(* Types and tools for 'modeling' und 'specifying' to be used in

   modspec.sml. The types are separated from calchead.sml into this file,

   because some of them are stored in the calc-tree, and thus are required

   _before_ ctree.sml. 

   author: Walther Neuper

   (c) due to copyright terms

use"ME/mstools.sml" (*re-evaluate sml/ from scratch!*);

use"mstools.sml";

12345678901234567890123456789012345678901234567890123456789012345678901234567890

        10        20        30        40        50        60        70        80

*)

signature SPECIFY_TOOLS =

  sig

    type envv

    datatype

      item =

          Correct of cterm'

        | False of cterm'

        | Incompl of cterm'

        | Missing of cterm'

        | Superfl of string

        | SyntaxE of string

        | TypeE of string

    val item2str : item -> string

    type itm

    val itm2str_ : Proof.context -> itm -> string

    datatype

      itm_ =

          Cor of (term * term list) * (term * term list)

        | Inc of (term * term list) * (term * term list)

        | Mis of term * term

        | Par of cterm'

        | Sup of term * term list

        | Syn of cterm'

        | Typ of cterm'

    val itm_2str : itm_ -> string

    val itm_2str_ : Proof.context -> itm_ -> string

    val itms2str_ : Proof.context -> itm list -> string

    type 'a ppc

    val ppc2str :

       {Find: string list, With: string list, Given: string list,

         Where: string list, Relate: string list} -> string

    datatype

      match =

          Matches of pblID * item ppc

        | NoMatch of pblID * item ppc

    val match2str : match -> string

    datatype

      match_ =

          Match_ of pblID * (itm list * (bool * term) list)

        | NoMatch_

    val matchs2str : match list -> string

    type ori

    val ori2str : ori -> string

    val oris2str : ori list -> string

    type preori

    val preori2str : preori -> string

    val preoris2str : preori list -> string

    type penv

    (* val penv2str_ : Proof.context -> penv -> string *)

    type vats

    (*----------------------------------------------------------------------*)

    val all_ts_in : itm_ list -> term list

    val check_preconds :

       'a ->

       rls ->

       term list -> itm list -> (bool * term) list

    val check_preconds' :

       rls ->

       term list ->

       itm list -> 'a -> (bool * term) list

   (* val chkpre2item : rls -> term -> bool * item  *)

    val pres2str : (bool * term) list -> string

   (* val evalprecond : rls -> term -> bool * term  *)

   (* val cnt : itm list -> int -> int * int *)

    val comp_dts : theory -> term * term list -> term

    val comp_dts' : term * term list -> term

    val comp_dts'' : term * term list -> string

    val comp_ts : term * term list -> term

    val d_in : itm_ -> term

    val de_item : item -> cterm'

    val dest_list : term * term list -> term list (* for testing *)

    val dest_list' : term -> term list

    val dts2str : term * term list -> string

    val e_itm : itm

  (*  val e_listBool : term  *)

  (*  val e_listReal : term  *)

    val e_ori : ori

    val e_ori_ : ori

    val empty_ppc : item ppc

   (* val empty_ppc_ct' : cterm' ppc *)

   (* val getval : term * term list -> term * term *)

   (*val head_precond :

       domID * pblID * 'a ->

       term option ->

       rls ->

       term list ->

       itm list -> 'b -> term * (bool * term) list*)

   (* val init_item : string -> item *)

   (* val is_matches : match -> bool *)

   (* val is_matches_ : match_ -> bool *)

    val is_var : term -> bool

   (* val item_ppc :

       string ppc -> item ppc  *)

    val itemppc2str : item ppc -> string

   (* val matches_pblID : match -> pblID *)

    val max2 : ('a * int) list -> 'a * int

    val max_vt : itm list -> int

    val mk_e : itm_ -> (term * term) list

    val mk_en : int -> itm -> (term * term) list

    val mk_env : itm list -> (term * term) list

    val mkval : 'a -> term list -> term

    val mkval' : term list -> term

   (* val pblID_of_match : match -> pblID *)

    val pbl_ids : Proof.context -> term -> term -> term list

    val pbl_ids' : 'a -> term -> term list -> term list

   (* val pen2str : theory -> term * term list -> string *)

    val penvval_in : itm_ -> term list

    val refined : match list -> pblID

    val refined_ :

       match_ list -> match_ option

  (*  val refined_IDitms :

       match list -> match option  *)

    val split_dts : 'a -> term -> term * term list

    val split_dts' : term * term -> term list

  (*  val take_apart : term -> term list  *)

  (*  val take_apart_inv : term list -> term *)

    val ts_in : itm_ -> term list

   (* val unique : term  *)

    val untouched : itm list -> bool

    val upd :

       Proof.context ->

       (''a * (''b * term list) list) list ->

       term ->

       ''b * term -> ''a -> ''a * (''b * term list) list

    val upd_envv :

       Proof.context ->

       envv ->

       vats ->

       term -> term -> term -> envv

    val upd_penv :

       Proof.context ->

       (''a * term list) list ->

       term -> ''a * term -> (''a * term list) list

   (* val upds_envv :

       Proof.context ->

       envv ->

       (vats * term * term * term) list ->

       envv                         *)

    val vts_cnt : int list -> itm list -> (int * int) list

    val vts_in : itm list -> int list

   (* val w_itms2str_ : Proof.context -> itm list -> unit *)

  end

(*----------------------------------------------------------*)

structure SpecifyTools : SPECIFY_TOOLS =

struct

(*----------------------------------------------------------*)

val e_listReal = (term_of o the o (parse (theory "Script"))) "[]::(real list)";

val e_listBool = (term_of o the o (parse (theory "Script"))) "[]::(bool list)";

(*.take list-term apart w.r.t. handling elementwise input.*)

fun take_apart t =

    let val elems = isalist2list t

    in map ((list2isalist (type_of (hd elems))) o single) elems end;

(*val t = str2term "[a, b]";

> val ts = take_apart t; writeln (terms2str ts);

["[a]","[b]"] 

> t = (take_apart_inv o take_apart) t;

true*)

fun take_apart_inv ts =

    let val elems = (flat o (map isalist2list)) ts;

    in list2isalist (type_of (hd elems)) elems end;

(*val ts = [str2term "[a]", str2term "[b]"];

> val t = take_apart_inv ts; term2str t;

"[a, b]"

ts = (take_apart o take_apart_inv) ts;

true*)

(*.revert split_dts only for ts; compare comp_dts.*)

fun comp_ts (d, ts) = 

    if is_list_dsc d

    then if is_list (hd ts)

	 then if is_unl d

	      then (hd ts)            (*e.g. someList [1,3,2]*)

	      else (take_apart_inv ts) 

	 (*             SML[ [a], [b] ]SML --> [a,b]             *)

	 else (hd ts) (*a variable or metavariable for a list*)

    else (hd ts);

(*.revert split_.

 WN050903 we do NOT know which is from subtheory, description or term;

 typecheck thus may lead to TYPE-error 'unknown constant';

 solution: typecheck with Isac.thy; i.e. arg 'thy' superfluous*)

(*fun comp_dts thy (d,[]) = 

    cterm_of (*(sign_of o assoc_thy) "Isac.thy"*)

	     (theory "Isac")

	     (*comp_dts:FIXXME stay with term for efficiency !!!*)

	     (if is_reall_dsc d then (d $ e_listReal)

	      else if is_booll_dsc d then (d $ e_listBool)

	      else d)

  | comp_dts thy (d,ts) =

    (cterm_of (*(sign_of o assoc_thy) "Isac.thy"*)

	      (theory "Isac")

	      (*comp_dts:FIXXME stay with term for efficiency !!*)

	      (d $ (comp_ts (d, ts)))

       handle _ => raise error ("comp_dts: "^(term2str d)^

				" $ "^(term2str (hd ts))));*)

fun comp_dts thy (d,[]) = 

	     (if is_reall_dsc d then (d $ e_listReal)

	      else if is_booll_dsc d then (d $ e_listBool)

	      else d)

  | comp_dts thy (d,ts) =

	      (d $ (comp_ts (d, ts)))

       handle _ => raise error ("comp_dts: "^(term2str d)^

				" $ "^(term2str (hd ts))); 

(*25.8.03*)

fun comp_dts' (d,[]) = 

    if is_reall_dsc d then (d $ e_listReal)

    else if is_booll_dsc d then (d $ e_listBool)

    else d

  | comp_dts' (d,ts) = (d $ (comp_ts (d, ts)))

       handle _ => raise error ("comp_dts': "^(term2str d)^

				" $ "^(term2str (hd ts))); 

(*val t = str2term "maximum A"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

val it = "maximum A" : cterm

> val t = str2term "fixedValues [r=Arbfix]"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"fixedValues [r = Arbfix]"

> val t = str2term "valuesFor [a]"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"valuesFor [a]"

> val t = str2term "valuesFor [a,b]"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"valuesFor [a, b]"

> val t = str2term "relations [A=a*b, (a/2)^^^2 + (b/2)^^^2 = r^^^2]"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

relations [A = a * b, (a / 2) ^^^ 2 + (b / 2) ^^^ 2 = r ^^^ 2]"

> val t = str2term "boundVariable a";

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"boundVariable a"

> val t = str2term "interval {x::real. 0 <= x & x <= 2*r}"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"interval {x. 0 <= x & x <= 2 * r}"

> val t = str2term "equality (sqrt(9+4*x)=sqrt x + sqrt(5+x))"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"equality (sqrt (9 + 4 * x) = sqrt x + sqrt (5 + x))"

> val t = str2term "solveFor x"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"solveFor x"

> val t = str2term "errorBound (eps=0)"; 

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"errorBound (eps = 0)"

> val t = str2term "solutions L";

> val (d,ts) = split_dts thy t; comp_dts thy (d,ts);

"solutions L"

before 6.5.03:

> val t = (term_of o the o (parse thy)) "testdscforlist [#1]";

> val (d,ts) = split_dts t;

> comp_dts thy (d,ts);

val it = "testdscforlist [#1]" : cterm

> val t = (term_of o the o (parse thy)) "(A::real)";

> val (d,ts) = split_dts t;

val d = Const ("empty","empty") : term

val ts = [Free ("A","RealDef.real")] : term list

> val t = (term_of o the o (parse thy)) "[R=(R::real)]";

> val (d,ts) = split_dts t;

val d = Const ("empty","empty") : term

val ts = [Const # $ Free # $ Free (#,#)] : term list

> val t = (term_of o the o (parse thy)) "[#1,#2]";

> val (d,ts) = split_dts t;

val ts = [Free ("#1","'a"),Free ("#2","'a")] : NOT WANTED

*)

(*for input_icalhd 11.03*)

fun comp_dts'' (d,[]) = 

    if is_reall_dsc d then term2str (d $ e_listReal)

    else if is_booll_dsc d then term2str (d $ e_listBool)

    else term2str d

  | comp_dts'' (d,ts) = term2str (d $ (comp_ts (d, ts)))

       handle _ => raise error ("comp_dts'': "^(term2str d)^

				" $ "^(term2str (hd ts))); 

(* this may decompose an object-language isa-list;

   use only, if description is not available, eg. not input ?WN:14.5.03 ??!?*)

fun dest_list' t = if is_list t then isalist2list t  else [t];

(*fun is_metavar (Free (str, _)) =

    if (last_elem o explode) str = "_" then true else false

  | is_metavar _ = false;*)

fun is_var (Free _) = true

  | is_var _ = false;

(*.special handling for lists. ?WN:14.5.03 ??!?*)

fun dest_list (d,ts) = 

  let fun dest t = 

    if is_list_dsc d andalso not (is_unl d) 

      andalso not (is_var t) (*..for pbt*)

      then isalist2list t  else [t]

  in (flat o (map dest)) ts end;

(*.decompose an input into description, terms (ev. elems of lists),

    and the value for the problem-environment; inv to comp_dts .*)

(*WN.8.6.03: corrected with minimal effort,

fn : theory -> term ->

     term *       description

     term list *  lists decomposed for elementwise input

     term list    pbl_ids not _HERE_: dont know which list-elems input*)

fun split_dts thy (t as d $ arg) =

    if is_dsc d

    then if is_list_dsc d

	 then if is_list arg

	      then if is_unl d

		   then (d, [arg])                 (*e.g. someList [1,3,2]*)

		   else (d, take_apart arg)(*[a,b] --> SML[ [a], [b] ]SML*)

	      else (d, [arg])      (*a variable or metavariable for a list*)

	 else (d, [arg])

    else (e_term, dest_list' t(*9.01 ???*))

  | split_dts thy t = (*either dsc or term*)

  let val (h,argl) = strip_comb t

  in if (not o is_dsc) h then (e_term, dest_list' t)

     else (h, dest_list (h,argl))

  end;

(* tests see fun comp_dts 

> val t = str2term "someList []";

> val (_,ts) = split_dts thy t; writeln (terms2str ts);

["[]"]

> val t = str2term "valuesFor []";

> val (_,ts) = split_dts thy t; writeln (terms2str ts);

["[]"]*)

(*.version returning ts only.*)

fun split_dts' (d, arg) = 

    if is_dsc d

    then if is_list_dsc d

	 then if is_list arg

	      then if is_unl d

		   then ([arg])                 (*e.g. someList [1,3,2]*)

		   else (take_apart arg)(*[a,b] --> SML[ [a], [b] ]SML*)

	      else ([arg])      (*a variable or metavariable for a list*)

	 else ([arg])

    else (dest_list' arg(*9.01 ???*))

  | split_dts' (d, t) = (*either dsc or term; 14.5.03 only copied*)

  let val (h,argl) = strip_comb t

  in if (not o is_dsc) h then (dest_list' t)

     else (dest_list (h,argl))

  end;

(*27.8.01: problem-environment

WN.6.5.03: FIXXME reconsider if penv is worth the effort --

           -- just rerun a whole expl with num/var may show the same ?!

WN.9.5.03: penv-concept stalled, immediately generate script env !

           but [#0, epsilon] only outcommented for eventual reconsideration  

*)

type penv = (term          (*err_*)

	     * (term list) (*[#0, epsilon] 9.5.03 outcommented*)

	     ) list;

fun pen2str ctxt (t, ts) =

    pair2str(Syntax.string_of_term ctxt t,

	     (strs2str' o map (Syntax.string_of_term ctxt)) ts);

fun penv2str_ thy (penv:penv) = (strs2str' o (map (pen2str thy))) penv;

(*

  9.5.03: still unused, but left for eventual future development*)

type envv = (int * penv) list; (*over variants*)

(*. 14.9.01: not used after putting penv-values into itm_

      make the result of split_* a value of problem-environment .*)

fun mkval dsc [] = raise error "mkval called with []"

  | mkval dsc [t] = t

  | mkval dsc ts = list2isalist ((type_of o hd) ts) ts;

(*WN.12.12.03*)

fun mkval' x = mkval e_term x;

(*. get the constant value from a penv .*)

fun getval (id, values) = 

    case values of

	[] => raise error ("penv_value: no values in '"^

			   (Syntax.string_of_term (thy2ctxt "Tools") id))

      | [v] => (id, v)

      | (v1::v2::_) => (case v1 of 

			     Const ("Script.Arbfix",_) => (id, v2)

			   | _ => (id, v1));

(*

  val e_ = (term_of o the o (parse thy)) "e_::bool";

  val ev = (term_of o the o (parse thy)) "#4 + #3 * x^^^#2 = #0";

  val v_ = (term_of o the o (parse thy)) "v_";

  val vv = (term_of o the o (parse thy)) "x";

  val r_ = (term_of o the o (parse thy)) "err_::bool";

  val rv1 = (term_of o the o (parse thy)) "#0";

  val rv2 = (term_of o the o (parse thy)) "eps";

  val penv = [(e_,[ev]),(v_,[vv]),(r_,[rv2,rv2])]:penv;

  map getval penv;

[(Free ("e_","bool"),

  Const (#,#) $ (# $ # $ (# $ #)) $ Free ("#0","RealDef.real")),

 (Free ("v_","RealDef.real"),Free ("x","RealDef.real")),

 (Free ("err_","bool"),Free ("#0","RealDef.real"))] : (term * term) list      

*)

(*23.3.02 TODO: ideas on redesign of type itm_,type item,type ori,type item ppc

(1) kinds of itms:

  (1.1) untouched: for modeling only dsc displayed(impossible after match_itms)

        =(presently) Mis (? should be Inc initially, and Mis after match_itms?)

  (1.2)  Syn,Typ,Sup: not related to oris

    Syn, Typ (presently) should be accepted in appl_add (instead Error')

    Sup      (presently) should be accepted in appl_add (instead Error')

         _could_ be w.r.t current vat (and then _is_ related to vat

    Mis should _not_ be  made Inc ((presently, by appl_add & match_itms)

- dsc in itm_ is timeconsuming -- keep id for respective queries ?

- order of items in ppc should be stable w.r.t order of itms

- stepwise input of itms --- match_itms (in one go) ..not coordinated

  - unify code

  - match_itms / match_itms_oris ..2 versions ?!

    (fast, for refine / slow, for modeling)

- clarify: efficiency <--> simplicity !!!

  ?: shift dsc itm_ -> itm | discard int in ori,itm | take int instead dsc 

    | take int for perserving order of item ppc in itms 

    | make all(!?) handling of itms stable against reordering(?)

    | field in ori ?? (not from fmz!) -- meant for efficiency (not doc!???)

      -"- "#undef" ?= not touched ?= (id,..)

-----------------------------------------------------------------

27.3.02:

def: type pbt = (field, (dsc, pid))

(1) fmz + pbt -> oris

(2) input + oris -> itm

(3) match_itms      : schnell(?) f"ur refine

    match_itms_oris : r"uckmeldung f"ur item ppc

(1.1) in oris fehlt daher pid: (i,v,f,d,ts,pid)

---------- ^^^^^ --- dh. pbt meist als argument zu viel !!!

(3.1) abwarten, wie das matchen mehr unterschiedlicher pbt's sich macht;

      wenn Problem pbt v"ollig neue, dann w"are eigentlich n"otig ????:

      (a) (_,_,d1,ts,_):ori + pbt -> (i,vt,d2,ts,pid)  dh.vt neu  ????

      (b) 

*)

(*the internal representation of a models' item

  4.9.01: not consistent:

  after Init_Proof 'Inc', but after copy_probl 'Mis' - for same situation

  (involves 'is_error');

  bool in itm really necessary ???*)

datatype itm_ = 

    Cor of (term *              (* description *)

	    (term list)) *      (* for list: elem-wise input *) 

	   (*split_dts <-> comp_dts*)

	   (term * (term list)) (* elem of penv *)

	 (*9.5.03:  ---- is already for script -- penv delayed to future*)

  | Syn of cterm'

  | Typ of cterm'

  | Inc of (term * (term list))	* (term * (term list)) (*lists,

				+ init_pbl WN.11.03 FIXXME: empty penv .. bad

                                init_pbl should return Mis !!!*)

  | Sup of (term * (term list)) (* user-input not found in pbt(+?oris?11.03)*)

  | Mis of (term * term)        (* after re-specification pbt-item not found 

                                   in pbl: only dsc, pid_*)

  | Par of cterm';  (*internal state from fun parsitm*)

type vats = int list;      (*variants in formalizations*)

(*.data-type for working on pbl/met-ppc: 

   in pbl initially holds descriptions (only) for user guidance.*)

type itm = 

  int *        (* id  =0 .. untouched - descript (only) from init 

		  23.3.02: seems to correspond to ori (fun insert_ppc)

		           <> maintain order in item ppc?*)

  vats *       (* variants - copy from ori *)

  bool *       (* input on this item is not/complete *)

  string *     (* #Given | #Find | #Relate *)

  itm_;        (*  *)

(* use"ME/sequent.sml";

   *)

val e_itm = (0,[],false,"e_itm",Syn"e_itm"):itm;

(*in CalcTree/Subproblem an 'untouched' model is created

  FIXME.WN.9.03 model should be filled to 'untouched' by Model/Refine_Problem*)

fun untouched (itms: itm list) = 

    foldl and_ (true ,map ((curry op= 0) o #1) itms);

(*> untouched [];

val it = true : bool

> untouched [e_itm];

val it = true : bool

> untouched [e_itm, (1,[],false,"e_itm",Syn "e_itm")];

val it = false : bool*)

(* find most frequent variant v in itms *)

fun vts_in itms = (distinct o flat o (map #2)) (itms:itm list);

fun cnt itms v = (v,(length o (filter (curry op= v)) o 

		     flat o (map #2)) (itms:itm list));

fun vts_cnt vts itms = map (cnt itms) vts;

fun max2 [] = raise error "max2 of []"

  | max2 (y::ys) =

  let fun mx (a,x) [] = (a,x)

	| mx (a,x) ((b,y)::ys) = 

    if x < y then mx (b,y) ys else mx (a,x) ys;

in mx y ys end;

(*. find the variant with most items already input .*)

fun max_vt itms = 

    let val vts = (vts_cnt (vts_in itms)) itms;

    in if vts = [] then 0 else (fst o max2) vts end;

(* TODO ev. make more efficient by avoiding flat *)

fun mk_e (Cor (_, iv)) = [getval iv]

  | mk_e (Syn _) = []

  | mk_e (Typ _) = [] 

  | mk_e (Inc (_, iv)) = [getval iv]

  | mk_e (Sup _) = []

  | mk_e (Mis _) = [];

fun mk_en vt ((i,vts,b,f,itm_):itm) =

    if member op = vts vt then mk_e itm_ else [];

(*. extract the environment from an item list; 

    takes the variant with most items .*)

fun mk_env itms = 

    let val vt = max_vt itms

    in (flat o (map (mk_en vt))) itms end;

(*. example as provided by an author, complete w.r.t. pbt specified 

    not touched by any user action                                 .*)

type ori = (int *      (* id: 10.3.00ff impl. only <>0 .. touched 

			  21.3.02: insert_ppc needs it ! ?:purpose maintain

				   order in item ppc ???*)

	    vats *     (* variants 21.3.02: related to pbt..discard ?*)

	    string *   (* #Given | #Find | #Relate 21.3.02: discard ?*)

	    term *     (* description *)

	    term list  (* isalist2list t | [t] *)

	    );

val e_ori_ = (0,[],"",e_term,[e_term]):ori;

val e_ori = (0,[],"",e_term,[e_term]):ori;

fun ori2str ((i,vs,fi,t,ts):ori) = 

    "("^(string_of_int i)^", "^((strs2str o (map string_of_int)) vs)^", "^fi^","^

    (term2str t)^", "^((strs2str o (map term2str)) ts)^")";

val oris2str = 

    let val s = !show_types

	val _ = show_types:= true

	val str = (strs2str' o (map (linefeed o ori2str)))

	val _ = show_types:= s

    in str end;

(*.an or without leading integer.*)

type preori = (vats *  

	       string *   

	       term *     

	       term list);

fun preori2str ((vs,fi,t,ts):preori) = 

    "("^((strs2str o (map string_of_int)) vs)^", "^fi^", "^

    (term2str t)^", "^((strs2str o (map term2str)) ts)^")";

val preoris2str = (strs2str' o (map (linefeed o preori2str)));

(*. given the input value (from split_dts)

    make the value in a problem-env according to description-type .*)

(*28.8.01: .nam and .una impl. properly, others copied .. TODO*)

fun pbl_ids ctxt (Const(_,Type("fun",[_,Type("Tools.nam",_)]))) v =

    if is_list v 

    then [v]         (*eg. [r=Arbfix]*)

    else (case v of  (*eg. eps=#0*)

	      (Const ("op =",_) $ l $ r) => [r,l]

	    | _ => raise error ("pbl_ids Tools.nam: no equality "

				^(Syntax.string_of_term ctxt v)))

  | pbl_ids ctxt (Const(_,Type("fun",[_,Type("Tools.una",_)]))) v = [v]

  | pbl_ids ctxt (Const(_,Type("fun",[_,Type("Tools.unl",_)]))) v = [v]

  | pbl_ids ctxt (Const(_,Type("fun",[_,Type("Tools.str",_)]))) v = [v]

  | pbl_ids ctxt (Const(_,Type("fun",[_,Type("Tools.toreal",_)]))) v = [v] 

  | pbl_ids ctxt (Const(_,Type("fun",[_,Type("Tools.toreall",_)])))v = [v] 

  | pbl_ids ctxt (Const(_,Type("fun",[_,Type("Tools.unknown",_)])))v = [v] 

  | pbl_ids ctxt _ v = raise error ("pbl_ids: not implemented for "

				    ^(Syntax.string_of_term ctxt v));

(*

val t as t1 $ t2 = str2term "antiDerivativeName M_b";

pbl_ids ctxt t1 t2;

  val t = (term_of o the o (parse thy)) "fixedValues [r=Arbfix]";

  val (d,argl) = strip_comb t;

  is_dsc d;                      (*see split_dts*)

  dest_list (d,argl);

  val (_ $ v) = t;

  is_list v;

  pbl_ids ctxt d v;

[Const ("List.list.Cons","[bool, bool List.list] => bool List.list") $

       (Const # $ Free # $ Const (#,#)) $ Const ("List.list.Nil","bool List..

  val (dsc,vl) = (split_dts o term_of o the o (parse thy)) "solveFor x";

val dsc = Const ("Descript.solveFor","RealDef.real => Tools.una") : term

val vl = Free ("x","RealDef.real") : term 

  val (dsc,id) = (split_did o term_of o the o (parse thy)) "solveFor v_";

  pbl_ids ctxt dsc vl;

val it = [Free ("x","RealDef.real")] : term list

  val (dsc,vl) = (split_dts o term_of o the o(parse thy))

		       "errorBound (eps=#0)";

  val (dsc,id) = (split_did o term_of o the o(parse thy)) "errorBound err_";

  pbl_ids ctxt dsc vl;

val it = [Free ("#0","RealDef.real"),Free ("eps","RealDef.real")] : term list     *)

(*. given an already input itm, ((14.9.01: no difference to pbl_ids jet!!))

    make the value in a problem-env according to description-type .*)

(*28.8.01: .nam and .una impl. properly, others copied .. TODO*)

fun pbl_ids' (Const(_,Type("fun",[_,Type("Tools.nam",_)]))) vs =

    (case vs of 

	 [] => raise error ("pbl_ids' Tools.nam called with []")

       | [t] => (case t of  (*eg. eps=#0*)

		     (Const ("op =",_) $ l $ r) => [r,l]

		   | _ => raise error ("pbl_ids' Tools.nam: no equality "

				       ^(Syntax.string_of_term (ctxt_Isac"")t)))

       | vs' => vs (*14.9.01: ???TODO *))

  | pbl_ids' (Const(_,Type("fun",[_,Type("Tools.una",_)]))) vs = vs

  | pbl_ids' (Const(_,Type("fun",[_,Type("Tools.unl",_)]))) vs = vs

  | pbl_ids' (Const(_,Type("fun",[_,Type("Tools.str",_)]))) vs = vs

  | pbl_ids' (Const(_,Type("fun",[_,Type("Tools.toreal",_)]))) vs = vs 

  | pbl_ids' (Const(_,Type("fun",[_,Type("Tools.toreall",_)])))vs = vs 

  | pbl_ids' (Const(_,Type("fun",[_,Type("Tools.unknown",_)])))vs = vs 

  | pbl_ids'  _ vs = 

    raise error ("pbl_ids': not implemented for "

		 ^(terms2str vs));

(*9.5.03 penv postponed: pbl_ids'*)

fun pbl_ids' thy d vs = [comp_ts (d, vs)];

(*14.9.01: not used after putting values for penv into itm_

  WN.5.5.03: used in upd .. upd_envv*)

fun upd_penv ctxt penv dsc (id, vl) =

(writeln"### upd_penv used !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!";

 writeln"### upd_penv used !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!";

 writeln"### upd_penv used !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!";

  overwrite (penv, (id, pbl_ids ctxt dsc vl))

);

(* 

  val penv = [];

  val (dsc,vl) = (split_did o term_of o the o (parse thy)) "solveFor x";

  val (dsc,id) = (split_did o term_of o the o (parse thy)) "solveFor v_";

  val penv = upd_penv thy penv dsc (id, vl);

[(Free ("v_","RealDef.real"),

  [Const (#,#) $ Free (#,#) $ Free ("#0","RealDef.real")])]

: (term * term list) list                                                     

  val (dsc,vl) = (split_did o term_of o the o(parse thy))"errorBound (eps=#0)";

  val (dsc,id) = (split_did o term_of o the o(parse thy))"errorBound err_";

  upd_penv thy penv dsc (id, vl);

[(Free ("v_","RealDef.real"),

  [Const (#,#) $ Free (#,#) $ Free ("#0","RealDef.real")]),

 (Free ("err_","bool"),

  [Free ("#0","RealDef.real"),Free ("eps","RealDef.real")])]

: (term * term list) list    ^.........!!!!

*)

(*WN.9.5.03: not reconsidered; looks strange !!!*)

fun upd thy envv dsc (id, vl) i =

    let val penv = case assoc (envv, i) of

		       SOME e => e

		     | NONE => [];

        val penv' = upd_penv thy penv dsc (id, vl);

    in (i, penv') end;

(*

  val i = 2;

  val envv = [(1,[]:penv),(2,[]:penv),(3,[]:penv)]:envv;

  val (dsc,vl) = (split_did o term_of o the o(parse thy))"boundVariable b";

  val (dsc,id) = (split_did o term_of o the o(parse thy))"boundVariable v_";

  upd thy envv dsc (id, vl) i;

val it = (2,[(Free ("v_","RealDef.real"),[Free ("b","RealDef.real")])])

  : int * (term * term list) list*)

(*14.9.01: not used after putting pre-penv into itm_*)

fun upd_envv thy (envv:envv) (vats:vats) dsc id vl  =

    let val vats = if length vats = 0 

		   then (*unknown id to _all_ variants*)

		       if length envv = 0 then [1]

		       else (intsto o length) envv 

		   else vats

	fun isin vats (i,_) = member op = vats i;

	val envs_notin_vat = filter_out (isin vats) envv;

    in ((map (upd thy envv dsc (id, vl)) vats) @ envs_notin_vat):envv end;

(*

  val envv = [(1,[]:penv),(2,[]:penv),(3,[]:penv)]:envv;

  val vats = [2] 

  val (dsc,vl) = (split_did o term_of o the o(parse thy))"boundVariable b";

  val (dsc,id) = (split_did o term_of o the o(parse thy))"boundVariable v_";

  val envv = upd_envv thy envv vats dsc id vl;

val envv = [(2,[(Free ("v_","RealDef.real"),[Free ("b","RealDef.real")])])]

  : (int * (term * term list) list) list

  val vats = [1,2,3];

  val (dsc,vl) = (split_did o term_of o the o(parse thy))"maximum A";

  val (dsc,id) = (split_did o term_of o the o(parse thy))"maximum m_";

  upd_envv thy envv vats dsc id vl;

[(1,[(Free ("m_","bool"),[Free ("A","bool")])]),

 (2,

  [(Free ("v_","RealDef.real"),[Free ("b","RealDef.real")]),

   (Free ("m_","bool"),[Free ("A","bool")])]),

 (3,[(Free ("m_","bool"),[Free ("A","bool")])])]

: (int * (term * term list) list) list

  val env = []:envv;

  val (d,ts) = (split_dts o term_of o the o (parse thy))

		   "fixedValues [r=Arbfix]";

  val (_,id) = (split_did o term_of o the o (parse thy))"fixedValues fix_";

  val vats = [1,2,3];

  val env = upd_envv thy env vats d id (mkval ts);

*)

(*. update envv by folding from a list of arguments .*)

fun upds_envv thy envv [] = envv

  | upds_envv thy envv ((vs, dsc, id, vl)::ps) = 

    upds_envv thy (upd_envv thy envv vs dsc id vl) ps;

(* eval test-maximum.sml until Specify_Method ...

  val PblObj{probl=(_,pbl),origin=(_,(_,_,mI),_),...} = get_obj I pt [];

  val met = (#ppc o get_met) mI;

  val envv = [];

  val eargs = flat eargs;

  val (vs, dsc, id, vl) = hd eargs;

  val envv = upds_envv thy envv [(vs, dsc, id, vl)];

  val (vs, dsc, id, vl) = hd (tl eargs);

  val envv = upds_envv thy envv [(vs, dsc, id, vl)];

  val (vs, dsc, id, vl) = hd (tl (tl eargs));

  val envv = upds_envv thy envv [(vs, dsc, id, vl)];

  val (vs, dsc, id, vl) = hd (tl (tl (tl eargs)));

  val envv = upds_envv thy envv [(vs, dsc, id, vl)];

[(1,

  [(Free ("fix_","bool List.list"),[Const (#,#),Free (#,#)]),

   (Free ("m_","bool"),[Free (#,#)]),

   (Free ("vs_","bool List.list"),[# $ # $ Const #]),

   (Free ("rs_","bool List.list"),[# $ # $ (# $ #)])]),

 (2,

  [(Free ("fix_","bool List.list"),[Const (#,#),Free (#,#)]),

   (Free ("m_","bool"),[Free (#,#)]),

   (Free ("vs_","bool List.list"),[# $ # $ Const #]),

   (Free ("rs_","bool List.list"),[# $ # $ (# $ #)])]),

 (3,

  [(Free ("fix_","bool List.list"),[Const (#,#),Free (#,#)]),

   (Free ("m_","bool"),[Free (#,#)]),

   (Free ("vs_","bool List.list"),[# $ # $ Const #])])] : envv *)

(*for _output_ of the items of a Model*)

datatype item = 

    Correct of cterm' (*labels a correct formula (type cterm')*)

  | SyntaxE of string (**)

  | TypeE   of string (**)

  | False   of cterm' (*WN050618 notexistent in itm_: only used in Where*)

  | Incompl of cterm' (**)

  | Superfl of string (**)

  | Missing of cterm';

fun item2str (Correct  s) ="Correct " ^ s

  | item2str (SyntaxE  s) ="SyntaxE " ^ s

  | item2str (TypeE    s) ="TypeE " ^ s

  | item2str (False    s) ="False " ^ s

  | item2str (Incompl  s) ="Incompl " ^ s

  | item2str (Superfl  s) ="Superfl " ^ s

  | item2str (Missing  s) ="Missing " ^ s;

(*make string for error-msgs*)

fun itm_2str_ ctxt (Cor ((d,ts), penv)) = 

    "Cor " ^ Syntax.string_of_term ctxt (comp_dts ctxt (d,ts)) ^ " ,"

    ^ pen2str ctxt penv

  | itm_2str_ ctxt (Syn c)      = "Syn " ^ c

  | itm_2str_ ctxt (Typ c)      = "Typ " ^ c

  | itm_2str_ ctxt (Inc ((d,ts), penv)) = 

    "Inc " ^ Syntax.string_of_term ctxt (comp_dts ctxt (d,ts)) ^ " ,"

    ^ pen2str ctxt penv

  | itm_2str_ ctxt (Sup (d,ts)) = 

    "Sup " ^ Syntax.string_of_term ctxt (comp_dts ctxt (d,ts))

  | itm_2str_ ctxt (Mis (d,pid))= 

    "Mis "^ Syntax.string_of_term ctxt d ^

    " "^ Syntax.string_of_term ctxt pid

  | itm_2str_ ctxt (Par s) = "Trm "^s;

fun itm_2str t = itm_2str_ (thy2ctxt "Isac") t;

fun itm2str_ ctxt ((i,is,b,s,itm_):itm) = 

    "("^(string_of_int i)^" ,"^(ints2str' is)^" ,"^(bool2str b)^" ,"^

    s^" ,"^(itm_2str_ ctxt itm_)^")";

fun itms2str_ ctxt itms = strs2str' (map (linefeed o (itm2str_ ctxt)) itms);

fun w_itms2str_ ctxt itms = writeln (itms2str_ ctxt itms);

fun init_item str = SyntaxE str;

type 'a ppc = 

    {Given : 'a list,

     Where: 'a list,

     Find  : 'a list,

     With : 'a list,

     Relate: 'a list};

fun ppc2str {Given=Given,Where=Where,Find=Find,With=With,Relate=Relate}=

    ("{Given =" ^ (strs2str Given ) ^

     ",Where=" ^ (strs2str Where) ^

     ",Find  =" ^ (strs2str Find  ) ^

     ",With =" ^ (strs2str With ) ^

     ",Relate=" ^ (strs2str Relate) ^ "}");

fun item_ppc ({Given = gi,Where= wh,

		 Find = fi,With = wi,Relate= re}: string ppc) =

  {Given = map init_item gi,Where= map init_item wh,

   Find = map init_item fi,With = map init_item wi,

   Relate= map init_item re}:item ppc;

fun itemppc2str ({Given=Given,Where=Where,

		 Find=Find,With=With,Relate=Relate}:item ppc)=

    ("{Given =" ^ ((strs2str' o (map item2str))	 Given ) ^

     ",Where=" ^ ((strs2str' o (map item2str))	 Where) ^

     ",Find  =" ^ ((strs2str' o (map item2str))	 Find  ) ^

     ",With =" ^ ((strs2str' o (map item2str))	 With ) ^

     ",Relate=" ^ ((strs2str' o (map item2str))	 Relate) ^ "}");

fun de_item (Correct x) = x

  | de_item (SyntaxE x) = x

  | de_item (TypeE   x) = x

  | de_item (False   x) = x

  | de_item (Incompl x) = x

  | de_item (Superfl x) = x

  | de_item (Missing x) = x;

val empty_ppc ={Given = [],

		Where= [],

		Find  = [], 

		With = [],

		Relate= []}:item ppc;

val empty_ppc_ct' ={Given = [],

		Where = [],

		Find  = [], 

		With  = [],

		Relate= []}:cterm' ppc;

datatype match = 

  Matches of pblID * item ppc

| NoMatch of pblID * item ppc;

fun match2str (Matches (pI, ppc)) = 

    "Matches ("^(strs2str pI)^", "^(itemppc2str ppc)^")"

  | match2str(NoMatch (pI, ppc)) = 

    "NoMatch ("^(strs2str pI)^", "^(itemppc2str ppc)^")";

fun matchs2str ms = (strs2str o (map match2str)) ms;

fun pblID_of_match (Matches (pI,_)) = pI

  | pblID_of_match (NoMatch (pI,_)) = pI;

(*10.03 for Refine_Problem*)

datatype match_ = 

  Match_ of pblID * ((itm list) * ((bool * term) list))

| NoMatch_;

(*. the refined pbt is the last_element Matches in the list .*)

fun is_matches (Matches _) = true

  | is_matches _ = false;

fun matches_pblID (Matches (pI,_)) = pI;

fun refined ms = ((matches_pblID o the o (find_first is_matches) o rev) ms)

    handle _ => []:pblID;

fun refined_IDitms ms = ((find_first is_matches) o rev) ms;

(*. the refined pbt is the last_element Matches in the list,

    for Refine_Problem, tryrefine .*)

fun is_matches_ (Match_ _) = true

  | is_matches_ _ = false;

fun refined_ ms = ((find_first is_matches_) o rev) ms;

fun ts_in (Cor ((_,ts),_)) = ts

  | ts_in (Syn  (c)) = []

  | ts_in (Typ  (c)) = []

  | ts_in (Inc ((_,ts),_)) = ts

  | ts_in (Sup (_,ts)) = ts

  | ts_in (Mis _) = [];

(*WN050629 unused*)

fun all_ts_in itm_s = (flat o (map ts_in)) itm_s;

val unique = (term_of o the o (parse (theory "Real"))) "UnIqE_tErM";

fun d_in (Cor ((d,_),_)) = d

  | d_in (Syn  (c)) = (writeln("*** d_in: Syn ("^c^")"); unique)

  | d_in (Typ  (c)) = (writeln("*** d_in: Typ ("^c^")"); unique)

  | d_in (Inc ((d,_),_)) = d

  | d_in (Sup (d,_)) = d

  | d_in (Mis (d,_)) = d;

fun dts2str (d,ts) = pair2str (term2str d, terms2str ts);

fun penvval_in (Cor ((d,_),(_,ts))) = [comp_ts (d,ts)]

  | penvval_in (Syn  (c)) = (writeln("*** penvval_in: Syn ("^c^")"); [])

  | penvval_in (Typ  (c)) = (writeln("*** penvval_in: Typ ("^c^")"); [])

  | penvval_in (Inc (_,(_,ts))) = ts

  | penvval_in (Sup dts) = (writeln("*** penvval_in: Sup "^(dts2str dts)); [])

  | penvval_in (Mis (d,t)) = (writeln("*** penvval_in: Mis "^

				      (pair2str(term2str d, term2str t))); []);

(*. check a predicate labelled with indication of incomplete substitution;

rls ->    (*for eval_true*)

bool * 	  (*have _all_ variables(Free) from the model-pattern 

            been substituted by a value from the pattern's environment ?*)

term (*the precondition*)

->

bool * 	  (*has the precondition evaluated to true*)

term (*the precondition (for map)*)

.*)

fun evalprecond prls (false, pre) = 

  (*NOT ALL Free's have been substituted, eg. because of incomplete model*)

    (false, pre)

  | evalprecond prls (true, pre) =

(* val (prls, pre) = (prls, hd pres');

   val (prls, pre) = (prls, hd (tl pres'));

   *)

    if eval_true (assoc_thy "Isac.thy") (*for Pattern.match   *)

		 [pre] prls             (*pre parsed, prls.thy*)

    then (true , pre)

    else (false , pre);

fun pre2str (b, t) = pair2str(bool2str b, term2str t);

fun pres2str pres = strs2str' (map (linefeed o pre2str) pres);

(*. check preconditions, return true if all true .*)

fun check_preconds' _ [] _ _ = []  (*empty preconditions are true*)

  | check_preconds' prls pres pbl _(*FIXME.WN0308 mvat re-introduce*) =

(* val (prls, pres, pbl, _) = (prls, where_, probl, 0);

   val (prls, pres, pbl, _) = (prls, pre, itms, mvat);

   *)

    let val env = mk_env pbl;

        val pres' = map (subst_atomic_all env) pres;

    in map (evalprecond prls) pres' end;

fun check_preconds thy prls pres pbl = 

    check_preconds' prls pres pbl (max_vt pbl);

(*----------------------------24.3.02: done too much-----

(**. copy the already input items from probl to meth (in PblObj):

     for each item in met search the related one in pbl,

     items not found in probl are (1) inserted as 'untouched' (0,...),

     and (2) completed from oris (via max_vt)  

    ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ "uberkomplett 21.2.02 ------------ .**)

(* val (pbl, met) = (itms, ppc);

   *)

fun copy_pbl thy oris pbl met =

  let val vt = max_vt pbl;

      fun vt_and_dsc d' ((i,v,f,d,ts):ori) =

	  vt mem v andalso d'= d

      fun cpy its [] (f, (d, id)) = 

	  if length its = 0        (*no dsc found in pbl*)

	  then case find_first (vt_and_dsc d) oris

		of SOME (i,v,_,_,ts) => 

		   [(i,v,true,f, Cor ((d,ts), (id,pbl_ids' thy d ts)))]

		 | NONE => [(0,[],false,f,Mis (d, id))]

	  else its	       

	| cpy its ((it as (i, vs, b, f, itm_))::itms) (pb as (x, (d, id))) =

	  if d = d_in itm_ andalso i<>0 (*already touched by user*)

	  then cpy (its @ [it]) itms pb else cpy its itms pb;	  

  in ((flat o (map (cpy [] pbl))) met):itm list end;