
-    fun make
+    (app: app_type, windowWidth, windowHeight, wStart, wFinish, hStart, hFinish) :
-      ( app: app_type
+    app_type =
-      , windowWidth
-      , windowHeight
-      , wStart
-      , wFinish
-      , hStart
-      , hFinish
-      ) : app_type =
     let
       val
         { xClickPoints = _
@@ -84,17 +93,18 @@ struct
       , windowHeight = windowHeight
       }
     end
-  in
+
   fun windowResize (app: app_type, windowWidth, windowHeight) =
     if windowWidth = windowHeight then
-        make (app, windowWidth, windowHeight, 0, windowWidth, 0, windowHeight)
+      helpWindowResize
+        (app, windowWidth, windowHeight, 0, windowWidth, 0, windowHeight)
     else if windowWidth > windowHeight then
       let
         val difference = windowWidth - windowHeight
         val wStart = difference div 2
         val wFinish = wStart + windowHeight
       in
-          make
+        helpWindowResize
           (app, windowWidth, windowHeight, wStart, wFinish, 0, windowHeight)
       end
     else
@@ -103,7 +113,7 @@ struct
         val hStart = difference div 2
         val hFinish = hStart + windowWidth
       in
-          make (app, windowWidth, windowHeight, 0, windowWidth, hStart, hFinish)
+        helpWindowResize
-        end
+          (app, windowWidth, windowHeight, 0, windowWidth, hStart, hFinish)
       end
 end

functional-core/click-points.sml

@@ -1,4 +1,20 @@
-structure ClickPoints =
+signature CLICK_POINTS =
+sig
+  val generate: int * int -> Real32.real vector
+  val getClickPosition:
+    Real32.real
+    * Real32.real
+    * Real32.real
+    * Real32.real
+    * Real32.real
+    * Real32.real vector
+    * Real32.real vector
+    * int
+    * int
+    -> Real32.real vector * Real32.real * Real32.real
+end
+
+structure ClickPoints :> CLICK_POINTS =
 struct
   fun generate (start, finish) =
     let
@@ -9,7 +25,6 @@ struct
       Vector.tabulate (41, fn idx => (Real32.fromInt idx * increment) + start)
     end
 
-  local
   (*
    * Range to detect from clickable position. 
    * For example, if we have a clickable position at (x, y) = (500, 500),
@@ -37,8 +52,7 @@ struct
         val curVerticalPos = Vector.sub (yClickPoints, idx)
       in
         if
-            mouseY < curVerticalPos - range
+          mouseY < curVerticalPos - range orelse mouseY > curVerticalPos + range
-            orelse mouseY > curVerticalPos + range
         then
           getVerticalClickPos
             ( yClickPoints
@@ -171,7 +185,7 @@ struct
             , windowHeight
             )
       end
-  in
+
   (*
    * This function returns a vector containing the position data of the
    * clicked square.
@@ -202,4 +216,3 @@ struct
       , windowHeight
       )
 end
-end

functional-core/graph-lines.sml

@@ -1,11 +1,17 @@
-structure GraphLines =
+signature GRAPH_LINES =
+sig
+  val generate: int * int * Real32.real vector * Real32.real vector
+                -> Real32.real vector
+end
+
+structure GraphLines :> GRAPH_LINES =
 struct
-  local
+  (* 
-    (* This function only produces the desired result 
+   * This function only produces the desired result 
    * when the window is a square and has the aspect ratio 1:1.
    * This is because the function assumes it can use 
    * the same position coordinates both horizontally and vertically.
-     * *)
+   *)
   fun helpGenGraphLinesSquare (pos: Real32.real, limit, acc) =
     if pos >= limit then
       Vector.concat acc
@@ -21,6 +27,7 @@ struct
            , pos + 0.002, 1.0
            , pos - 0.002, 1.0
            , pos - 0.002, ~1.0
+
              (* y = _.1 *)
            , ~1.0, pos - 0.002
            , ~1.0, pos + 0.002
@@ -54,7 +61,8 @@ struct
         helpGenGraphLinesSquare (nextPos, limit, acc)
       end
 
-    fun helpGenGraphLinesHorizontal (pos, xClickPoints, acc, halfWidth, yMin, yMax) =
+  fun helpGenGraphLinesHorizontal
+    (pos, xClickPoints, acc, halfWidth, yMin, yMax) =
     if pos = Vector.length xClickPoints then
       acc
     else
@@ -125,7 +133,7 @@ struct
         helpGenGraphLinesVertical
           (pos + 1, yClickPoints, acc, halfHeight, xMin, xMax)
       end
-  in
+
   fun generate (windowWidth, windowHeight, xClickPoints, yClickPoints) =
     if windowWidth = windowHeight then
       helpGenGraphLinesSquare (~1.0, 1.0, [])
@@ -173,4 +181,3 @@ struct
         Vector.concat lines
       end
 end
-end

functional-core/triangles.sml

@@ -1,10 +1,13 @@
-structure Triangles =
+signature TRIANGLES =
+sig
+  val toVector: AppType.app_type -> Real32.real vector
+end
+
+structure Triangles :> TRIANGLES =
 struct
   open AppType
 
-  local
+  fun helpToVector (lst, acc, windowWidth, windowHeight, halfWidth, halfHeight) =
-    fun helpToVector
-      (lst, acc, windowWidth, windowHeight, halfWidth, halfHeight) =
     case lst of
       {x1, y1, x2, y2, x3, y3} :: tl =>
         let
@@ -30,7 +33,7 @@ struct
             (tl, acc, windowWidth, windowHeight, halfWidth, halfHeight)
         end
     | [] => acc
-  in
+
   fun toVector (app: app_type) =
     let
       val windowWidth = #windowWidth app
@@ -43,4 +46,3 @@ struct
       Vector.concat lst
     end
 end
-end