Fixes defined variables, fixes live variables, implements reduces registers, fixes risc semantic

lib/utility/utility.ml

@@ -52,6 +52,7 @@ let rec fromIntToString (alphabet: string) (x: int) : string =
                                                  |> String.make 1)
 
 
+(* true if every element of la is in lb *)
 let inclusion la lb =
   let rec aux la =
     function
@@ -63,6 +64,11 @@ let inclusion la lb =
   in
   aux lb la
 
+(* true if lb includes la and la includes lb *)
+let equality la lb =
+  inclusion la lb && inclusion lb la
+
+(* computes the result of la \setminus lb *)
 let subtraction la lb =
   let rec aux la =
     function
@@ -89,23 +95,40 @@ let unique l =
 let unique_union la lb =
   unique (la @ lb)
 
+(* returns all elements both in la and in lb *)
 let unique_intersection la lb =
-  let rec aux la lb acc =
+  let rec aux la acc =
     match la with
       [] -> acc
     | a::la ->
       if List.mem a lb
-      then aux la lb (a::acc)
-      else aux la lb acc
+      then aux la (a::acc)
+      else aux la acc
   in
-  aux la lb [] |> unique
+  aux la [] |> unique
 
+(* returns a list with at most n items and the rest in the second *)
+let rec take (n: int) (l: 'a list) : ('a list * 'a list) =
+  match n with
+  | 0 -> ([], l)
+  | n ->
+    match l with
+    | [] -> ([], [])
+    | i::ls ->
+      let (t1, t2) = (take (n - 1) ls) in
+      ((i :: t1), (t2))
 
+(* returns the list without the last element *)
 let drop_last_element_list =
   function
   | [] -> []
   | l -> l |> List.rev |> List.tl |> List.rev
 
+let drop_first_element_list =
+  function
+  | [] -> []
+  | _::l -> l
+
 (* Complicated way to drop the last element and add a new option element to the
    beginning *)
 let prev l a =
@@ -152,6 +175,13 @@ let add_to_last_list (la: 'a list list) (a: 'a) : 'a list list =
   in
   aux la a
 
+let rec combine_twice la lb =
+  match (la, lb) with
+  | [], [] -> []
+  | [a], [b] -> [a, b]
+  | a::la, b::lb -> (a, b) :: (combine_twice la lb)
+  | _ -> []
+
 let rec combine_thrice la lb lc =
   match (la, lb, lc) with
   | [], [], [] -> []