(* use"library.sml";

    WN.22.10.99

    for both, math-engine and isa-98-1-HOL-plus

    however, functions closely related to original isabelle-98-1 functions

             are in isa-98-1-HOL-plus/rewrite-parse/library_G

 *)

 (* Isabelle2002 -> Isabelle2009 library changed:

 signature LIBRARY =

 sig

   include BASIC_LIBRARY

   val foldl: ('a * 'b -> 'a) -> 'a * 'b list -> 'a

   val foldr: ('a * 'b -> 'b) -> 'a list * 'b -> 'b

   val foldl_map: ('a * 'b -> 'a * 'c) -> 'a * 'b list -> 'a * 'c list

   val take: int * 'a list -> 'a list

   val drop: int * 'a list -> 'a list

   val last_elem: 'a list -> 'a

 end;

 FIXME: overwritten again...*)

 fun foldl (f: 'a * 'b -> 'a) : 'a * 'b list -> 'a = (*FIXME.2009*)

   let fun itl (e, [])  = e

         | itl (e, a::l) = itl (f(e, a), l)

   in  itl end;

 fun foldr f (l, e) = (*FIXME.2009*)

   let fun itr [] = e

         | itr (a::l) = f(a, itr l)

   in  itr l  end;

 fun take (n, []) = [] (*FIXME.2009*)

   | take (n, x :: xs) =

       if n > 0 then x :: take (n - 1, xs) else [];

 fun drop (n, []) = [] (*FIXME.2009*)

   | drop (n, x :: xs) =

       if n > 0 then drop (n - 1, xs) else x :: xs;

 (*exn LIST has disappeared in 2009 ... replaced by error...*)

 fun last_elem [] = raise error "last_elem" (*FIXME.2009*)

   | last_elem [x] = x

   | last_elem (_ :: xs) = last_elem xs;

 fun gen_mem eq (x, []) = false (*FIXME.2009*)

   | gen_mem eq (x, y :: ys) = eq (x, y) orelse gen_mem eq (x, ys);

 fun gen_insert (les : 'a * 'a -> bool) ([], a) = [a]

   | gen_insert les (x::xs, a) = if les (x, a) then x::(gen_insert les (xs, a)) 

 			    else a::x::xs;

 fun gen_sort les xs = foldl (gen_insert les) (xs, []);

 fun gen_distinct eq lst =

   let

     val memb = gen_mem eq;

     fun dist (rev_seen, []) = rev rev_seen

       | dist (rev_seen, x :: xs) =

           if memb (x, rev_seen) then dist (rev_seen, xs)

           else dist (x :: rev_seen, xs);

   in

     dist ([], lst)

   end;

 fun gen_rems eq (xs, ys) = filter_out (fn x => gen_mem eq (x, ys)) xs;

 fun distinct l = gen_distinct (op =) l;

 (*.see 'fun (y :: ys) \ x' in Pure/library.ML.*)

 fun gen_dif eq (y :: ys, x) = if eq (y, x) then ys 

 			      else y :: (gen_dif eq (ys, x))

   | gen_dif eq ([], x) = [];

 (* val (eq, (y :: ys, x)) = ();*)

 (*.see 'fun ys \\ xs' in Pure/library.ML.*)

 fun gen_diff eq (ys, xs) = foldl (gen_dif eq) (ys,xs);

 (* val (eq, (ys, xs)) = (eq_thmI, (isacrlsthms, isacthms));

  *)

 (* gen_diff op= ([1,2,3,4,5,6,7],[2,3,5]);

 val it = [1, 4, 6, 7] : int list*)

 (*an indulgent version of Isabelle/src/Pure/library.ML ~~*)

 infix ~~~;

 fun xs ~~~ ys =

     let fun aaa xys []        []        = xys

 	  | aaa xys []        (y :: ys) = xys

 	  | aaa xys (x :: xs) []        = xys

 	  | aaa xys (x :: xs) (y :: ys) = aaa (xys @ [(x, y)]) xs ys

     in aaa [] xs ys end;

 (*[1,2,3] ~~~ ["1","2","3"];

 val it = [(1, "1"), (2, "2"), (3, "3")] : (int * string) list

 > [1,2] ~~~ ["1","2","3"];

 val it = [(1, "1"), (2, "2")] : (int * string) list

 > [1,2,3] ~~~ ["1","2"];

 val it = [(1, "1"), (2, "2")] : (int * string) list*)

 (*from Isabelle2002/src/Pure/library.ML; has changed in 2009 FIXME replace*)

 fun gen_ins eq (x, xs) = if gen_mem eq (x, xs) then xs else x :: xs;

 fun gen_insI eq pr (x, xs) = 

     if gen_mem eq (x, xs) 

     then (writeln ("### occurs twice: "^(pr x)); xs) 

     else x :: xs;

 fun gen_union eq pr (xs, []) = xs

   | gen_union eq pr ([], ys) = ys

   | gen_union eq pr (x :: xs, ys) = gen_union eq pr (xs, gen_ins eq (x, ys));

 fun cons2 (f,g) x = (f x, g x); (*PL softwareparadigmen*)

 fun nth _ []      = raise error "nth _ []"

   | nth 1 (x::_) = x

   | nth n (_::xs) = nth (n-1) xs;

 (*WN050106 quick for test: doesn't check for exns*)

 fun drop_nth ls (_, []) = ls

   | drop_nth ls (n, x :: xs) = 

       if n = 1 

       then ls @ xs

       else drop_nth (ls @ [x]) (n - 1, xs);

 (*> drop_nth [] (3,[1,2,3,4,5]); 

 val it = [1, 2, 4, 5] : int list

  > drop_nth [] (1,[1,2,3,4,5]); 

 val it = [2, 3, 4, 5] : int list

  > drop_nth [] (5,[1,2,3,4,5]); 

 val it = [1, 2, 3, 4] : int list *)

 fun and_ (b1,b2) = b1 andalso b2;(* ~/Design.98/ModelSpec.sml/library_G.sml *) 

 fun or_ (b1,b2) = b1 orelse b2;

 fun takerest (i, ls) = (rev o take) (length ls - i, rev ls);

 (*> takerest (3, ["normalize","polynomial","univariate","equation"]);

 val it = ["equation"] : string list

 *)

 fun takelast (i, ls) = (rev o take) (i, rev ls);

 (* > takelast (2, ["normalize","polynomial","univariate","equation"]);

 val it = ["univariate", "equation"] : pblID

 > takelast (2, ["equation"]);

 val it = ["equation"] : pblID

 > takelast (3, ["normalize","polynomial","univariate","equation"]);

 val it = ["polynomial", "univariate", "equation"]*)

 fun split_nlast (i, ls) =

     let val rv = rev ls

     in (rev (takelast (i - 1, rv)), rev (take (i, rv))) end;

 fun split_nlast (i, ls) = (take (length ls - i, ls), rev (take (i, rev ls)));

 (* val (a, b) = split_nlast (3, ["a","b","[",".","]"]);

 val a = ["a", "b"] : string list

 val b = ["[", ".", "]"] : string list

 >  val (a, b) = split_nlast (3, [".","]"]);

 val a = [] : string list

 val b = [".", "]"] : string list   *)

 (*.analoguous to dropwhile in Pure/libarary.ML.*)

 fun dropwhile P [] = []

   | dropwhile P (ys as x::xs) = if P x then dropwhile P xs else ys;

 fun takewhile col P [] = col

   | takewhile col P (ys as x::xs) = if P x then takewhile (col @ [x]) P xs

 				     else col;

 (* > takewhile [] (not o (curry op= 4)) [1,2,3,4,5,6,7];

    val it = [1, 2, 3] : int list*)

 fun dropuntil P [] = []

   | dropuntil P (ys as x::xs) = if P x then ys else dropuntil P xs;

 fun pair2tri ((a,b),c) = (a,b,c);

 fun fst3 (a,_,_) = a;

 fun snd3 (_,b,_) = b;

 fun thd3 (_,_,c) = c;

 fun skip_blanks strl = 

   let 

     fun skip strl []        = strl

       | skip strl (" "::ss) = skip strl ss

       | skip strl ( s ::ss) = skip (strl @ [s]) ss

   in skip [] strl end;

 fun de_quote str =

   let fun scan ss' [] = ss'

 	| scan ss' ("\""::ss) = scan ss' ss

 	| scan ss' (s::ss) = scan (ss' @ [s]) ss;

   in (implode o (scan []) o explode) str end;

 (*> de_quote "\"d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v\"";

 val it = "d_d ?bdv (?u + ?v) = d_d ?bdv ?u + d_d ?bdv ?v" : string*)

 (* conversions to (quoted) strings 

    FIXME: rename *2str --> *2strq (quoted elems) 

              now *2str' (elems NOT quoted) instead of *2str *)

 val commas = space_implode ",";

 fun strs2str strl = "[" ^ (commas (map quote strl)) ^ "]";

 (*> val str = strs2str ["123","asd"]; writeln str;

 val it = "[\"123\", \"asd\"]" : string

 "123", "asd"] *)

 fun strs2str' strl = "[" ^ (commas strl) ^ "]";

 fun list2str strl = "[" ^ (commas strl) ^ "]";

 (*> val str = list2str ["123","asd"]; writeln str;

 val str = "[123, asd]" : string

 [123, asd] *)

 fun spair2str (s1,s2) =   "(" ^ (quote s1) ^ ", " ^ (quote s2) ^ ")";

 fun pair2str (s1,s2) =   "(" ^ s1 ^ ", " ^ s2 ^ ")";

 (*16.11.00

 fun subs2str (subs:(string * string) list) = 

   (list2str o (map pair2str)) subs;*)

 fun subs2str (subs: string list) = list2str  subs;

 (*> val sss = ["(bdv,x)","(err,#0)"];

 > subs2str sss;

 val it = "[(bdv,x),(err,#0)]" : string*)

 fun subs2str' (subs:(string * string) list) = (*12.12.99???*)

   (list2str o (map pair2str)) subs;

 (*> val subs = subs2str [("bdv","x")]; writeln subs;

 val subs = "[(\"bdv\", \"x\")]" : string

 [("bdv", "x")] *)

 fun con2str land_lor = quote " &| ";

 val int2str = string_of_int;

 fun ints2str ints = (strs2str o (map string_of_int)) ints;

 fun ints2str' ints = (strs2str' o (map string_of_int)) ints;

 (* use"library.sml";

    *)

 (*needed in Isa + ME*)

 fun get_thy str = 

   let fun get strl []        = strl

 	| get strl ("."::ss) = strl

 	| get strl ( s ::ss) = get (strl @ [s]) ss

   in implode( get [] (explode str)) end;

 fun strip_thy str =

   let fun strip bdVar []        = implode (rev bdVar)

 	| strip bdVar ("."::_ ) = implode (rev bdVar)

 	| strip bdVar (c  ::cs) = strip (bdVar @[c]) cs

   in strip [] (rev(explode str)) end;

 fun id_of (Var ((id,ix),_)) = if ix=0 then id else id^(string_of_int ix)

   | id_of (Free (id    ,_)) = id

   | id_of (Const(id    ,_)) = id

   | id_of _                 = ""; (* never such an identifier *)

 fun ids_of t =

   let fun con ss (Const (s,_)) = s::ss

 	| con ss (Free (s,_)) = s::ss

 	| con ss (Abs (s,_,b)) = s::(con ss b)

 	| con ss (t1 $ t2) = (con ss t1) @ (con ss t2)

 	| con ss _ = ss

   in map strip_thy ((distinct o (con [])) t) end;

 (*

 > val t = (term_of o the o (parse thy))

   "solve_univar (R, [univar, equation], no_met) (a = b + #1) a";

 > ids_of t;

 ["solve'_univar","Pair","R","Cons","univar","equation","Nil",...]*)

 (*FIXME.WN090819 fun overwrite missing in ..2009/../library.ML*)

 fun overwrite (al, p as (key, _)) =               (*FIXME.2009*)

   let fun over ((q as (keyi, _)) :: pairs) =

             if keyi = key then p :: pairs else q :: (over pairs)

         | over [] = [p]

   in over al end;

 fun overwritel (al, []) = al

   | overwritel (al, b::bl) = overwritel (overwrite (al, b), bl);

 (*> val aaa = [(1,11),(2,22),(3,33)];

 > overwritel (aaa, [(2,2222),(4,4444)]);

 val it = [(1,11),(2,2222),(3,33),(4,4444)] : (int * int) list*)

 local

 fun intsto1 0 = []

   | intsto1 n = (intsto1 (n-1)) @ [n]

 in

 fun intsto n  = if n < 0 then (raise error "intsto < 0") else intsto1 n

 end;

 type 'a stack = 'a list;

 fun top ((x::xs):'a stack) = x

   | top _ = raise error "top called for empty list";

 fun pop ((x::xs):'a stack) = xs:'a stack

   | pop _ = raise error "pop called for empty list";

 fun push x (xs:'a stack) = x::xs:'a stack;

 fun drop_last l = ((rev o tl o rev) l);

 fun drop_last_n n l = rev (takerest (n, rev l));

 (*> drop_last_n 2 [1,2,3,4,5];

 val it = [1, 2, 3] : int list

 > drop_last_n 3 [1,2,3,4,5];

 val it = [1, 2] : int list

 > drop_last_n 7 [1,2,3,4,5];

 val it = [] : int list

 *)

 fun bool2str true = "true"

   | bool2str false = "false";

 (*.take elements from b to e including both.*)

 fun take_fromto from to l = 

     if from > to then raise error ("take_fromto from="^string_of_int from^

 				  " > to="^string_of_int to)

     else drop (from - 1, take (to, l));

 (*> take_fromto 3 5 [1,2,3,4,5,6,7];

 val it = [3,4,5] : int list 

 > take_fromto 3 3  [1,2,3,4,5,6,7];

 val it = [3] : int list*)

 fun idt str 0 = " "

   | idt str n = str ^ idt str (n-1);

 (*fun indt 0 = ""

   | indt n = " " ^ indt (n-1);---------does not terminate with negatives*)

 fun indt n = if n <= 0 then "" else " " ^ indt (n-1);

 fun indent 0 = ""

   | indent n = ". " ^ indent(n-1);

 fun dashs i = if 0<i then "-"^ dashs (i-1) else "";

 fun dots i = if 0<i then "."^ dots (i-1) else "";

 fun assoc ([], key) = NONE(*cp 2002 Pure/library.ML FIXXXME take AList.lookup*)

   | assoc ((keyi, xi) :: pairs, key) =

       if key = keyi then SOME xi else assoc (pairs, key);

 (*association list lookup, optimized version for strings*)

 fun assoc_string ([], (key:string)) = NONE

   | assoc_string ((keyi, xi) :: pairs, key) =

       if key = keyi then SOME xi else assoc_string (pairs, key);

 fun if_none NONE y = y (*cp from 2002 Pure/library.ML FIXXXME replace*)

   | if_none (SOME x) _ = x;