diff -r 0eaa1851a5b6 -r db0ff630bbb7 progs/sml/re-bit.ML
--- a/progs/sml/re-bit.ML	Sat Mar 16 11:15:22 2019 +0000
+++ b/progs/sml/re-bit.ML	Thu Apr 11 17:37:00 2019 +0100
@@ -1,20 +1,27 @@
+
+datatype bit =
+  Z | S | C of char
+
+type bits = bit list
 
 datatype rexp =
    ZERO
  | ONE 
- | CHAR of char
- | ALT  of rexp * rexp
+ | CHAR of char 
+ | ALTS of rexp list
  | SEQ  of rexp * rexp 
  | STAR of rexp 
  | RECD of string * rexp
 
+fun alt r1 r2 = ALTS [r1, r2]
+
 datatype arexp =
    AZERO
- | AONE  of (bool list)
- | ACHAR of (bool list) * char
- | AALT  of (bool list) * arexp * arexp
- | ASEQ  of (bool list) * arexp * arexp 
- | ASTAR of (bool list) * arexp 
+ | AONE  of bits
+ | ACHAR of bits * char
+ | AALTS of bits * (arexp list)
+ | ASEQ  of bits * arexp * arexp 
+ | ASTAR of bits * arexp 
 
 datatype value =
    Empty
@@ -44,269 +51,54 @@
 infix 9 --
 infix 9 $
 
-fun op ++ (r1, r2) = ALT(r1, r2)
+fun op ++ (r1, r2) = ALTS [r1, r2]
 
 fun op -- (r1, r2) = SEQ(r1, r2)
 
 fun op $ (x, r) = RECD(x, r)
 
-fun alts rs = case rs of
+fun alts rs = case rs of 
     [] => ZERO
   | [r] => r
-  | r::rs => List.foldl (op ++) r rs
+  | r::rs => ALTS([r, alts rs])
+
+
+fun sum (nil) = 0 
+  | sum (head::tail) = head + sum(tail);
 
 (* size of a regular expressions - for testing purposes *)
 fun size r = case r of
     ZERO => 1
   | ONE => 1
   | CHAR(_) => 1
-  | ALT(r1, r2) => 1 + (size r1) + (size r2)
+  | ALTS(rs) => 1 + sum (map size rs)
   | SEQ(r1, r2) => 1 + (size r1) + (size r2)
   | STAR(r) => 1 + (size r)
   | RECD(_, r) => 1 + (size r)
 
-(* nullable function: tests whether the regular 
-   expression can recognise the empty string *)
-fun nullable r = case r of
-    ZERO => false
-  | ONE => true
-  | CHAR(_) => false
-  | ALT(r1, r2) => nullable(r1) orelse nullable(r2)
-  | SEQ(r1, r2) => nullable(r1) andalso nullable(r2)
-  | STAR(_) => true
-  | RECD(_, r) => nullable(r)
 
-(* derivative of a regular expression r w.r.t. a character c *)
-fun der c r = case r of
-    ZERO => ZERO
-  | ONE => ZERO
-  | CHAR(d) => if c = d then ONE else ZERO
-  | ALT(r1, r2) => ALT(der c r1, der c r2)
-  | SEQ(r1, r2) => 
-      if nullable r1 then ALT(SEQ(der c r1, r2), der c r2)
-      else SEQ(der c r1, r2)
-  | STAR(r) => SEQ(der c r, STAR(r))
-  | RECD(_, r) => der c r
-
-(* derivative w.r.t. a list of chars (iterates der) *)
-fun ders s r = case s of 
-    [] => r
-  | c::s => ders s (der c r)
-
-(* extracts a string from value *)
-fun flatten v = case v of 
-    Empty => ""
-  | Chr(c) => Char.toString c
-  | Left(v) => flatten v
-  | Right(v) => flatten v
-  | Sequ(v1, v2) => flatten v1 ^ flatten v2
-  | Stars(vs) => String.concat (List.map flatten vs)
-  | Rec(_, v) => flatten v
-
-
-(* extracts an environment from a value *)
-fun env v = case v of 
-    Empty => []
-  | Chr(c) => []
-  | Left(v) => env v
-  | Right(v) => env v
-  | Sequ(v1, v2) => env v1 @ env v2
-  | Stars(vs) => List.foldr (op @) [] (List.map env vs)
-  | Rec(x, v) => (x, flatten v) :: env v
-
-fun string_of_pair (x, s) = "(" ^ x ^ "," ^ s ^ ")"
-fun string_of_env xs = String.concatWith "," (List.map string_of_pair xs)
+fun erase r = case r of
+    AZERO => ZERO
+  | AONE(_) => ONE
+  | ACHAR(_, c) => CHAR(c)
+  | AALTS(_, rs) => ALTS(map erase rs)
+  | ASEQ(_, r1, r2) => SEQ(erase r1, erase r2)
+  | ASTAR(_, r)=> STAR(erase r)
 
 
-(* the value for a nullable rexp *)
-fun mkeps r = case r of 
-    ONE => Empty
-  | ALT(r1, r2) => 
-      if nullable r1 then Left(mkeps r1) else Right(mkeps r2)
-  | SEQ(r1, r2) => Sequ(mkeps r1, mkeps r2)
-  | STAR(r) => Stars([])
-  | RECD(x, r) => Rec(x, mkeps r)
-
-exception Error
-
-(* injection of a char into a value *)
-fun inj r c v = case (r, v) of
-    (STAR(r), Sequ(v1, Stars(vs))) => Stars(inj r c v1 :: vs)
-  | (SEQ(r1, r2), Sequ(v1, v2)) => Sequ(inj r1 c v1, v2)
-  | (SEQ(r1, r2), Left(Sequ(v1, v2))) => Sequ(inj r1 c v1, v2)
-  | (SEQ(r1, r2), Right(v2)) => Sequ(mkeps r1, inj r2 c v2)
-  | (ALT(r1, r2), Left(v1)) => Left(inj r1 c v1)
-  | (ALT(r1, r2), Right(v2)) => Right(inj r2 c v2)
-  | (CHAR(d), Empty) => Chr(d) 
-  | (RECD(x, r1), _) => Rec(x, inj r1 c v)
-  | _ => (print ("\nr: " ^ PolyML.makestring r ^ "\n");
-          print ("v: " ^ PolyML.makestring v ^ "\n");
-          raise Error)
-
-(* some "rectification" functions for simplification *)
-fun f_id v = v
-fun f_right f = fn v => Right(f v)
-fun f_left f = fn v => Left(f v)
-fun f_alt f1 f2 = fn v => case v of
-    Right(v) => Right(f2 v)
-  | Left(v) => Left(f1 v)
-fun f_seq f1 f2 = fn v => case v of 
-  Sequ(v1, v2) => Sequ(f1 v1, f2 v2)
-fun f_seq_Empty1 f1 f2 = fn v => Sequ(f1 Empty, f2 v)
-fun f_seq_Empty2 f1 f2 = fn v => Sequ(f1 v, f2 Empty)
-fun f_rec f = fn v => case v of
-    Rec(x, v) => Rec(x, f v)
-
-exception ShouldNotHappen
-
-fun f_error v = raise ShouldNotHappen
-
-(* simplification of regular expressions returning also an 
-   rectification function; no simplification under STARs *)
-fun simp r = case r of
-    ALT(r1, r2) => 
-      let val (r1s, f1s) = simp r1  
-          val (r2s, f2s) = simp r2 in
-        (case (r1s, r2s) of
-            (ZERO, _) => (r2s, f_right f2s)
-          | (_, ZERO) => (r1s, f_left f1s)
-          | (_, _)    => if r1s = r2s then (r1s, f_left f1s)
-                         else (ALT (r1s, r2s), f_alt f1s f2s))
-      end 
-  | SEQ(r1, r2) => 
-      let val (r1s, f1s) = simp r1 
-          val (r2s, f2s) = simp r2 in
-        (case (r1s, r2s) of
-          (ZERO, _)  => (ZERO, f_error)
-        | (_, ZERO)  => (ZERO, f_error)
-        | (ONE, _) => (r2s, f_seq_Empty1 f1s f2s)
-        | (_, ONE) => (r1s, f_seq_Empty2 f1s f2s)
-        | (_, _)     => (SEQ(r1s, r2s), f_seq f1s f2s))
-      end  
-  | RECD(x, r1) => 
-      let val (r1s, f1s) = simp r1 in
-        (RECD(x, r1s), f_rec f1s)
-      end
-  | r => (r, f_id)
-
-fun der_simp c r = case r of
-    ZERO => (ZERO, f_id)
-  | ONE => (ZERO, f_id)
-  | CHAR(d) => ((if c = d then ONE else ZERO), f_id)
-  | ALT(r1, r2) => 
-      let 
-        val (r1d, f1d) = der_simp c r1 
-        val (r2d, f2d) = der_simp c r2 
-      in
-        case (r1d, r2d) of
-          (ZERO, _) => (r2d, f_right f2d)
-        | (_, ZERO) => (r1d, f_left f1d)
-        | (_, _)    => if r1d = r2d then (r1d, f_left f1d)
-                       else (ALT (r1d, r2d), f_alt f1d f2d)
-      end
-  | SEQ(r1, r2) => 
-      if nullable r1 
-      then 
-        let 
-          val (r1d, f1d) = der_simp c r1 
-          val (r2d, f2d) = der_simp c r2
-          val (r2s, f2s) = simp r2 
-        in
-          case (r1d, r2s, r2d) of
-            (ZERO, _, _)  => (r2d, f_right f2d)
-          | (_, ZERO, _)  => (r2d, f_right f2d)
-          | (_, _, ZERO)  => (SEQ(r1d, r2s), f_left (f_seq f1d f2s))
-          | (ONE, _, _) => (ALT(r2s, r2d), f_alt (f_seq_Empty1 f1d f2s) f2d)
-          | (_, ONE, _) => (ALT(r1d, r2d), f_alt (f_seq_Empty2 f1d f2s) f2d)
-          | (_, _, _)     => (ALT(SEQ(r1d, r2s), r2d), f_alt (f_seq f1d f2s) f2d)
-        end
-      else 
-        let 
-          val (r1d, f1d) = der_simp c r1 
-          val (r2s, f2s) = simp r2
-        in
-          case (r1d, r2s) of
-            (ZERO, _) => (ZERO, f_error)
-          | (_, ZERO) => (ZERO, f_error)
-          | (ONE, _) => (r2s, f_seq_Empty1 f1d f2s)
-          | (_, ONE) => (r1d, f_seq_Empty2 f1d f2s)
-          | (_, _) => (SEQ(r1d, r2s), f_seq f1d f2s)
-  	end	  
-  | STAR(r1) => 
-      let 
-        val (r1d, f1d) = der_simp c r1 
-      in
-        case r1d of
-          ZERO => (ZERO, f_error)
-        | ONE => (STAR r1, f_seq_Empty1 f1d f_id)
-        | _ => (SEQ(r1d, STAR(r1)), f_seq f1d f_id)
-      end
-  | RECD(x, r1) => der_simp c r1 
-
-(* matcher function *)
-fun matcher r s = nullable(ders (explode s) r)
-
-(* lexing function (produces a value) *)
-exception LexError
-
-fun lex r s = case s of 
-    [] => if (nullable r) then mkeps r else raise LexError
-  | c::cs => inj r c (lex (der c r) cs)
-
-fun lexing r s = lex r (explode s)
-
-(* lexing with simplification *)
-fun lex_simp r s = case s of 
-    [] => if (nullable r) then mkeps r else raise LexError
-  | c::cs => 
-    let val (r_simp, f_simp) = simp (der c r) in
-      inj r c (f_simp (lex_simp r_simp cs))
-    end
-
-fun lexing_simp r s = lex_simp r (explode s)
-
-fun lex_simp2 r s = case s of 
-    [] => if (nullable r) then mkeps r else raise LexError
-  | c::cs => 
-    let val (r_simp, f_simp) = der_simp c r in
-      inj r c (f_simp (lex_simp2 r_simp cs))
-    end
-
-fun lexing_simp2 r s = lex_simp2 r (explode s)
-
-fun lex_acc r s f = case s of 
-    [] => if (nullable r) then f (mkeps r) else raise LexError
-  | c::cs => 
-    let val (r_simp, f_simp) = simp (der c r) in
-      lex_acc r_simp cs (fn v => f (inj r c (f_simp v)))
-    end
-
-fun lexing_acc r s  = lex_acc r (explode s) (f_id)
-
-fun lex_acc2 r s f = case s of 
-    [] => if (nullable r) then f (mkeps r) else raise LexError
-  | c::cs => 
-    let val (r_simp, f_simp) = der_simp c r in
-      lex_acc2 r_simp cs (fn v => f (inj r c (f_simp v)))
-    end
-
-fun lexing_acc2 r s  = lex_acc2 r (explode s) (f_id)
-
-(* bit-coded version *)
-
 fun fuse bs r = case r of
-  AZERO => AZERO
-| AONE(cs) => AONE(bs @ cs)
-| ACHAR(cs, c) => ACHAR(bs @ cs, c)
-| AALT(cs, r1, r2) => AALT(bs @ cs, r1, r2)
-| ASEQ(cs, r1, r2) => ASEQ(bs @ cs, r1, r2)
-| ASTAR(cs, r) => ASTAR(bs @ cs, r)
+    AZERO => AZERO
+  | AONE(cs) => AONE(bs @ cs)
+  | ACHAR(cs, c) => ACHAR(bs @ cs, c)
+  | AALTS(cs, rs) => AALTS(bs @ cs, rs)
+  | ASEQ(cs, r1, r2) => ASEQ(bs @ cs, r1, r2)
+  | ASTAR(cs, r) => ASTAR(bs @ cs, r)
 
 fun internalise r = case r of
   ZERO => AZERO
 | ONE => AONE([])
 | CHAR(c) => ACHAR([], c)
-| ALT(r1, r2) => AALT([], fuse [false] (internalise r1), fuse [true] (internalise r2))
+| ALTS([r1, r2]) => AALTS([], [fuse [Z] (internalise r1), fuse [S] (internalise r2)])
 | SEQ(r1, r2) => ASEQ([], internalise r1, internalise r2)
 | STAR(r) => ASTAR([], internalise r)
 | RECD(x, r) => internalise r
@@ -314,21 +106,22 @@
 fun decode_aux r bs = case (r, bs) of
   (ONE, bs) => (Empty, bs)
 | (CHAR(c), bs) => (Chr(c), bs)
-| (ALT(r1, r2), false::bs) => 
-     let val (v, bs1) = decode_aux r1 bs
-     in (Left(v), bs1) end
-| (ALT(r1, r2), true::bs) => 
-     let val (v, bs1) = decode_aux r2 bs
-     in (Right(v), bs1) end
+| (ALTS([r1]), bs) => decode_aux r1 bs
+| (ALTS(rs), Z::bs1) => 
+     let val (v, bs2) = decode_aux (hd rs) bs1
+     in (Left(v), bs2) end
+| (ALTS(rs), S::bs1) => 
+     let val (v, bs2) = decode_aux (ALTS (tl rs)) bs1
+     in (Right(v), bs2) end
 | (SEQ(r1, r2), bs) => 
     let val (v1, bs1) = decode_aux r1 bs 
         val (v2, bs2) = decode_aux r2 bs1 
     in (Sequ(v1, v2), bs2) end
-| (STAR(r1), false::bs) => 
+| (STAR(r1), Z::bs) => 
     let val (v, bs1) = decode_aux r1 bs 
         val (Stars(vs), bs2) = decode_aux (STAR r1) bs1
     in (Stars(v::vs), bs2) end
-| (STAR(_), true::bs) => (Stars [], bs)
+| (STAR(_), S::bs) => (Stars [], bs)
 | (RECD(x, r1), bs) => 
     let val (v, bs1) = decode_aux r1 bs
     in (Rec(x, v), bs1) end
@@ -339,61 +132,95 @@
   (v, []) => v
 | _ => raise DecodeError
 
-fun anullable r = case r of
+fun bnullable r = case r of
   AZERO => false
 | AONE(_) => true
-| ACHAR(_,_) => false
-| AALT(_, r1, r2) => anullable(r1) orelse anullable(r2)
-| ASEQ(_, r1, r2) => anullable(r1) andalso anullable(r2)
+| ACHAR(_, _) => false
+| AALTS(_, rs) => List.exists bnullable rs
+| ASEQ(_, r1, r2) => bnullable(r1) andalso bnullable(r2)
 | ASTAR(_, _) => true
 
-fun mkepsBC r = case r of
+fun bmkeps r = case r of
   AONE(bs) => bs
-| AALT(bs, r1, r2) => 
-    if anullable(r1) then bs @ mkepsBC(r1) else bs @ mkepsBC(r2)
-| ASEQ(bs, r1, r2) => bs @ mkepsBC(r1) @ mkepsBC(r2)
-| ASTAR(bs, r) => bs @ [true]
+| AALTS(bs, rs) => 
+    let 
+      val SOME(r) = List.find bnullable rs
+    in bs @ bmkeps(r) end
+| ASEQ(bs, r1, r2) => bs @ bmkeps(r1) @ bmkeps(r2)
+| ASTAR(bs, r) => bs @ [S]
 
-fun ader c r = case r of
+fun bder c r = case r of
   AZERO => AZERO
 | AONE(_) => AZERO
 | ACHAR(bs, d) => if c = d then AONE(bs) else AZERO
-| AALT(bs, r1, r2) => AALT(bs, ader c r1, ader c r2)
+| AALTS(bs, rs) => AALTS(bs, map (bder c) rs)
 | ASEQ(bs, r1, r2) => 
-    if (anullable r1) then AALT(bs, ASEQ([], ader c r1, r2), fuse (mkepsBC r1) (ader c r2))
-    else ASEQ(bs, ader c r1, r2)
-| ASTAR(bs, r) => ASEQ(bs, fuse [false] (ader c r), ASTAR([], r))
+    if (bnullable r1) 
+    then AALTS(bs, [ASEQ([], bder c r1, r2), fuse (bmkeps r1) (bder c r2)])
+    else ASEQ(bs, bder c r1, r2)
+| ASTAR(bs, r) => ASEQ(bs, fuse [Z] (bder c r), ASTAR([], r))
 
-fun aders s r = case s of 
+fun bders s r = case s of 
   [] => r
-| c::s => aders s (ader c r)
+| c::s => bders s (bder c r)
+
+
+exception LexError
+
+fun blex r s = case s of 
+    [] => if (bnullable r) then bmkeps r else raise LexError
+  | c::cs => blex (bder c r) cs
+
+fun blexing r s = decode r (blex (internalise r) (explode s))
 
-fun alex r s = case s of 
-    [] => if (anullable r) then mkepsBC r else raise LexError
-  | c::cs => alex (ader c r) cs
+(* Simplification *)
 
-fun alexing r s = decode r (alex (internalise r) (explode s))
+fun distinctBy xs f acc = case xs of
+   [] => []
+ | x::xs =>
+    let   
+      val res = f x
+    in  if (List.exists (fn x => x = res) acc)
+        then distinctBy xs f acc  
+        else x::distinctBy xs f (res::acc)
+    end
 
-fun asimp r = case r of
-  ASEQ(bs1, r1, r2) => (case (asimp r1, asimp r2) of
-      (AZERO, _) => AZERO
-    | (_, AZERO) => AZERO
-    | (AONE(bs2), r2s) => fuse (bs1 @ bs2) r2s
-    | (r1s, r2s) => ASEQ(bs1, r1s, r2s)
-  )
-| AALT(bs1, r1, r2) => (case (asimp r1, asimp r2) of
-      (AZERO, r2s) => fuse bs1 r2s
-    | (r1s, AZERO) => fuse bs1 r1s
-    | (r1s, r2s) => AALT(bs1, r1s, r2s)
-  )
-| r => r
+fun flats rs = case rs of
+    [] => []
+  | AZERO::rs1 => flats rs1
+  | AALTS(bs, rs1)::rs2 => map (fuse bs) rs1 @ flats rs2
+  | r1::rs2 => r1::flats rs2
+
+
+fun stack r1 r2 = case r1 of
+    AONE(bs2) => fuse bs2 r2
+  | _ => ASEQ([], r1, r2)
+
 
-fun alex_simp r s = case s of 
-    [] => if (anullable r) then mkepsBC r else raise LexError
-  | c::cs => alex_simp (asimp (ader c r)) cs
+fun bsimp r = case r of
+    ASEQ(bs1, r1, r2) => (case (bsimp r1, bsimp r2) of
+        (AZERO, _) => AZERO
+      | (_, AZERO) => AZERO
+      | (AONE(bs2), r2s) => fuse (bs1 @ bs2) r2s
+      | (AALTS(bs2, rs), r2s) =>  
+           AALTS(bs1 @ bs2, map (fn r => stack r r2s) rs)
+      | (r1s, r2s) => ASEQ(bs1, r1s, r2s)) 
+  | AALTS(bs1, rs) => (case distinctBy (flats (map bsimp rs)) erase [] of
+        [] => AZERO
+      | [r] => fuse bs1 r
+      | rs2 => AALTS(bs1, rs2))  
+  | r => r
 
-fun alexing_simp r s = decode r (alex_simp (internalise r) (explode s))
+fun bders_simp r s = case s of 
+  [] => r
+| c::s => bders_simp (bsimp (bder c r)) s
 
+fun blex_simp r s = case s of 
+    [] => if (bnullable r) then bmkeps r else raise LexError
+  | c::cs => blex_simp (bsimp (bder c r)) cs
+
+fun blexing_simp r s = 
+    decode r (blex_simp (internalise r) (explode s))
 
 
 (* Lexing rules for a small WHILE language *)
@@ -428,45 +255,12 @@
 fun time f x =
   let
   val t_start = Timer.startCPUTimer()
-  val f_x = (f x; f x; f x; f x; f x; f x; f x; f x; f x; f x)
-  val t_end = Time.toReal(#usr(Timer.checkCPUTimer(t_start))) / 10.0
+  val f_x = (f x; f x; f x; f x; f x)
+  val t_end = Time.toReal(#usr(Timer.checkCPUTimer(t_start))) / 5.0
 in
   (print ((Real.toString t_end) ^ "\n"); f_x)
 end
 
-val prog = "ab";
-val reg = ("x" $ ((str "a") -- (str "b")));
-print("Simp: " ^ PolyML.makestring (lexing_simp reg prog) ^ "\n");
-print("Acc:  " ^ PolyML.makestring (lexing_acc  reg prog) ^ "\n");
-print("Env   " ^ string_of_env (env (lexing_acc reg prog)) ^ "\n");
-
-fun fst (x, y) = x;
-fun snd (x, y) = y;
-
-val derS = [reg,
-            der #"a" reg,
-            fst (simp (der #"a" reg)),
-            fst (der_simp #"a" reg)];
-
-val vS = [(snd (simp (der #"a" reg))) (Chr(#"b")),
-          (snd (der_simp #"a" reg)) (Chr(#"b"))
-         ];
-
-print("Ders: \n" ^ 
-       String.concatWith "\n" (List.map PolyML.makestring derS)
-       ^ "\n\n");
-print("Vs: \n" ^ 
-       String.concatWith "\n" (List.map PolyML.makestring vS)
-       ^ "\n\n");
-
-
-val prog0 = "read n";
-print("Env0 is: \n" ^  string_of_env (env (lexing_acc while_regs prog0)) ^ "\n");
-
-val prog1 = "read  n; write (n)";
-print("Env1 is: \n" ^ string_of_env (env (lexing_acc while_regs prog1)) ^ "\n");
-print("Env1 is: \n" ^ string_of_env (env (alexing while_regs prog1)) ^ "\n");
-
 
 val prog2 = String.concatWith "\n" 
   ["i := 2;",
@@ -483,12 +277,6 @@
    "}"];
 
 
-let 
-  val tst = (lexing_simp while_regs prog2 = lexing_acc while_regs prog2)
-in
-  print("Sanity test: >>" ^ (PolyML.makestring tst) ^ "<<\n")
-end;
-
 (* loops in ML *)
 datatype for = to of int * int
 infix to 
@@ -510,28 +298,7 @@
 
 fun step_simp i = 
   (print ((Int.toString i) ^ ": ") ;
-   time (lexing_simp while_regs) (string_repeat prog2 i)); 
-
-fun step_simp2 i = 
-  (print ((Int.toString i) ^ ": ") ;
-   time (lexing_simp2 while_regs) (string_repeat prog2 i));
-
-fun step_acc i = 
-  (print ((Int.toString i) ^ ": ") ;
-   time (lexing_acc while_regs) (string_repeat prog2 i));
-
-fun step_acc2 i = 
-  (print ((Int.toString i) ^ ": ") ;
-   time (lexing_acc2 while_regs) (string_repeat prog2 i));
-
-fun astep_basic i = 
-  (print ((Int.toString i) ^ ": ") ;
-   time (alexing while_regs) (string_repeat prog2 i)); 
-
-fun astep_simp i = 
-  (print ((Int.toString i) ^ ": ") ;
-   time (alexing_simp while_regs) (string_repeat prog2 i)); 
-
+   time (blexing_simp while_regs) (string_repeat prog2 i)); 
 
 (*
 val main1 = forby 1000 (1000 to 5000) step_simp;
@@ -544,4 +311,11 @@
 *)
 
 print "\n";
-val main5 = forby 1 (1 to 5) astep_simp; 
\ No newline at end of file
+val main5 = forby 10 (10 to 50) step_simp; 
+
+print("Size after 50: " ^ 
+  PolyML.makestring(size (erase (bders_simp (internalise while_regs) (explode (string_repeat prog2 50))))) ^ "\n");
+
+print("Size after 100: " ^ 
+  PolyML.makestring(size (erase (bders_simp (internalise while_regs) (explode (string_repeat prog2 100))))) ^ "\n");
+