lexing: comparison progs/sml/re-bit.ML

equal deleted inserted replaced

-:0eaa1851a5b6
+:db0ff630bbb7
+datatype bit =
+Z | S | C of char
+type bits = bit list
 datatype rexp =
 ZERO
 | ONE
 | CHAR of char
-| ALT  of rexp * rexp
+| 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)
+| AONE  of bits
-| ACHAR of (bool list) * char
+| ACHAR of bits * char
-| AALT  of (bool list) * arexp * arexp
+| AALTS of bits * (arexp list)
-| ASEQ  of (bool list) * arexp * arexp
+| ASEQ  of bits * arexp * arexp
-| ASTAR of (bool list) * arexp
+| ASTAR of bits * arexp
 datatype value =
 Empty
 | Chr of char
 | Sequ of value * value
 infix 9 ++
 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
 [] => 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 erase r = case r of
-fun nullable r = case r of
+AZERO => ZERO
-ZERO => false
+| AONE(_) => ONE
-| ONE => true
+| ACHAR(_, c) => CHAR(c)
-| CHAR(_) => false
+| AALTS(_, rs) => ALTS(map erase rs)
-| ALT(r1, r2) => nullable(r1) orelse nullable(r2)
+| ASEQ(_, r1, r2) => SEQ(erase r1, erase r2)
-| SEQ(r1, r2) => nullable(r1) andalso nullable(r2)
+| ASTAR(_, r)=> STAR(erase r)
-| 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)
-(* 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)
+| 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
 fun decode_aux r bs = case (r, bs) of
 (ONE, bs) => (Empty, bs)
 | (CHAR(c), bs) => (Chr(c), bs)
-| (ALT(r1, r2), false::bs) =>
+| (ALTS([r1]), bs) => decode_aux r1 bs
-let val (v, bs1) = decode_aux r1 bs
+| (ALTS(rs), Z::bs1) =>
-in (Left(v), bs1) end
+let val (v, bs2) = decode_aux (hd rs) bs1
-| (ALT(r1, r2), true::bs) =>
+in (Left(v), bs2) end
-let val (v, bs1) = decode_aux r2 bs
+| (ALTS(rs), S::bs1) =>
-in (Right(v), bs1) end
+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
 exception DecodeError
 fun decode r bs = case (decode_aux r bs) of
 (v, []) => v
 | _ => raise DecodeError
-fun anullable r = case r of
+fun bnullable r = case r of
 AZERO => false
 | AONE(_) => true
-| ACHAR(_,_) => false
+| ACHAR(_, _) => false
-| AALT(_, r1, r2) => anullable(r1) orelse anullable(r2)
+| AALTS(_, rs) => List.exists bnullable rs
-| ASEQ(_, r1, r2) => anullable(r1) andalso anullable(r2)
+| 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) =>
+| AALTS(bs, rs) =>
-if anullable(r1) then bs @ mkepsBC(r1) else bs @ mkepsBC(r2)
+let
-| ASEQ(bs, r1, r2) => bs @ mkepsBC(r1) @ mkepsBC(r2)
+val SOME(r) = List.find bnullable rs
-| ASTAR(bs, r) => bs @ [true]
+in bs @ bmkeps(r) end
+| ASEQ(bs, r1, r2) => bs @ bmkeps(r1) @ bmkeps(r2)
-fun ader c r = case r of
+| ASTAR(bs, r) => bs @ [S]
+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))
+if (bnullable r1)
-else ASEQ(bs, ader c r1, r2)
+then AALTS(bs, [ASEQ([], bder c r1, r2), fuse (bmkeps r1) (bder c r2)])
-| ASTAR(bs, r) => ASEQ(bs, fuse [false] (ader c r), ASTAR([], r))
+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)
-fun alex r s = case s of
-[] => if (anullable r) then mkepsBC r else raise LexError
+exception LexError
-| c::cs => alex (ader c r) cs
+fun blex r s = case s of
-fun alexing r s = decode r (alex (internalise r) (explode s))
+[] => if (bnullable r) then bmkeps r else raise LexError
+| c::cs => blex (bder c r) cs
-fun asimp r = case r of
-ASEQ(bs1, r1, r2) => (case (asimp r1, asimp r2) of
+fun blexing r s = decode r (blex (internalise r) (explode s))
-(AZERO, _) => AZERO
-| (_, AZERO) => AZERO
+(* Simplification *)
-| (AONE(bs2), r2s) => fuse (bs1 @ bs2) r2s
-| (r1s, r2s) => ASEQ(bs1, r1s, r2s)
+fun distinctBy xs f acc = case xs of
-)
+[] => []
-| AALT(bs1, r1, r2) => (case (asimp r1, asimp r2) of
+| x::xs =>
-(AZERO, r2s) => fuse bs1 r2s
+let
-| (r1s, AZERO) => fuse bs1 r1s
+val res = f x
-| (r1s, r2s) => AALT(bs1, r1s, r2s)
+in  if (List.exists (fn x => x = res) acc)
-)
+then distinctBy xs f acc
-| r => r
+else x::distinctBy xs f (res::acc)
+end
-fun alex_simp r s = case s of
-[] => if (anullable r) then mkepsBC r else raise LexError
+fun flats rs = case rs of
-| c::cs => alex_simp (asimp (ader c r)) cs
+[] => []
+| AZERO::rs1 => flats rs1
-fun alexing_simp r s = decode r (alex_simp (internalise r) (explode s))
+| 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 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 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 *)
 val sym = alts (List.map chr (explode "abcdefghijklmnopqrstuvwxyz"))
 val digit = alts (List.map chr (explode "0123456789"))
 ============ *)
 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 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 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;",
 "max := 100;",
 " if isprime == 1 then write i else skip;",
 " i := i + 1",
 "}"];
-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
 val for =
 in loop lo end)
 fun step_simp i =
 (print ((Int.toString i) ^ ": ") ;
-time (lexing_simp while_regs) (string_repeat prog2 i));
+time (blexing_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));
 (*
 val main1 = forby 1000 (1000 to 5000) step_simp;
 print "\n";
 val main2 = forby 1000 (1000 to 5000) step_simp2;
 print "\n";
 val main4 = forby 1000 (1000 to 5000) step_acc2;
 *)
 print "\n";
-val main5 = forby 1 (1 to 5) astep_simp;
+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");

changeset 317	db0ff630bbb7
parent 159	940530087f30