diff --git a/.gitignore b/.gitignore
new file mode 100644
index 0000000..bbe8fa9
--- /dev/null
+++ b/.gitignore
@@ -0,0 +1 @@
+.cm/
diff --git a/examples.sml b/examples.sml
index 4123e4d..fa28a4b 100644
--- a/examples.sml
+++ b/examples.sml
@@ -4,9 +4,7 @@ struct
 
   structure TM = Turing(
     structure T = BiinfiniteTape(open LRS)
-    structure SM = FunctionSM(
-      type direction = LRS.direction
-      type action = action))
+    structure SM = FunctionSM(type action = action))
 
   (* Have access to SM constructor and subroutine without an annoying prefix *)
   open TM.SM
@@ -33,18 +31,21 @@ struct
     | qLeftOne (SOME One)   = (SOME One,  Left, SM qLeftOne)
     | qLeftOne (SOME Zero)  = (SOME One,  Left, SM qLeftZero)
 
+  val sLeftZero = SM qLeftZero
+
   (* Let's separate every pair of ones *)
   fun qStart NONE              = (NONE,      Left,  Halt Accept)
     | qStart (SOME Zero)       = (SOME Zero, Right, SM qStart)
     | qStart (SOME One)        = (SOME One,  Right, SM qJustReadOne)
   and qJustReadOne NONE        = (NONE,      Left,  Halt Accept)
     | qJustReadOne (SOME Zero) = (SOME Zero, Right, SM qStart)
-    | qJustReadOne (SOME One)  = (SOME One, Left, SM (qDepair ()))
-  and qDepair () =
+    | qJustReadOne (SOME One)  =
         let
-          fun onHalt _ x = (x, Stay, SM qStart)
+          (* Upon completion of subroutine, go back to initial state *)
+          val qDepair = subroutine sLeftZero (fn (_, x) => (x, Stay, SM qStart))
         in
-          subroutine (SM qLeftZero) onHalt
+          (* Hand off control to subroutine *)
+          (SOME One, Left, SM qDepair)
         end
 end
 
@@ -52,13 +53,14 @@ structure TM_Tester =
 struct
   open TM_Creator
 
+  (* Test on empty input tape *)
   val (Accept, [SOME Zero]) = TM.simulate (SM qRightZero) []
 
   val tape = [One, One]
   val (Accept, [SOME Zero, SOME One, SOME One]) = TM.simulate (SM qRightZero) tape
   val (Accept, [SOME One, SOME One, SOME One]) = TM.simulate (SM qLeftOne) tape
 
-  (* Let's separate the ones in friends! *)
+  (* Separate all pairs of ones *)
   val depair = SM qStart
   val friends = [One, One, Zero, Zero, One, One, One]
   val result = [SOME One, SOME Zero, SOME One, SOME Zero, SOME Zero, SOME One,
diff --git a/turingMachine/stateMachine/functionsm.sml b/turingMachine/stateMachine/functionsm.sml
index 6c71f31..aba729c 100644
--- a/turingMachine/stateMachine/functionsm.sml
+++ b/turingMachine/stateMachine/functionsm.sml
@@ -1,17 +1,15 @@
 functor FunctionSM (OPTIONS : sig
                               type action
-                              type direction
                             end) : STATE_MACHINE =
 struct
   open OPTIONS
 
-  type direction = direction
   type 'a tapeSymbol = 'a option
-  datatype 'a sm = Halt of action
-               | SM of 'a state
-  withtype 'a state = 'a tapeSymbol -> ('a tapeSymbol * direction * 'a sm)
+  datatype ('a, 'b) sm = Halt of action
+               | SM of ('a, 'b) state
+  withtype ('a, 'b) move = 'a tapeSymbol * 'b * ('a, 'b) sm
+  and      ('a, 'b) state = 'a tapeSymbol -> ('a, 'b) move
 
-  type 'a move = 'a tapeSymbol * direction * 'a sm
 
   exception Halted
   (* Strip away datatype constructor and return transition function,
@@ -22,7 +20,7 @@ struct
   (* Allows us to make subroutines *)
   fun subroutine sm onHalt =
     let
-      fun subroutine' (Halt action) x = onHalt action x
+      fun subroutine' (Halt action) x = onHalt (action, x)
         | subroutine' (SM q) x =
           case q x of (sym, dir, act) => (sym, dir, SM (subroutine' act))
     in
diff --git a/turingMachine/stateMachine/stateMachine.sig b/turingMachine/stateMachine/stateMachine.sig
index b5c883d..d25309e 100644
--- a/turingMachine/stateMachine/stateMachine.sig
+++ b/turingMachine/stateMachine/stateMachine.sig
@@ -2,21 +2,21 @@ signature STATE_MACHINE =
 sig
   (* What to do when the TM has halted *)
   type action
-  (* Direction of the head to move. *)
-  type direction
-
-  type 'a state
   type 'a tapeSymbol
-  datatype 'a sm = Halt of action | SM of 'a state
-  type 'a move = 'a tapeSymbol * direction * 'a sm
+
+  (* Alpha represents the tape symbol, beta represents the direction *)
+  type ('a, 'b) state
+  datatype ('a, 'b) sm = Halt of action | SM of ('a, 'b) state
+  type ('a, 'b) move = 'a tapeSymbol * 'b * ('a, 'b) sm
 
   (* Exception raised when nextMove is called on a halted sm *)
   exception Halted
 
   (* Determine the next move (incl. symbol to write, direction of tape head, and
    * next state) based on current configuration *)
-  val nextMove : 'a sm -> 'a tapeSymbol -> 'a move
+  val nextMove : ('a, 'b) sm -> 'a tapeSymbol -> ('a, 'b) move
 
   (* Make subroutines *)
-  val subroutine : 'a sm -> (action -> 'a tapeSymbol -> 'a move) -> 'a tapeSymbol -> 'a move
+  val subroutine : ('a, 'b) sm -> (action * 'a tapeSymbol -> ('a, 'b) move)
+                     -> 'a tapeSymbol -> ('a, 'b) move
 end
diff --git a/turingMachine/turing.sig b/turingMachine/turing.sig
index e7fc885..90439cc 100644
--- a/turingMachine/turing.sig
+++ b/turingMachine/turing.sig
@@ -3,11 +3,12 @@ sig
   structure T : TAPE
   structure SM : STATE_MACHINE
   where type 'a tapeSymbol = 'a T.tapeSymbol
-  sharing type  T.direction =  SM.direction
+
+  type 'a sm = ('a, T.direction) SM.sm
 
   (* Simulate a single step on the turing machine *)
-  val step : 'a SM.sm -> 'a T.tape -> 'a SM.sm * 'a T.tape
+  val step : 'a sm -> 'a T.tape -> 'a sm * 'a T.tape
 
   (* Simulate the turing machine until it halts. *)
-  val simulate : 'a SM.sm -> 'a list -> SM.action * 'a T.tapeSymbol list
+  val simulate : 'a sm -> 'a list -> SM.action * 'a T.tapeSymbol list
 end
diff --git a/turingMachine/turing.sml b/turingMachine/turing.sml
index c5dffef..5fb439c 100644
--- a/turingMachine/turing.sml
+++ b/turingMachine/turing.sml
@@ -1,12 +1,13 @@
 functor Turing (
     structure T : TAPE
     structure SM : STATE_MACHINE
-    where type 'a tapeSymbol = 'a T.tapeSymbol
-    sharing type T.direction = SM.direction) : TURING_MACHINE =
+    where type 'a tapeSymbol = 'a T.tapeSymbol) : TURING_MACHINE =
 struct
   structure T = T
   structure SM = SM
 
+  type 'a sm = ('a, T.direction) SM.sm
+
   (* Simulate 1 step on the stateMachine and tape *)
   fun step stateMachine tape =
     let