(* Title: calchead.sml

          Specify-phase: specifying and modeling a problem or a subproblem. The

          most important types are declared in Selem and Stool (mstools.sml).

          TODO: allocate elements of structure Selem and of structure Stool appropriately.

   Author: Walther Neuper 991122, Mathias Lehnfeld

   (c) due to copyright terms

*)

(* Survey on type fmz_ .. type ori .. type itm (in probl, meth) .. formal args of root-/SubProblem

   and relations between respective list elements:                                       #1#

                  fmz      =             [ dsc $ v......................................(dsc $ v)..]

root problem on pos = ([], _)            

                  fmz_     =             [(dsc, v).......................................(dsc, v)..]

                  \<down>                                                                       

                  oris     =             [(dsc, v)..(dsc, v),(dsc, v),(dsc, v)...........(dsc, v)..]

                  \<down>                       #Given,..,#Relate  #Find     #undef............#undef   \<down>

                  \<down>                                                     \<down>                 \<down>       \<down>

  Specify_Problem + pbl.ppc=             [(dsc,id)..(dsc,id),(dsc,id)]  \<down>                 \<down>       \<down>

                  \<down>                                                     \<down>                 \<down>       \<down>

                  itms     =             [(dsc, v)..(dsc, v),(dsc, v)]  \<down>                 \<down>       \<down>

  int.modelling                           +Cor ++++++++++Cor +Cor       \<down>                 \<down>       \<down>

                  \<down>                                                     \<down>                 \<down>       \<down>

  Specify_Method  + met.ppc=             [(dsc,id)..(dsc,id),(dsc,id)]  \<down>                 \<down>       \<down>

                  \<down>                                                     \<down>                 \<down>       \<down>

                  itms     =             [(dsc, v)..(dsc, v),(dsc, v),(dsc, v)..(dsc, v)] \<down>       \<down>

  int.modelling                                                       +Cor ++++++Cor      \<down>       \<down>

                  form.args=             [ id ..... id      , ///////  id ....... id    ] \<down>       \<down>

                  env =                  [(id, v)..(id, v)  , /////// (id, v)....(id, v)] \<down>       \<down>

  interpret code env = [(id, v)..(id, v),(id, v)..(id, v)  , /////// (id, v)....(id, v)] \<down>       \<down>

    ..extends env       ^^^^^^^^^^^^^^^^   \<down>                           \<down>   \<down>              \<down>       \<down>

                                   \<down>       \<down>                           \<down>   \<down>              \<down>       \<down>

SubProblem on pos = ([2], _)       \<down>       \<down>                           \<down>   \<down>              \<down>       \<down>

                  form.args=      [id ................................ id ]\<down>              \<down>       \<down>

                  \<down>                REAL..BOOL..                            \<down>              \<down>       \<down>

                  \<down>                                                        \<down>              \<down>       \<down>

                  + met.ppc=      [(dsc,id).......................(dsc,id)]\<down>              \<down>       \<down>

                                    \<down>                               \<down>      \<down>              \<down>       \<down>

                  oris     =      [(dsc, v)...................... (dsc,   v) ........... (dsc, v)]\<down>

  Specify_Problem, int.modelling, Specify_Method, interpret code as above                 #1#    \<down>

                                                                                                  \<down>

SubProblem on pos = ([3, 4], _)                                                                   \<down>

                  form.args=              [id ...................... id ]                         \<down>

                  \<down>                        REAL..BOOL..                                           \<down>

                  + met.ppc=              [(dsc,id).............(dsc,id)]                         \<down>

                  oris     =              [(dsc, v).............(dsc, v)...................(dsc, v)] 

  Specify_Problem, int.modelling, Specify_Method, interpret code as above                    #1#

Notes:

(1) SubProblem implements sub-function calls such, that the arguments (+ pre- + post-condition)

    of the functions become concern of interactive modelling.

(2) In Isac-terms, the above concerns the phases of modelling and 

    and of specifying (Specify_Problem, Specify_Method),

    while stepwise construction of solutions is called solving.

    The latter is supported by Lucas-Interpretation of the functions' body.

(3) ori list is determined by fmz_ (in root-pbl) or by args of SubProblem;

    it is as complete as possible (this has been different up to now).

(4) itm list is initialised by pbl-ppc | met-pps and completed (Cor) by stepwise user input.

(5) model-pattern of pbl can omit technical items, e.g. boundVariable or functionName,

    add them to the model-pattern of met and let this input be done automatically;

    respective items must be in fmz.

#1# fmz contains items, which are stored in oris of the root(!)-problem.

    This allows to specify methods, which require more input as anticipated

    in writing partial_functions: such an item can be fetched from the root-problem's oris.

    A candidate for this situation is "errorBound" in case an equation cannot be solved symbolically

    and thus is solved numerically.

#2# TODO

*)

signature CALC_HEAD =

sig

  type calcstate

  type calcstate'

  val nxt_spec : Pos.pos_ -> bool -> O_Model.T -> Spec.T -> I_Model.T * I_Model.T ->

    (string * (term * 'a)) list * (string * (term * 'b)) list -> Spec.T -> Pos.pos_ * Tactic.input

  val reset_calchead : Calc.T -> Calc.T

  val get_ocalhd : Calc.T -> Ctree.ocalhd

  val ocalhd_complete : I_Model.T -> (bool * term) list -> ThyC.id * Problem.id * Method.id -> bool

  val all_modspec : Calc.T -> Calc.T 

  val complete_metitms : O_Model.T -> I_Model.T -> I_Model.T -> Model_Pattern.T -> I_Model.T

  val insert_ppc' : I_Model.single -> I_Model.T -> I_Model.T

  val complete_mod : Calc.T -> Calc.T

  val is_complete_mod : Calc.T -> bool

  val complete_spec : Calc.T -> Calc.T

  val is_complete_spec : Calc.T -> bool

  val some_spec : Spec.T -> Spec.T -> Spec.T

  (* these could go to Ctree ..*)

  val show_pt : Ctree.ctree -> unit

  val show_pt_tac : Ctree.ctree -> unit

  val pt_extract : Calc.T -> Ctree.ptform * Tactic.input option * term list 

  val get_interval : Pos.pos' -> Pos.pos' -> int -> Ctree.ctree -> (Pos.pos' * term * Tactic.input option) list

  val match_ags : theory -> Model_Pattern.T -> term list -> O_Model.T

  val match_ags_msg : Problem.id -> term -> term list -> unit

  val oris2fmz_vals : O_Model.T -> string list * term list

  val vars_of_pbl_' : ('a * ('b * term)) list -> term list

  val is_known : Proof.context -> string -> O_Model.T -> term -> string * O_Model.single * term list

  val is_notyet_input : Proof.context -> I_Model.T -> term list -> O_Model.single -> ('a * (term * term)) list

    -> string * I_Model.single

  val ppc2list : 'a Model.ppc -> 'a list

  val mk_delete: theory -> string -> I_Model.feedback -> Tactic.input

  val mk_additem: string -> TermC.as_string -> Tactic.input

  val nxt_add: theory -> O_Model.T -> (string * (term * 'a)) list -> (int * Model_Def.variants * bool * string * I_Model.feedback) list -> (string * string) option

  val is_error: I_Model.feedback -> bool

  val complete_mod_: (int * int list * string * term * term list) list * ('a * (term * term)) list * ('b * (term * term)) list * I_Model.T -> I_Model.T * I_Model.T

  val nxt_specif_additem: string -> TermC.as_string -> Calc.T -> calcstate'

  val vals_of_oris : O_Model.T -> term list

  val specify_additem: string -> TermC.as_string -> Calc.T -> string * calcstate'

(* ---- for tests only: shifted from below to remove the Warning "unused" at fun.def. --------- *)

  val e_calcstate : Calc.T * State_Steps.T

  val e_calcstate' : calcstate'

(*/-------------------------------------------------------- ! aktivate for Test_Isac BEGIN ---\* )

  val posterms2str : (Pos.pos' * term * 'a) list -> string

  val postermtacs2str : (Pos.pos' * term * Tactic.input option) list -> string

  val is_copy_named_idstr : string -> bool

  val is_copy_named_generating_idstr : string -> bool

  val is_copy_named_generating : 'a * ('b * term) -> bool

  val is_copy_named : 'a * ('b * term) -> bool

  val ori2Coritm : Model_Pattern.T -> O_Model.single -> I_Model.single

  val matc : theory -> (string * (term * term)) list -> term list -> O_Model.preori list -> O_Model.preori list

  val mtc : theory -> Model_Pattern.single -> term -> O_Model.preori option

  val cpy_nam : Model_Pattern.T -> O_Model.preori list -> Model_Pattern.single -> O_Model.preori

  datatype additm = Add of I_Model.single | Err of string

  val appl_add: Proof.context -> string -> O_Model.T ->

    I_Model.T -> (string * (term * term)) list -> TermC.as_string -> additm

  val seek_oridts: Proof.context -> ''a -> term * term list -> (int * 'b list * ''a * term * term list) list -> string * (int * 'b list * ''a * term * term list) * term list

( *\--- ! aktivate for Test_Isac END ----------------------------------------------------------/*)

(*----- kept as hints to initial design ideas; NOT in src/, NOT in test ------------------------*)

  val variants_in : term list -> int

  val is_untouched : I_Model.single -> bool

  val is_list_type : typ -> bool

  val parse_ok : I_Model.feedback list -> bool

  val all_dsc_in : I_Model.feedback list -> term list

  val chktyps : theory -> term list * term list -> term list (* only in old tests*)

  val chk_vars : term Model.ppc -> string * term list

  val unbound_ppc : term Model.ppc -> term list

  val is_complete_modspec : Calc.T -> bool

  val get_formress : (string * Pos.pos' * term) list list -> Pos.pos -> Ctree.ctree list ->

    (string * Pos.pos' * term) list

  val get_forms : (string * Pos.pos' * term) list list -> Pos.pos -> Ctree.ctree list ->

    (string * Pos.pos' * term) list

end

(**)

structure Chead(**): CALC_HEAD(**) =

struct

(**)

open Ctree

open Pos

(* datatypes *)

(* the state wich is stored after each step of calculation; it contains

   the calc-state and a list of [tac,istate](="tacis") to be applied next.

   the last_elem tacis is the first to apply to the calc-state and

   the (only) one shown to the front-end as the 'proposed tac'.

   the calc-state resulting from the application of tacis is not stored,

   because the tacis hold enough information for efficiently rebuilding

   this state just by "fun generate "

*)

type calcstate = 

  Calc.T *      (* the calc-state to which the tacis could be applied *)

  State_Steps.T (* ev. several (hidden) steps; 

                   in REVERSE order: first tac_ to apply is last_elem *)

val e_calcstate = ((EmptyPtree, e_pos'), [State_Steps.single_empty]);

(*the state used during one calculation within the mathengine; it contains

  a list of [tac,istate](="tacis") which generated the the calc-state;

  while this state's tacis are extended by each (internal) step,

  the calc-state is used for creating new nodes in the calc-tree

  (eg. applicable_in requires several particular nodes of the calc-tree)

  and then replaced by the the newly created;

  on leave of the mathengine the resuing calc-state is dropped anyway,

  because the tacis hold enought information for efficiently rebuilding

  this state just by "fun generate ".*)

type calcstate' = 

  State_Steps.T * (* cas. several (hidden) steps;

                       in REVERSE order: first tac_ to apply is last_elem                 *)

  pos' list *     (* a "continuous" sequence of pos', deleted by application of taci list *)     

  Calc.T          (* the calc-state resulting from the application of tacis               *)

val e_calcstate' = ([State_Steps.single_empty], [e_pos'], (EmptyPtree, e_pos')) : calcstate';

(* is the calchead complete ? *)

fun ocalhd_complete its pre (dI, pI, mI) = 

  foldl and_ (true, map #3 (its: I_Model.T)) andalso 

  foldl and_ (true, map #1 (pre: (bool * term) list)) andalso 

  dI <> ThyC.id_empty andalso pI <> Problem.id_empty andalso mI <> Method.id_empty

(* ["BOOL (1+x=2)","REAL x"] --match_ags--> oris 

   --oris2fmz_vals--> ["equality (1+x=2)","boundVariable x","solutions L"] *)

fun oris2fmz_vals oris =

  let fun ori2fmz_vals (_, _, _, dsc, ts) = 

	  ((UnparseC.term o O_Model.comp_dts') (dsc, ts), last_elem ts) 

	  handle _ => error ("ori2fmz_env called with " ^ UnparseC.terms ts)

  in (split_list o (map ori2fmz_vals)) oris end

(* make a term 'typeless' for comparing with another 'typeless' term;

   'type-less' usually is illtyped                                  *)

fun typeless (Const (s, _)) = (Const (s, TermC.typ_empty)) 

  | typeless (Free (s, _)) = (Free (s, TermC.typ_empty))

  | typeless (Var (n, _)) = (Var (n, TermC.typ_empty))

  | typeless (Bound i) = (Bound i)

  | typeless (Abs (s, _,t)) = Abs(s, TermC.typ_empty, typeless t)

  | typeless (t1 $ t2) = (typeless t1) $ (typeless t2)

(* to an input (d,ts) find the according ori and insert the ts)

  WN.11.03: + dont take first inter<>[]                       *)

fun seek_oridts ctxt sel (d, ts) [] =

    ("seek_oridts: input ('" ^

        (UnparseC.term_in_ctxt ctxt (O_Model.comp_dts (d, ts))) ^ "') not found in oris (typed)",

      (0, [], sel, d, ts),

      [])

  | seek_oridts ctxt sel (d, ts) ((id, vat, sel', d', ts') :: oris) =

    if sel = sel' andalso d = d' andalso (inter op = ts ts') <> []

    then ("", (id, vat, sel, d, inter op = ts ts'), ts')

    else seek_oridts ctxt sel (d, ts) oris

(* to an input (_,ts) find the according ori and insert the ts *)

fun seek_orits ctxt _ ts [] = 

    ("seek_orits: input (_, '" ^ strs2str (map (UnparseC.term_in_ctxt ctxt) ts) ^

    "') not found in oris (typed)", O_Model.single_empty, [])

  | seek_orits ctxt sel ts ((id, vat, sel', d, ts') :: oris) =

    if sel = sel' andalso (inter op = ts ts') <> [] 

    then

      if sel = sel' 

      then ("", (id, vat, sel, d, inter op = ts ts'), ts')

      else (((strs2str' o map (UnparseC.term_in_ctxt ctxt)) ts) ^ " not for " ^ sel, O_Model.single_empty, [])

    else seek_orits ctxt sel ts oris

(* find_first item with #1 equal to id *)

fun seek_ppc _ [] = NONE

  | seek_ppc id (p :: ppc) = if id = #1 (p: I_Model.single) then SOME p else seek_ppc id ppc

fun ppc2list {Given = gis, Where = whs, Find = fis, With = wis, Relate = res} =

  gis @ whs @ fis @ wis @ res

(* get the number of variants in a problem in 'original',

   assumes equal descriptions in immediate sequence    *)

fun variants_in ts =

  let

    fun eq (x, y) = head_of x = head_of y

    fun cnt _ [] _ n = ([n], [])

      | cnt eq (x :: xs) y n = if eq (x, y) then cnt eq xs y (n + 1) else ([n], x :: xs)

    fun coll _  xs [] = xs

      | coll eq  xs (y :: ys) = 

        let val (n, ys') = cnt eq (y :: ys) y 0

        in if ys' = [] then xs @ n else coll eq  (xs @ n) ys' end

    val vts = subtract op = [1] (distinct (coll eq [] ts))

  in

    case vts of 

      [] => 1

    | [n] => n

    | _ => error "different variants in formalization"

  end

fun is_list_type (Type ("List.list", _)) = true

  | is_list_type _ = false

fun is_parsed (I_Model.Syn _) = false

  | is_parsed _ = true

fun parse_ok its = foldl and_ (true, map is_parsed its)

fun all_dsc_in itm_s =

  let    

    fun d_in (I_Model.Cor ((d, _), _)) = [d]

      | d_in (I_Model.Syn _) = []

      | d_in (I_Model.Typ _) = []

      | d_in (I_Model.Inc ((d,_),_)) = [d]

      | d_in (I_Model.Sup (d,_)) = [d]

      | d_in (I_Model.Mis (d,_)) = [d]

      | d_in i = raise ERROR ("all_dsc_in: uncovered case with " ^ I_Model.feedback_to_string' i)

  in (flat o (map d_in)) itm_s end; 

fun is_error (I_Model.Cor _) = false

  | is_error (I_Model.Sup _) = false

  | is_error (I_Model.Inc _) = false

  | is_error (I_Model.Mis _) = false

  | is_error _ = true

(* get the first term in ts from ori *)

fun getr_ct thy (_, _, fd, d, ts) =

  (fd, ((UnparseC.term_in_thy thy) o O_Model.comp_dts) (d,[hd ts]))

(* get a term from ori, notyet input in itm.

   the term from ori is thrown back to a string in order to reuse

   machinery for immediate input by the user. *)

fun geti_ct thy (_, _, _, d, ts) (_, _, _, fd, itm_) =

  (fd, ((UnparseC.term_in_thy thy) o O_Model.comp_dts) (d, subtract op = (I_Model.ts_in itm_) ts))

(* in FE dsc, not dat: this is in itms ...*)

fun is_untouched (_, _, false, _, I_Model.Inc ((_, []), _)) = true

  | is_untouched _ = false

(* select an item in oris, notyet input in itms 

   (precondition: in itms are only I_Model.Cor, I_Model.Sup, I_Model.Inc) *)

(*args of nxt_add

  thy : for?

  oris: from formalization 'type fmz', structured for efficient access 

  pbt : the problem-pattern to be matched with oris in order to get itms

  itms: already input items

*)

fun nxt_add thy [] pbt itms = (*root (only) ori...fmz=[]*)

    let

      fun test_d d (i, _, _, _, itm_) = (d = (I_Model.d_in itm_)) andalso i <> 0

      fun is_elem itms (_, (d, _)) = 

        case find_first (test_d d) itms of SOME _ => true | NONE => false

    in

      case filter_out (is_elem itms) pbt of

        (f, (d, _)) :: _ => SOME (f, ((UnparseC.term_in_thy thy) o O_Model.comp_dts) (d, []))

      | _ => NONE

    end

  | nxt_add thy oris _ itms =

    let

      fun testr_vt v ori = member op= (#2 (ori : O_Model.single)) v andalso (#3 ori) <> "#undef"

      fun testi_vt v itm = member op= (#2 (itm : I_Model.single)) v

      fun test_id ids r = member op= ids (#1 (r : O_Model.single))

      fun test_subset itm (_, _, _, d, ts) = 

        (I_Model.d_in (#5 (itm: I_Model.single))) = d andalso subset op = (I_Model.ts_in (#5 itm), ts)

      fun false_and_not_Sup (_, _, false, _, I_Model.Sup _) = false

        | false_and_not_Sup (_, _, false, _, _) = true

        | false_and_not_Sup _ = false

      val v = if itms = [] then 1 else I_Model.max_vt itms

      val vors = if v = 0 then oris else filter (testr_vt v) oris  (* oris..vat *)

      val vits =

        if v = 0

        then itms                                 (* because of dsc without dat *)

  	    else filter (testi_vt v) itms;                             (* itms..vat *)

      val icl = filter false_and_not_Sup vits;                    (* incomplete *)

    in

      if icl = [] 

      then case filter_out (test_id (map #1 vits)) vors of

  	    [] => NONE

  	  | miss => SOME (getr_ct thy (hd miss))

      else

        case find_first (test_subset (hd icl)) vors of

          NONE => error "nxt_add: types or dsc DO NOT MATCH BETWEEN fmz --- pbt"

        | SOME ori => SOME (geti_ct thy ori (hd icl))

    end

fun mk_delete thy "#Given" itm_ = Tactic.Del_Given (Specify.itm_out thy itm_)

  | mk_delete thy "#Find" itm_ = Tactic.Del_Find (Specify.itm_out thy itm_)

  | mk_delete thy "#Relate" itm_ = Tactic.Del_Relation (Specify.itm_out thy itm_)

  | mk_delete _ str _ = error ("mk_delete: called with field \"" ^ str ^ "\"")

fun mk_additem "#Given" ct = Tactic.Add_Given ct

  | mk_additem "#Find" ct = Tactic.Add_Find ct    

  | mk_additem "#Relate"ct = Tactic.Add_Relation ct

  | mk_additem str _ = error ("mk_additem: called with field \"" ^ str ^ "\"")

(* determine the next step of specification;

   not done here: Refine_Tacitly (otherwise *** unknown method: (..., no_met))

   eg. in rootpbl 'no_met': 

args:

  preok          predicates are _all_ ok (and problem matches completely)

  oris           immediately from formalization 

  (dI',pI',mI')  specification coming from author/parent-problem

  (pbl,          item lists specified by user

   met)          -"-, tacitly completed by copy_probl

  (dI,pI,mI)     specification explicitly done by the user

  (pbt, mpc)     problem type, guard of method

*)

fun nxt_spec Pbl preok oris (dI', pI', mI') (pbl, met) (pbt, mpc) (dI, pI, mI) = 

    (if dI' = ThyC.id_empty andalso dI = ThyC.id_empty then (Pbl, Tactic.Specify_Theory dI')

     else if pI' = Problem.id_empty andalso pI = Problem.id_empty then (Pbl, Tactic.Specify_Problem pI')

     else

       case find_first (is_error o #5) pbl of

	       SOME (_, _, _, fd, itm_) =>

	         (Pbl, mk_delete (ThyC.get_theory (if dI = ThyC.id_empty then dI' else dI)) fd itm_)

	     | NONE => 

	       (case nxt_add (ThyC.get_theory (if dI = ThyC.id_empty then dI' else dI)) oris pbt pbl of

	          SOME (fd, ct') => (Pbl, mk_additem fd ct')

	        | NONE => (*pbl-items complete*)

	          if not preok then (Pbl, Tactic.Refine_Problem pI')

	          else if dI = ThyC.id_empty then (Pbl, Tactic.Specify_Theory dI')

		        else if pI = Problem.id_empty then (Pbl, Tactic.Specify_Problem pI')

		        else if mI = Method.id_empty then (Pbl, Tactic.Specify_Method mI')

		        else

			        case find_first (is_error o #5) met of

			          SOME (_, _, _, fd, itm_) => (Met, mk_delete (ThyC.get_theory dI) fd itm_)

			        | NONE => 

			          (case nxt_add (ThyC.get_theory dI) oris mpc met of

				          SOME (fd, ct') => (Met, mk_additem fd ct') (*30.8.01: pre?!?*)

				        | NONE => (Met, Tactic.Apply_Method mI))))

  | nxt_spec Met preok oris (dI', pI', _) (_, met) (_ ,mpc) (dI, pI, mI) = 

    (case find_first (is_error o #5) met of

      SOME (_,_,_,fd,itm_) => (Met, mk_delete (ThyC.get_theory (if dI = ThyC.id_empty then dI' else dI)) fd itm_)

    | NONE => 

      case nxt_add (ThyC.get_theory (if dI = ThyC.id_empty then dI' else dI)) oris mpc met of

	      SOME (fd,ct') => (Met, mk_additem fd ct')

      | NONE => 

	      (if dI = ThyC.id_empty then (Met, Tactic.Specify_Theory dI')

	       else if pI = Problem.id_empty then (Met, Tactic.Specify_Problem pI')

		     else if not preok then (Met, Tactic.Specify_Method mI)

		     else (Met, Tactic.Apply_Method mI)))

  | nxt_spec p _ _ _ _ _ _ = error ("nxt_spec: uncovered case with " ^ pos_2str p)

(* update the itm_ already input, all..from ori *)

fun ori_2itm itm_ pid all (id, vt, fd, d, ts) = 

  let 

    val ts' = union op = (I_Model.ts_in itm_) ts;

    val pval = Model.pbl_ids' d ts'

	  (* WN.9.5.03: FIXXXME [#0, epsilon] here would upd_penv be called for [#0, epsilon] etc *)

    val complete = if eq_set op = (ts', all) then true else false

  in

    case itm_ of

      (I_Model.Cor _) => 

        (if fd = "#undef" then (id, vt, complete, fd, I_Model.Sup (d, ts')) 

	       else (id, vt, complete, fd, I_Model.Cor ((d, ts'), (pid, pval))))

    | (I_Model.Syn c) => error ("ori_2itm wants to overwrite " ^ c)

    | (I_Model.Typ c) => error ("ori_2itm wants to overwrite " ^ c)

    | (I_Model.Inc _) =>

      if complete

  	  then (id, vt, true, fd, I_Model.Cor ((d, ts'), (pid, pval)))

  	  else (id, vt, false, fd, I_Model.Inc ((d, ts'), (pid, pval)))

    | (I_Model.Sup (d,ts')) => (*4.9.01 lost env*)

  	  (*if fd = "#undef" then*) (id,vt,complete,fd,I_Model.Sup(d,ts'))

  	  (*else (id,vt,complete,fd,I_Model.Cor((d,ts'),e))*)

      (* 28.1.00: not completely clear ---^^^ etc.*)

    | (I_Model.Mis _) => (* 4.9.01: I_Model.Mis just copied *)

       if complete

  		 then (id, vt, true, fd, I_Model.Cor ((d,ts'), (pid, pval)))

  		 else (id, vt, false, fd, I_Model.Inc ((d,ts'), (pid, pval)))

    | i => error ("ori_2itm: uncovered case of "^ I_Model.feedback_to_string' i)

  end

fun eq1 d (_, (d', _)) = (d = d')

fun eq3 f d (_, _, _, f', itm_) = f = f' andalso d = (I_Model.d_in itm_) 

(* 'all' ts from ori; ts is the input; (ori carries rest of info)

   9.01: this + ori_2itm is _VERY UNCLEAR_ ? overhead ?

   pval: value for problem-environment _NOT_ checked for 'inter' --

   -- FIXXME.WN.11.03 the generation of penv has to go to insert_ppc

  (as it has been done for input_icalhd+insert_ppc' in 11.03)*)

(*. is_input ori itms <=> 

    EX itm. (1) ori(field,dsc) = itm(field,dsc) & (2..4)

            (2) ori(ts) subset itm(ts)        --- Err "already input"       

	    (3) ori(ts) inter itm(ts) = empty --- new: ori(ts)

	    (4) -"- <> empty                  --- new: ori(ts) \\ inter .*)

fun is_notyet_input ctxt itms all (i, v, f, d, ts) pbt =

  case find_first (eq1 d) pbt of

    SOME (_, (_, pid)) =>

      (case find_first (eq3 f d) itms of

        SOME (_,_,_,_,itm_) =>

          let val ts' = inter op = (I_Model.ts_in itm_) ts

          in 

            if subset op = (ts, ts') 

            then (((strs2str' o map (UnparseC.term_in_ctxt ctxt)) ts') ^ " already input", I_Model.empty) (*2*)

	          else ("", ori_2itm itm_ pid all (i,v,f,d, subtract op = ts' ts))              (*3,4*)

	          end

	    | NONE => ("", ori_2itm (I_Model.Inc ((TermC.empty, []), (pid, []))) pid all (i, v, f, d, ts)))    (*1*)

  | NONE => ("", ori_2itm (I_Model.Sup (d, ts)) TermC.empty all (i, v, f, d, ts))

fun test_types ctxt (d,ts) =

  let 

    val opt = (try O_Model.comp_dts) (d, ts)

    val msg = case opt of 

      SOME _ => "" 

    | NONE => (UnparseC.term_in_ctxt ctxt d ^ " " ^

	    (strs2str' o map (UnparseC.term_in_ctxt ctxt)) ts ^ " is illtyped")

  in msg end

(* is the term t input (or taken from fmz) known in oris ?

   give feedback on all(?) strange input;

   return _all_ terms already input to this item (e.g. valuesFor a,b) *)

fun is_known ctxt sel ori t =

  let

    val ots = (distinct o flat o (map #5)) ori

    val oids = ((map (fst o dest_Free)) o distinct o flat o (map TermC.vars)) ots

    val (d, ts) = O_Model.split_dts t

    val ids = map (fst o dest_Free) ((distinct o (flat o (map TermC.vars))) ts)

  in

    if (subtract op = oids ids) <> []

    then ("identifiers " ^ strs2str' (subtract op = oids ids) ^ " not in example", O_Model.single_empty, [])

    else 

	    if d = TermC.empty 

	    then 

	      if not (subset op = (map typeless ts, map typeless ots))

	      then ("terms '" ^ (strs2str' o (map (UnparseC.term_in_ctxt ctxt))) ts ^

		      "' not in example (typeless)", O_Model.single_empty, [])

	      else 

          (case seek_orits ctxt sel ts ori of

		         ("", ori_ as (_,_,_,d,ts), all) =>

		            (case test_types ctxt (d,ts) of

		              "" => ("", ori_, all)

		            | msg => (msg, O_Model.single_empty, []))

		       | (msg, _, _) => (msg, O_Model.single_empty, []))

	    else 

	      if member op = (map #4 ori) d

	      then seek_oridts ctxt sel (d, ts) ori

	      else (UnparseC.term_in_ctxt ctxt d ^ " not in example", (0, [], sel, d, ts), [])

  end

datatype additm =

	Add of I_Model.single   (* return-value of appl_add *)

| Err of string       (* error-message            *)

(* add an item to the model; check wrt. oris and pbt.

   in contrary to oris<>[] below, this part handles user-input

   extremely acceptive, i.e. accept input instead error-msg  *)

fun appl_add ctxt sel [] ppc pbt ct =

    let

      val i = 1 + (if ppc = [] then 0 else map #1 ppc |> maxl)

      in 

        case TermC.parseNEW ctxt ct of

          NONE => Add (i, [], false, sel, I_Model.Syn ct)

        | SOME t =>

            let val (d, ts) = O_Model.split_dts t

            in 

              if d = TermC.empty 

              then Add (i, [], false, sel, I_Model.Mis (Specify.dsc_unknown, hd ts)) 

              else

                (case find_first (eq1 d) pbt of

                   NONE => Add (i, [], true, sel, I_Model.Sup (d,ts))

                 | SOME (f, (_, id)) =>

                     let fun eq2 d (i, _, _, _, itm_) = d = (I_Model.d_in itm_) andalso i <> 0

                     in case find_first (eq2 d) ppc of

                       NONE => Add (i, [], true, f,I_Model.Cor ((d, ts), (id, Model.pbl_ids' d ts)))

                     | SOME (i', _, _, _, itm_) => 

                         if Input_Descript.is_list_dsc d 

                         then 

                           let

                             val in_itm = I_Model.ts_in itm_

                             val ts' = union op = ts in_itm

                             val i'' = if in_itm = [] then i else i'

                           in Add (i'', [], true, f, I_Model.Cor ((d, ts'), (id, Model.pbl_ids' d ts')))end

                         else Add (i', [], true, f, I_Model.Cor ((d, ts), (id, Model.pbl_ids' d ts)))

                     end)

            end

    end

  | appl_add ctxt sel oris ppc pbt str =

    case TermC.parseNEW ctxt str of

      NONE => Err ("appl_add: syntax error in '" ^ str ^ "'")

    | SOME t => 

        case is_known ctxt sel oris t of

          ("", ori', all) => 

            (case is_notyet_input ctxt ppc all ori' pbt of

               ("", itm) => Add itm

             | (msg, _) => Err ("[error] appl_add: is_notyet_input: " ^ msg))

        | (msg, _, _) => Err ("[error] appl_add: is_known: " ^ msg);

(* make oris from args of the stac SubProblem and from pbt.

   can this formal argument (of a model-pattern) be omitted in the arg-list

   of a SubProblem ? see calcelems.sml 'type met '                        *)

fun is_copy_named_idstr str =

  case (rev o Symbol.explode) str of

	  "'" :: _ :: "'" :: _ => true

  | _ => false

fun is_copy_named (_, (_, t)) = (is_copy_named_idstr o TermC.free2str) t

(* should this formal argument (of a model-pattern) create a new identifier? *)

fun is_copy_named_generating_idstr str =

  if is_copy_named_idstr str

  then

    case (rev o Symbol.explode) str of

	    "'" :: "'" :: "'" :: _ => false

    | _ => true

  else false

fun is_copy_named_generating (_, (_, t)) = (is_copy_named_generating_idstr o TermC.free2str) t

(* split type-wrapper from scr-arg and build part of an ori;

   an type-error is reported immediately, raises an exn, 

   subsequent handling of exn provides 2nd part of error message *)

fun mtc thy (str, (dsc, _)) (ty $ var) =

    ((Thm.global_cterm_of thy (dsc $ var);(*type check*)

      SOME (([1], str, dsc, (*[var]*)

	    O_Model.split_dts' (dsc, var))) (*:ori without leading #*))

      handle e as TYPE _ => 

	      (tracing (dashs 70 ^ "\n"

	        ^ "*** ERROR while creating the items for the model of the ->problem\n"

	        ^ "*** from the ->stac with ->typeconstructor in arglist:\n"

	        ^ "*** item (->description ->value): " ^ UnparseC.term dsc ^ " " ^ UnparseC.term var ^ "\n"

	        ^ "*** description: " ^ TermC.term_detail2str dsc

	        ^ "*** value: " ^ TermC.term_detail2str var

	        ^ "*** typeconstructor in script: " ^ TermC.term_detail2str ty

	        ^ "*** checked by theory: " ^ Context.theory_name thy ^ "\n"

	        ^ "*** " ^ dots 66);

          writeln (@{make_string} e);

          Exn.reraise e; (*raise ERROR "actual args do not match formal args";FIXXXME.WN100916*)

      NONE))

  | mtc _ _ t = error ("mtc: uncovered case with" ^ UnparseC.term t)

(* match each pat of the model-pattern with an actual argument;

   precondition: copy-named vars are filtered out            *)

fun matc _ [] _ oris = oris

  | matc _ pbt [] _ =

    (tracing (dashs 70);

     error ("actual arg(s) missing for '" ^ Model_Pattern.to_string pbt ^ "' i.e. should be 'copy-named' by '*_._'"))

  | matc thy ((p as (_, (_, t))) :: pbt) (a :: ags) oris =

    (*del?..*)if (is_copy_named_idstr o TermC.free2str) t then oris

    else(*..del?*)

      let val opt = mtc thy p a

      in

        case opt of

          SOME ori => matc thy pbt ags (oris @ [ori])

	      | NONE => [](*WN050903 skipped by exn handled in match_ags*)

	 end

(* generate a new variable "x_i" name from a related given one "x"

   by use of oris relating "v_v'i'" (is_copy_named!) to "v_v"

   e.g. (v_v, x) & (v_v'i', ?) --> (v_v'i', x_i),

   but leave is_copy_named_generating as is, e.t. ss''' *)

fun cpy_nam pbt oris (p as (field, (dsc, t))) =

  (if is_copy_named_generating p

   then (*WN051014 kept strange old code ...*)

     let fun sel (_,_,d,ts) = O_Model.comp_ts (d, ts) 

       val cy' = (implode o (drop_last_n 3) o Symbol.explode o TermC.free2str) t

       val ext = (last_elem o drop_last o Symbol.explode o TermC.free2str) t

       val vars' = map (Term.term_name o snd o snd) pbt (*cpy-nam filtered_out*)

       val vals = map sel oris

       val cy_ext = (Term.term_name o the) (assoc (vars' ~~ vals, cy')) ^ "_" ^ ext

     in ([1], field, dsc, [TermC.mk_free (type_of t) cy_ext]) end

   else ([1], field, dsc, [t])

	) handle _ => error ("cpy_nam: for "^ UnparseC.term t)

(* match the actual arguments of a SubProblem with a model-pattern

   and create an ori list (in root-pbl created from formalization).

   expects ags:pats = 1:1, while copy-named are filtered out of pats;

   if no 1:1 then exn raised by matc/mtc and handled at call.

   copy-named pats are appended in order to get them into the model-items *)

fun match_ags thy pbt ags =

  let

    fun flattup (i, (var, bool, str, itm_)) = (i, var, bool, str, itm_)

    val pbt' = filter_out is_copy_named pbt

    val cy = filter is_copy_named pbt  (* cy is NOT a (formal) argument, but the fun's result *)

    val oris' = matc thy pbt' ags []

    val cy' = map (cpy_nam pbt' oris') cy

    val ors = O_Model.add_id (oris' @ cy') (*...appended in order to get into the model-items *)

  in (map flattup ors) end

(* report part of the error-msg which is not available in match_args *)

fun match_ags_msg pI stac ags =

  let

    val pats = (#ppc o Specify.get_pbt) pI

    val msg = (dots 70 ^ "\n"

       ^ "*** problem " ^ strs2str pI ^ " has the ...\n"

       ^ "*** model-pattern " ^ Model_Pattern.to_string pats ^ "\n"

       ^ "*** stac   '" ^ UnparseC.term stac ^ "' has the ...\n"

       ^ "*** arg-list " ^ UnparseC.terms ags ^ "\n"

       ^ dashs 70)

	  (*WN100921 ^^^^ expect TYPE errormsg below; lost with Isa09*)

  in tracing msg end

(* get the variables out of a pbl_; FIXME.WN.0311: is_copy_named ...obscure!!! *)

fun vars_of_pbl_' pbl_ = 

  let

    fun var_of_pbl_ (_, (_, t)) = t: term

  in ((map var_of_pbl_)(* o (filter_out is_copy_named)*)) pbl_ end

fun overwrite_ppc thy itm ppc =

  let 

    fun repl _ (_, _, _, _, itm_) [] =

        error ("overwrite_ppc: " ^ (I_Model.feedback_to_string (ThyC.to_ctxt thy) itm_) ^ " not found")

      | repl ppc' itm (p :: ppc) =

	      if (#1 itm) = (#1 p)

	      then ppc' @ [itm] @ ppc

	      else repl (ppc' @ [p]) itm ppc

  in repl [] itm ppc end

(* 10.3.00: insert the already compiled itm into model;

   ev. filter_out  untouched (in FE: (0,...)) item related to insert-item *)

fun insert_ppc thy itm ppc =

  let 

    fun eq_untouched d (0, _, _, _, itm_) = (d = I_Model.d_in itm_)

      | eq_untouched _ _ = false

    val ppc' = case seek_ppc (#1 itm) ppc of

      SOME _ => overwrite_ppc thy itm ppc (*itm updated in is_notyet_input WN.11.03*)

    | NONE => (ppc @ [itm])

  in filter_out (eq_untouched ((I_Model.d_in o #5) itm)) ppc' end

fun eq_dsc ((_, _, _, _, itm_), (_, _, _, _, iitm_)) = (I_Model.d_in itm_ = I_Model.d_in iitm_)

(* insert_ppc = insert_ppc' for appl_add', input_icalhd 11.03,

   handles superfluous items carelessly                       *)

fun insert_ppc' itm itms = if member eq_dsc itms itm then itms else itms @ [itm] (* @ new itm *)

(* output the headline to a ppc *)

fun header p_ pI mI =

  case p_ of Pbl => Generate.Problem (if pI = Problem.id_empty then [] else pI) 

	   | Met => Generate.Method mI

	   | pos => error ("header called with "^ pos_2str pos)

fun specify_additem sel ct (pt, (p, Met)) = 

    let

      val (met, oris, dI', pI', mI', pbl, dI ,pI, mI, ctxt) = case get_obj I pt p of

        (PblObj {meth = met, origin = (oris, (dI', pI', mI'),_), probl = pbl, spec = (dI, pI, mI), ctxt, ...})

          => (met, oris, dI', pI', mI', pbl, dI ,pI, mI, ctxt)

  	  | _ => error "specify_additem: uncovered case of get_obj I pt p"

      val thy = if dI = ThyC.id_empty then ThyC.get_theory dI' else ThyC.get_theory dI

      val cpI = if pI = Problem.id_empty then pI' else pI

      val cmI = if mI = Method.id_empty then mI' else mI

      val {ppc, pre, prls, ...} = Specify.get_met cmI

    in 

      case appl_add ctxt sel oris met ppc ct of

        Add itm =>  (*..union old input *)

  	      let

            val met' = insert_ppc thy itm met

            val arg = case sel of

  			      "#Given" => Tactic.Add_Given'   (ct, met')

  		      | "#Find"  => Tactic.Add_Find'    (ct, met')

  		      | "#Relate"=> Tactic.Add_Relation'(ct, met')

  		      | str => error ("specify_additem: uncovered case with " ^ str)

  	        val (p, pt') = case Specify_Step.add arg (Istate_Def.Uistate, ctxt) (pt, (p, Met)) of

  	          ((p, Met), _, _, pt') => (p, pt')

  	        | _ => error "specify_additem: uncovered case of generate1"

  	        val pre' = Stool.check_preconds thy prls pre met'

  	        val pb = foldl and_ (true, map fst pre')

  	        val (p_, nxt) =

  	          nxt_spec Met pb oris (dI',pI',mI') (pbl,met') 

  	            ((#ppc o Specify.get_pbt) cpI,ppc) (dI,pI,mI);

  	      in 

            ("ok", ([], [], (pt', (p, p_))))

          end

      | Err msg =>

  	      let

            val pre' = Stool.check_preconds thy prls pre met

  	        val pb = foldl and_ (true, map fst pre')

  	        val (p_, nxt) =

  	          nxt_spec Met pb oris (dI',pI',mI') (pbl,met) 

  	            ((#ppc o Specify.get_pbt) cpI,(#ppc o Specify.get_met) cmI) (dI,pI,mI);

  	      in

            (msg, ([], [], (pt, (p, p_))))

  	      end

    end

  | specify_additem sel ct (pt, (p,_(*Frm, Pbl*))) =

      let

        val (met, oris, dI', pI', mI', pbl, dI ,pI, mI, ctxt) = case get_obj I pt p of

          (PblObj {meth = met, origin = (oris, (dI', pI', mI'),_), probl = pbl, spec = (dI, pI, mI), ctxt, ...})

            => (met, oris, dI', pI', mI', pbl, dI ,pI, mI, ctxt)

  	    | _ => error "specify_additem Frm, Pbl: uncovered case of get_obj I pt p"

        val thy = if dI = ThyC.id_empty then ThyC.get_theory dI' else ThyC.get_theory dI

        val cpI = if pI = Problem.id_empty then pI' else pI

        val cmI = if mI = Method.id_empty then mI' else mI

        val {ppc, where_, prls, ...} = Specify.get_pbt cpI

      in

        case appl_add ctxt sel oris pbl ppc ct of

          Add itm => (*..union old input *)

	          let

	            val pbl' = insert_ppc thy itm pbl

              val arg = case sel of

  			        "#Given" => Tactic.Add_Given'   (ct, pbl')

  		        | "#Find"  => Tactic.Add_Find'    (ct, pbl')

  		        | "#Relate"=> Tactic.Add_Relation'(ct, pbl')

  		        | str => error ("specify_additem Frm, Pbl: uncovered case with " ^ str)

	            val (p, pt') =

	              case Specify_Step.add arg (Istate_Def.Uistate, ctxt) (pt, (p, Pbl)) of

  	              ((p, Pbl), _, _, pt') => (p, pt')

  	            | _ => error "specify_additem: uncovered case of Specify_Step.add"

	            val pre = Stool.check_preconds thy prls where_ pbl'

	            val pb = foldl and_ (true, map fst pre)

	            val (p_, nxt) =

	              nxt_spec Pbl pb oris (dI',pI',mI') (pbl',met) (ppc, (#ppc o Specify.get_met) cmI) (dI, pI, mI)

	            val ppc = if p_= Pbl then pbl' else met

	          in

              ("ok", ([], [], (pt', (p, p_))))

            end

        | Err msg =>

	          let

              val pre = Stool.check_preconds thy prls where_ pbl

	            val pb = foldl and_ (true, map fst pre)

	            val (p_, nxt) =

	              nxt_spec Pbl pb oris (dI', pI', mI') (pbl, met) 

	                (ppc, (#ppc o Specify.get_met) cmI) (dI, pI, mI)

	          in

            (msg, ([], [], (pt, (p, p_))))

	          end

      end

(*FIXME.WN110515 declare_constraints for ct (without dsc) into PblObj{ctxt, ...}

  -- for input from scratch*)

fun nxt_specif_additem sel ct (ptp as (pt, (p, Pbl))) = 

    let

      val (oris, dI', pI', dI, pI, pbl, ctxt) = case get_obj I pt p of

        PblObj {origin = (oris, (dI', pI', _), _), spec = (dI, pI, _), probl = pbl, ctxt, ...} =>

           (oris, dI', pI', dI, pI, pbl, ctxt)

      | _ => error "specify (Specify_Theory': uncovered case get_obj"

      val thy = if dI = ThyC.id_empty then ThyC.get_theory dI' else ThyC.get_theory dI;

      val cpI = if pI = Problem.id_empty then pI' else pI;

    in

      case appl_add ctxt sel oris pbl ((#ppc o Specify.get_pbt) cpI) ct of

	      Add itm (*..union old input *) =>

	        let

	          val pbl' = insert_ppc thy itm pbl

	          val (tac, tac_) = case sel of

		          "#Given" => (Tactic.Add_Given    ct, Tactic.Add_Given'   (ct, pbl'))

		        | "#Find"  => (Tactic.Add_Find     ct, Tactic.Add_Find'    (ct, pbl'))

		        | "#Relate"=> (Tactic.Add_Relation ct, Tactic.Add_Relation'(ct, pbl'))

		        | sel => error ("nxt_specif_additem: uncovered case of" ^ sel)

		        val (p, c, pt') =

		          case Specify_Step.add tac_ (Istate_Def.Uistate, ctxt) (pt, (p, Pbl)) of

  		          ((p, Pbl), c, _, pt') =>  (p, c, pt')

  		        | _ => error "nxt_specif_additem: uncovered case generate1"

	        in

	          ([(tac, tac_, ((p, Pbl), (Istate_Def.Uistate, ctxt)))], c, (pt', (p, Pbl)))

          end	       

	    | Err msg => (*TODO.WN03 pass error-msgs to the frontend..

                     FIXME ..and dont abuse a tactic for that purpose*)

	        ([(Tactic.Tac msg, Tactic.Tac_ (ThyC.get_theory "Isac_Knowledge", msg,msg,msg),

	          (e_pos', (Istate_Def.empty, ContextC.empty)))], [], ptp) 

    end

  | nxt_specif_additem sel ct (ptp as (pt, (p, Met))) = 

    let

      val (oris, dI', mI', dI, mI, met, ctxt) = case get_obj I pt p of

        PblObj {origin = (oris, (dI', _, mI'), _), spec = (dI, _, mI), meth = met,ctxt, ...} =>

           (oris, dI', mI', dI, mI, met, ctxt)

      | _ => error "nxt_specif_additem Met: uncovered case get_obj"

      val thy = if dI = ThyC.id_empty then ThyC.get_theory dI' else ThyC.get_theory dI;

      val cmI = if mI = Method.id_empty then mI' else mI;

    in 

      case appl_add ctxt sel oris met ((#ppc o Specify.get_met) cmI) ct of

        Add itm (*..union old input *) =>

	        let

	          val met' = insert_ppc thy itm met;

	          val (tac,tac_) = case sel of

		          "#Given" => (Tactic.Add_Given    ct, Tactic.Add_Given'   (ct, met'))

		        | "#Find"  => (Tactic.Add_Find     ct, Tactic.Add_Find'    (ct, met'))

		        | "#Relate"=> (Tactic.Add_Relation ct, Tactic.Add_Relation'(ct, met'))

		        | sel => error ("nxt_specif_additem Met: uncovered case of" ^ sel)

	          val (p, c, pt') =

	            case Specify_Step.add tac_ (Istate_Def.Uistate, ctxt) (pt, (p, Met)) of

  	            ((p, Met), c, _, pt') => (p, c, pt')

  		        | _ => error "nxt_specif_additem: uncovered case generate1 (WARNING WHY ?)"

	        in

	          ([(tac, tac_, ((p, Met), (Istate_Def.Uistate, ctxt)))], c, (pt', (p, Met)))

	        end

      | Err _ => ([(*tacis*)], [], ptp) (*nxt_me collects tacis until not hide; here just no progress*)

    end

  | nxt_specif_additem _ _ (_, p) = error ("nxt_specif_additem not impl. for" ^ pos'2str p)

fun ori2Coritm pbt (i, v, f, d, ts) =

  (i, v, true, f, I_Model.Cor ((d,ts),((snd o snd o the o (find_first (eq1 d))) pbt,ts)))

    handle _ => (i, v, true, f, I_Model.Cor ((d, ts), (d, ts)))

      (*dsc in oris, but not in pbl pat list: keep this dsc*)

(* filter out oris which have same description in itms *)

fun filter_outs oris [] = oris

  | filter_outs oris (i::itms) = 

    let

      val ors = filter_out ((curry op = ((I_Model.d_in o #5) i)) o (#4)) oris

    in

      filter_outs ors itms

    end

(* filter oris which are in pbt, too *)

fun filter_pbt oris pbt =

  let

    val dscs = map (fst o snd) pbt

  in

    filter ((member op= dscs) o (#4)) oris

  end

(* combine itms from pbl + met and complete them wrt. pbt *)

(* FIXXXME.WN031205 complete_metitms doesnt handle incorrect itms !*)

fun complete_metitms oris pits mits met = 

  let

    val vat = I_Model.max_vt pits;

    val itms = pits @ (filter ((member_swap op = vat) o (#2 )) mits)

    val ors = filter ((member_swap op= vat) o (#2)) oris

    val os = filter_outs ors itms (*WN.12.03?: does _NOT_ add itms from met ?!*)

  in

    itms @ (map (ori2Coritm met) os)

  end

(* complete model and guard of a calc-head *)

fun complete_mod_ (oris, mpc, ppc, probl) =

  let

    val pits = filter_out ((curry op= false) o (#3)) probl

    val vat = if probl = [] then 1 else I_Model.max_vt probl

    val pors = filter ((member_swap op = vat) o (#2)) oris

    val pors = filter_outs pors pits (*which are in pbl already*)

    val pors = (filter_pbt pors ppc) (*which are in pbt, too*)

    val pits = pits @ (map (ori2Coritm ppc) pors)

    val mits = complete_metitms oris pits [] mpc

  in (pits, mits) end

fun some_spec (odI, opI, omI) (dI, pI, mI) =

  (if dI = ThyC.id_empty then odI else dI,

   if pI = Problem.id_empty then opI else pI,

   if mI = Method.id_empty then omI else mI)

(* get the values from oris; handle the term list w.r.t. penv *)

fun vals_of_oris (oris: O_Model.T) =

  ((map (Model.mkval' o (#5))) o 

    (filter ((member_swap op= 1) o (#2)))) oris

(* fun tag_form thy (formal, given) = Thm.global_cterm_of thy

	 (((head_of o Thm.term_of) given) $ (Thm.term_of formal)); WN100819 *)

fun tag_form thy (formal, given) =

 (let

    val gf = (head_of given) $ formal;

    val _ = Thm.global_cterm_of thy gf

  in gf end)

  handle _ => error ("calchead.tag_form: " ^ UnparseC.term_in_thy thy given ^

    " .. " ^ UnparseC.term_in_thy thy formal ^ " ..types do not match")

fun chktyps thy (fs, gs) = map (tag_form thy) (fs ~~ gs)

(* check pbltypes, announces one failure a time *)

fun chk_vars ctppc = 

  let

    val {Given = gi, Where = wh, Find = fi, Relate = re, ...} = Specify.appc flat (Specify.mappc TermC.vars ctppc)

    val chked = subtract op = gi wh

  in

    if chked <> [] then ("wh\\gi", chked)

    else

      let val chked = subtract op = (union op = gi fi) re

      in

        if chked  <> []

	      then ("re\\(gi union fi)", chked)

	      else ("ok", []) 

      end

  end

(* check a new pbltype: variables (Free) unbound by given, find*) 

fun unbound_ppc ctppc =

  let

    val {Given = gi, Find = fi, Relate = re, ...} = Specify.appc flat (Specify.mappc TermC.vars ctppc)

  in

    distinct (subtract op = (union op = gi fi) re)

  end

(* complete _NON_empty calc-head for autocalc (sub-)pbl from oris

  + met from fmz; assumes pos on PblObj, meth = []                    *)

fun complete_mod (pt, pos as (p, p_) : pos') =

  let

    val _ = if p_ <> Pbl 

	    then error ("###complete_mod: only impl.for Pbl, called with " ^ pos'2str pos)

	    else ()

	  val (oris, ospec, probl, spec) = case get_obj I pt p of

	    PblObj {origin = (oris, ospec, _), probl, spec, ...} => (oris, ospec, probl, spec)

	  | _ => error "complete_mod: unvered case get_obj"

  	val (_, pI, mI) = some_spec ospec spec

  	val mpc = (#ppc o Specify.get_met) mI

  	val ppc = (#ppc o Specify.get_pbt) pI

  	val (pits, mits) = complete_mod_ (oris, mpc, ppc, probl)

    val pt = update_pblppc pt p pits

	  val pt = update_metppc pt p mits

  in (pt, (p, Met) : pos') end

(* do all specification in one single step:

   complete calc-head for autocalc (sub-)pbl from oris (+ met from fmz);

   oris and spec (incl. pbl-refinement) given from init_calc or SubProblem

*)

fun all_modspec (pt, (p, _)) =

  let

    val (pors, dI, pI, mI) = case get_obj I pt p of

      PblObj {origin = (pors, (dI, pI, mI), _), ...}

        => (pors, dI, pI, mI)

    | _ => raise ERROR "all_modspec: uncovered case get_obj"

	  val {ppc, ...} = Specify.get_met mI

    val (_, vals) = oris2fmz_vals pors

	  val ctxt = ContextC.initialise dI vals

    val (pt, _) = cupdate_problem pt p ((dI, pI, mI),

      map (ori2Coritm ppc) pors, map (ori2Coritm ppc) pors, ctxt)

  in

    (pt, (p, Met))

  end

(* WN0312: use in nxt_spec, too ? what about variants ??? *)

fun is_complete_mod_ [] = false

  | is_complete_mod_ itms = foldl and_ (true, (map #3 itms))

fun is_complete_mod (pt, pos as (p, Pbl) : pos') =

    if (is_pblobj o (get_obj I pt)) p 

    then (is_complete_mod_ o (get_obj g_pbl pt)) p

    else error ("is_complete_mod: called by PrfObj at "^pos'2str pos)

  | is_complete_mod (pt, pos as (p, Met)) = 

    if (is_pblobj o (get_obj I pt)) p 

    then (is_complete_mod_ o (get_obj g_met pt)) p

    else error ("is_complete_mod: called by PrfObj at "^pos'2str pos)

  | is_complete_mod (_, pos) =

    error ("is_complete_mod called by " ^ pos'2str pos ^ " (should be Pbl or Met)")

(* have (thy, pbl, met) _all_ been specified explicitly ? *)

fun is_complete_spec (pt, pos as (p, _) : pos') = 

  if (not o is_pblobj o (get_obj I pt)) p 

  then error ("is_complete_spec: called by PrfObj at "^pos'2str pos)

  else

    let val (dI,pI,mI) = get_obj g_spec pt p

    in dI <> ThyC.id_empty andalso pI <> Problem.id_empty andalso mI <> Method.id_empty end

(* complete empty items in specification from origin (pbl, met ev.refined);

   assumes 'is_complete_mod' *)

fun complete_spec (pt, pos as (p, _) : pos') = 

  let

    val (ospec, spec) = case get_obj I pt p of

      PblObj {origin = (_,ospec,_), spec,...} => (ospec, spec)

    | _ => error "complete_spec: uncovered case get_obj"

    val pt = update_spec pt p (some_spec ospec spec)

  in

    (pt, pos)

  end

fun is_complete_modspec ptp = is_complete_mod ptp andalso is_complete_spec ptp