(* Title:  Specify/i-model.sml

    Author: Walther Neuper 110226

    (c) due to copyright terms

 \<open>I_Model\<close> serves students' interactive modelling and gives feedback in the specify-phase.

 *)

 signature MODEL_FOR_INTERACTION =

 sig

   type T

   type single

   val empty: single 

   type variant

   type variants

   type m_field

   type descriptor

   datatype feedback = datatype Model_Def.i_model_feedback

   type message

   val feedback_to_string': feedback -> string

   val feedback_to_string: Proof.context -> feedback -> string

   val single_to_string: Proof.context -> single -> string

   val to_string: Proof.context -> T -> string

 (*/------- rename -------\*)

   datatype additm = Add of single | Err of string

 (*\------- rename -------/*)

   val initPIDE: Problem.id -> T

   val init: Model_Pattern.T -> T

 (*val check_single: Proof.context -> *)

   val check_single: Proof.context -> m_field -> O_Model.T -> T -> Model_Pattern.T ->

     TermC.as_string -> additm

   val add_single: theory -> single -> T -> T

 (*/------- rename -------\*)

 (*val make_tactic: m_field -> TermC.as_string * T -> Tactic.T*)

   val get_tac: m_field -> TermC.as_string * T -> Tactic.T

 (*val d_in: feedback -> descriptor*)

   val d_in: feedback -> descriptor

 (*val ts_in: feedback -> O_Model.values*)

   val ts_in: feedback -> O_Model.values

 (*val vars_of: T -> term list*)

   val vars_of: T -> term list

 (*val max_vt: T -> int*)

   val max_vt: T -> int

 (*val is_notyet_input : Proof.context -> T -> O_Model.values -> O_Model.single -> Model_Pattern.T

     -> message * single*)

   val is_notyet_input : Proof.context -> T -> O_Model.values -> O_Model.single -> Model_Pattern.T

     -> message * single

 (*val dsc_unknown: term*)

   val dsc_unknown: term

 (*val geti_ct: theory -> O_Model.single -> single -> m_field * UnparseC.term_as_string*)

   val geti_ct: theory -> O_Model.single -> single -> m_field * UnparseC.term_as_string

 (*val pbl_ids': term -> term list -> term list*)

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

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

   val penvval_in: feedback -> term list

 (*\------- rename -------/*)

   val complete: O_Model.T -> T -> T -> Model_Pattern.T -> T

   val add: single -> T -> T

 (*val complete_method: O_Model.T -> Model_Pattern.T * Model_Pattern.T * T -> T * T*)

   val complete_method: O_Model.T * Model_Pattern.T * Model_Pattern.T * T -> T * T

   val is_error: feedback -> bool

   val complete': Model_Pattern.T -> O_Model.single -> single

   val is_complete: T -> bool

   val to_p_model: theory -> feedback -> string

 (*/------- rename -------\*)

 (*val dts2str: term * (term list) -> string*)

   val dts2str: term * (term list) -> string

   val eq1: ''a -> 'b * (''a * 'c) -> bool

 (*\------- rename -------/*)

 (*/------- rename -------\*)

 \<^isac_test>\<open>

   val vts_in: T -> int list

 \<close>

 end

 (**)

 structure I_Model(**) : MODEL_FOR_INTERACTION(**) =

 struct

 (**)

 (** data types **)

 type variant =  Model_Def.variant;

 type variants =  Model_Def.variants;

 type m_field = Model_Def.m_field;

 type descriptor = Model_Def.descriptor;

 type T = Model_Def.i_model_single list;

 datatype feedback = datatype Model_Def.i_model_feedback;

 type single = Model_Def.i_model_single;

 val empty = Model_Def.i_model_empty;

 type message = string;

 fun pen2str ctxt (t, ts) =

   pair2str (UnparseC.term_in_ctxt ctxt t, (strs2str' o map (UnparseC.term_in_ctxt  ctxt)) ts);

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

     "Cor " ^ UnparseC.term_in_ctxt  ctxt (Input_Descript.join (d, ts)) ^ " ," ^ pen2str ctxt penv

   | feedback_to_string _ (Syn c) = "Syn " ^ c

   | feedback_to_string _ (Typ c) = "Typ " ^ c

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

     "Inc " ^ UnparseC.term_in_ctxt  ctxt (Input_Descript.join (d, ts)) ^ " ," ^ pen2str ctxt penv

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

     "Sup " ^ UnparseC.term_in_ctxt  ctxt (Input_Descript.join (d, ts))

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

     "Mis "^ UnparseC.term_in_ctxt  ctxt d ^ " " ^ UnparseC.term_in_ctxt  ctxt pid

   | feedback_to_string _ (Par s) = "Trm "^s;

 fun feedback_to_string' t = feedback_to_string (ThyC.id_to_ctxt "Isac_Knowledge") t;

 fun single_to_string ctxt (i, is, b, s, itm_) = 

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

   s ^ " ," ^ feedback_to_string ctxt itm_ ^ ")";

 fun to_string ctxt itms = strs2str' (map (linefeed o (single_to_string ctxt)) itms);

 fun get_tac m_field (term_as_string, i_model) =

   case m_field of

     "#Given" => Tactic.Add_Given' (term_as_string, i_model)

   | "#Find" => Tactic.Add_Find' (term_as_string, i_model)

   | "#Relate" => Tactic.Add_Relation'(term_as_string, i_model)

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

 (** initialise a model **)

 fun init pbt = 

   let

     fun pbt2itm (f, (d, _)) = (0, [], false, f, Inc ((d, []), (TermC.empty, [])))

   in map pbt2itm pbt end

 fun initPIDE pbl_id = pbl_id |> Problem.from_store |> #ppc |> init

 (** check input on a model **)

 (* find most frequent variant v in itms *)

 fun vts_in itms = ((distinct op =) o flat o (map #2)) (itms: T);

 fun cnt itms v = (v, (length o (filter (curry op = v)) o flat o (map #2)) itms);

 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;

 (* get the constant value from a penv *)

 fun getval (id, values) = 

   case values of

 	  [] => raise ERROR ("penv_value: no values in '" ^ UnparseC.term id)

   | [v] => (id, v)

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

 	      Const (\<^const_name>\<open>Program.Arbfix\<close>, _) => (id, v2)

 	    | _ => (id, v1));

 (* 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 _) = []

   | mk_e  _ = raise ERROR "mk_e: uncovered case in fun.def.";

 fun mk_en vt (_, vts, _, _, 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;

 (**)

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

   | ts_in (Syn _) = []

   | ts_in (Typ _) = []

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

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

   | ts_in (Mis _) = []

   | ts_in _ = raise ERROR "ts_in: uncovered case in fun.def.";

 val unique = TermC.parseNEW'' @{theory "Real"} "UnIqE_tErM";

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

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

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

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

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

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

   | d_in _ = raise ERROR "d_in: uncovered case in fun.def.";

 fun dts2str (d, ts) = pair2str (UnparseC.term d, UnparseC.terms ts);

 fun penvval_in (Cor ((d, _), (_, ts))) = [Input_Descript.join'''' (d, ts)]

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

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

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

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

   | penvval_in (Mis (_, _)) = ((*tracing ("*** penvval_in: Mis " ^

 			pair2str(UnparseC.term d, UnparseC.term t));*) [])

 	| penvval_in _ = raise ERROR "penvval_in: uncovered case in fun.def.";

 fun vars_of itms = itms |> mk_env |> map snd

 val dsc_unknown = TermC.parseNEW'' @{theory} "unknown::'a => unknow";

 (* 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 Input_Descript.join) (d, subtract op = (ts_in itm_) ts))

 (* 9.5.03 penv postponed: pbl_ids' *)

 fun pbl_ids' d vs = [Input_Descript.join'''' (d, vs)];

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

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

   let 

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

     val pval =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

       (Cor _) => 

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

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

     | (Syn c) => raise ERROR ("ori_2itm wants to overwrite " ^ c)

     | (Typ c) => raise ERROR ("ori_2itm wants to overwrite " ^ c)

     | (Inc _) =>

       if complete

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

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

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

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

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

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

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

        if complete

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

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

     | i => raise ERROR ("ori_2itm: uncovered case of " ^ feedback_to_string' i)

   end

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

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

 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 = (ts_in itm_) ts

           in 

             if subset op = (ts, ts') 

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

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

 	          end

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

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

 datatype additm =

 	Add of single   (* return-value of check_single *)

 | Err of string   (* error-message                *)

 (*

   Create feedback for input of TermC.as_string to m_field;

   check w.r.t. O_Model.T and Model_Pattern.T.

   In case of O_Model.T = [] (i.e. no data for user-guidance in Formalise.T)

   check_single is extremely permissive.

 *)

 fun check_single ctxt m_field [] i_model m_patt ct =

       let

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

       in 

         case TermC.parseNEW ctxt ct of

           NONE => Add (i, [], false, m_field, Syn ct)

         | SOME t =>

             let

               val (d, ts) = Input_Descript.split t

             in 

               if d = TermC.empty then

                 Add (i, [], false, m_field, Mis (dsc_unknown, hd ts)) 

               else

                 (case find_first (eq1 d) m_patt of

                   NONE => Add (i, [], true, m_field, Sup (d,ts))

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

                     let

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

                     in

                       case find_first (eq2 d) i_model of

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

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

                           if Input_Descript.for_list d then 

                             let

                               val in_itm = ts_in itm_

                               val ts' = union op = ts in_itm

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

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

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

                     end)

             end

       end

       (* for MethodC:  #undef  completed vvvvv vvvvvv term_as_string *)

   | check_single ctxt m_field o_model i_model m_patt str =

       case TermC.parseNEW ctxt str of

          NONE => Err ("ERROR I_Model.check_single: syntax error in \"" ^ str ^ "\"")

       | SOME (t as (descriptor $ _)) => 

         (case Model_Pattern.get_field descriptor m_patt of

           NONE => Err ("ERROR I_Model.check_single: unknown descriptor \"" ^

             UnparseC.term_in_ctxt ctxt descriptor ^ "\"")

         | SOME m_field' => 

           if m_field <> m_field' then

             Err ("ERROR I_Model.check_single: \"" ^ UnparseC.term_in_ctxt ctxt t ^ "\"" ^

              "\" not for field \"" ^ m_field ^ "\"")

           else

             case O_Model.is_known ctxt m_field o_model t of

               ("", ori', all) => 

                 (case is_notyet_input ctxt i_model all ori' m_patt of

                    ("", itm) => Add itm

                  | (msg, _) => Err ("ERROR I_Model.check_single: is_notyet_input: " ^ msg))

             | (msg, _, _) => Err ("ERROR I_Model.check_single: is_known: " ^ msg))

       | SOME t => Err ("ERROR I_Model.check_single: impossible for input \"" ^

           UnparseC.term_in_ctxt ctxt t ^ "\"");

 (** add input **)

 fun overwrite_ppc thy itm ppc =

   let 

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

         raise ERROR ("overwrite_ppc: " ^ (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

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

 fun seek_ppc _ [] = NONE

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

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

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

 fun add_single thy itm ppc =

   let 

     fun eq_untouched d (0, _, _, _, itm_) = (d = 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 ((d_in o #5) itm)) ppc' end

 fun complete' pbt (i, v, f, d, ts) =

   case \<^try>\<open> (i, v, true, f, Cor ((d, ts), ((snd o snd o the o (find_first (eq1 d))) pbt, ts)))\<close> of

     SOME x => x

   | NONE => (i, v, true, f, Cor ((d, ts), (d, ts)))

     (*descriptor in O_Model, but not in Problem_Pattern.T, thus keep this descriptor*)

 (* 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 = ((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

 fun is_error (Cor _) = false

   | is_error (Sup _) = false

   | is_error (Inc _) = false

   | is_error (Mis _) = false

   | is_error _ = true

 (*create output-string for itm_*)

 fun to_p_model _ (Cor ((d, ts), _)) = UnparseC.term (Input_Descript.join (d, ts))

   | to_p_model _ (Syn c) = c

   | to_p_model _ (Typ c) = c

   | to_p_model _ (Inc ((d, ts), _)) = UnparseC.term (Input_Descript.join (d, ts))

   | to_p_model _ (Sup (d, ts)) = UnparseC.term (Input_Descript.join (d, ts))

   | to_p_model _ (Mis (d, pid)) = UnparseC.term d ^ " " ^ UnparseC.term pid

   | to_p_model _ _ = raise ERROR "to_p_model: uncovered definition"

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

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

    handles superfluous items carelessly                       *)

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

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

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

 fun complete oris pits mits met = 

   let

     val vat = 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 (complete' met) os)

   end

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

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

   let

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

     val vat = if probl = [] then 1 else 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 (complete' ppc) pors)

     val mits = complete oris pits [] mpc

   in (pits, mits) end

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

 fun is_complete ([]: T) = false

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

 (**)end(**);