(* Title:  Specify/model.sml

    Author: Walther Neuper 110226

    (c) due to copyright terms

 Operations on models.

 *)

 signature MODEL =

 sig

   datatype match =

       Matches of Problem.id * P_Model.T

     | NoMatch of Problem.id * P_Model.T  

   val matchs2str : match list -> string

   val match_oris: theory -> Rule_Set.T -> O_Model.T -> Model_Pattern.T * term list -> bool

 (*unify                     ^^^^^^^^^^                                  vvvvvvvvvv 

                              vvvvvvvvv    ^^^^^^^^^*)

   val match_oris': theory -> O_Model.T -> Model_Pattern.T * term list * Rule_Set.T ->

     bool * (I_Model.T * Pre_Conds.T)

   val match_itms_oris : theory -> I_Model.T -> Model_Pattern.T * term list * Rule_Set.T ->

     O_Model.T -> bool * (I_Model.T * Pre_Conds.T)

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

   datatype match' = Matches' of P_Model.T | NoMatch' of P_Model.T

   val match_pbl : Formalise.model -> Problem.T -> match'

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

   (*NONE*)

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

 end

 (**)

 structure Model(** ) : MODEL( **) =

 struct

 (**)

 datatype match = 

   Matches of Problem.id *  P_Model.T

 | NoMatch of Problem.id *  P_Model.T;

 fun match2str (Matches (pI, ppc)) = "Matches (" ^ strs2str pI ^ ", " ^  P_Model.to_string ppc ^ ")"

   | match2str (NoMatch (pI, ppc)) = "NoMatch (" ^ strs2str pI ^ ", " ^  P_Model.to_string ppc ^ ")";

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

 fun field_eq f (_, _, f', _, _) = f = f';

 fun eq2' (_, (d, _)) (_, _, _, d', _) = d = d';

 fun eq2 (_, (d, _)) (_, _, _, _, itm_) = d = I_Model.d_in itm_;

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

 fun ori2itmSup (i, v, _, d, ts) = (i, v, true, "#Given", I_Model.Sup (d, ts));

 (* check an ori for matching a problemtype by description; 

    returns true only for itms found in pbt              *)

 fun chk1_ (_: theory) pbt (i, vats, f, d, vs) =

   case find_first (eq1 d) pbt of 

 	  SOME (_, (_, id)) => [(i, vats, true, f, I_Model.Cor ((d, vs), (id, I_Model.pbl_ids' d vs)))]

   | NONE => [];

 (* elem 'p' of pbt contained in itms ? *)

 fun chk1_m itms p = case find_first (eq2 p) itms of SOME _ => true | NONE => false;

 fun chk1_m' oris (p as (f, (d, t))) = 

   case find_first (eq2' p) oris of

 	  SOME _ => []

   | NONE => [(f, I_Model.Mis (d, t))];

 fun pair0vatsfalse (f, itm_) = (0, [], false, f, itm_);

 fun chk1_mis _(*mvat*) itms ppc = foldl and_ (true, map (chk1_m itms) ppc);

 fun chk1_mis' oris ppc = map pair0vatsfalse ((flat o (map (chk1_m' oris))) ppc);

 (* check a problem (ie. ori list) for matching a problemtype, 

    takes the I_Model.vars_of for concluding completeness (FIXME could be another!) *)

 fun match_oris thy prls oris (pbt,pre) = 

   let

     val itms = (flat o (map (chk1_ thy pbt))) oris;

     val mvat = I_Model.vars_of itms;

     val complete = chk1_mis mvat itms pbt;

     val pre' = Pre_Conds.check prls pre itms mvat;

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

   in if complete andalso pb then true else false end;

 (* check a problem (ie. ori list) for matching a problemtype, 

    returns items for output to math-experts *)

 fun match_oris' thy oris (ppc, pre, prls) =

   let

     val itms = (flat o (map (chk1_ thy ppc))) oris;

     val sups = ((map ori2itmSup) o (filter (field_eq "#undef"))) oris;

     val mvat = I_Model.vars_of itms;

     val miss = chk1_mis' oris ppc;

     val pre' = Pre_Conds.check prls pre itms mvat;

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

   in (miss = [] andalso pb, (itms @ miss @ sups, pre')) end;

 (** check a problem (ie. itm list) for matching a problemtype **)

 (* check a problem (or method) pbl (ie. itm list) for matching a problemtype pbt,

    for missing items get data from formalization (ie. ori list); 

    takes the I_Model.vars_of for concluding completeness (could be another!)

   (0) determine the most frequent variant mv in pbl

    ALL pbt. (1) dsc(pbt) notmem dsc(pbls) =>

             (2) filter (dsc(pbt) = dsc(oris)) oris; -> news;

             (3) newitms = filter (mv mem vat(news)) news 

    (4) pbt @ newitms                                           *)

 fun match_itms_oris (_: theory) pbl (pbt, pre, prls) oris =

   let 

  (*0*)val mv = I_Model.max_vt pbl;

       fun eqdsc_pbt_itm ((_,(d,_))) (_, _, _, _, itm_) = d = I_Model.d_in itm_;

       fun notmem pbl pbt1 = case find_first (eqdsc_pbt_itm pbt1) pbl of

 				SOME _ => false | NONE => true;

  (*1*)val mis = (filter (notmem pbl)) pbt;

       fun eqdsc_ori (_,(d,_)) (_, _, _, d', _) = d = d';

       fun ori2itmMis (f, (d, pid)) (i, v, _, _, _) = (i, v, false, f, I_Model.Mis (d, pid));

  (*2*)fun oris2itms oris mis1 = ((map (ori2itmMis mis1)) o (filter (eqdsc_ori mis1))) oris;

       val news = (flat o (map (oris2itms oris))) mis;

  (*3*)fun mem_vat (_, vats, _, _, _) = member op = vats mv;

       val newitms = filter mem_vat news;

  (*4*)val itms' = pbl @ newitms;

       val pre' = Pre_Conds.check prls pre itms' mv;

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

   in (length mis = 0 andalso pb, (itms', pre')) end;

 (** for use by math-authors **)

 datatype match' = (* for the user *)

   Matches' of P_Model.T

 | NoMatch' of P_Model.T;

 (* match a formalization with a problem type, for tests *)

 fun match_pbl fmz ({thy = thy, where_ = pre, ppc, prls = er, ...}: Problem.T) =

   let

     val oris = O_Model.init fmz thy ppc(* |> #1*);

     val (bool, (itms, pre')) = match_oris' thy oris (ppc, pre, er);

   in

     if bool

     then Matches' (P_Model.from thy itms pre')

     else NoMatch' (P_Model.from thy itms pre')

   end;

 (**)end(**)