(* Title: generate specific entries into Ctree

   Author: Walther Neuper

   (c) due to copyright terms

*)

signature GENERATE_CALC_TREE =

sig

  type taci

  val e_taci : taci

  datatype pblmet = Method of Celem.metID | Problem of Celem.pblID | Upblmet

  datatype mout =

    EmptyMout

  | Error' of string

  | FormKF of UnparseC.cterm'

  | PpcKF of pblmet * Model.item Model.ppc

  | RefinedKF of Celem.pblID * (Model.itm list * (bool * term) list)

  val generate1 : Tactic.T -> Istate_Def.T * Proof.context -> Calc.T

    -> Pos.pos' * Pos.pos' list * mout * Ctree.ctree

  val init_istate : Tactic.input -> term -> Istate_Def.T

  val init_pbl : (string * (term * 'a)) list -> Model.itm list

  val init_pbl' : (string * (term * term)) list -> Model.itm list

  val embed_deriv : taci list -> Calc.T -> Pos.pos' list * (Calc.T) (* for inform.sml *)

  val generate_hard : (* for solve.sml *)

    theory -> Tactic.T -> Pos.pos' -> Ctree.ctree -> Pos.pos' * Pos.pos' list * mout * Ctree.ctree

  val generate : (Tactic.input * Tactic.T * (Pos.pos' * (Istate_Def.T * Proof.context))) list ->

    Ctree.ctree * Pos.pos' list * Pos.pos' -> Ctree.ctree * Pos.pos' list * Pos.pos' (* for mathengine.sml *)

  val generate_inconsistent_rew : Selem.subs option * ThmC.thm'' -> term -> Istate_Def.T * Proof.context ->

    Pos.pos' -> Ctree.ctree -> Calc.T (* for interface.sml *)

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

  val tacis2str : taci list -> string

  val mout2str : mout -> string

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

  val res_from_taci : taci -> (term * term list)

  val insert_pos : Pos.pos -> taci list -> taci list

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

(*----- unused code, kept as hints to design ideas ---------------------------------------------*)

  (* NONE *)

end

structure Generate(**): GENERATE_CALC_TREE(**) =

struct

open Ctree

open Pos

(* initialize istate for Detail_Set *)

fun init_istate (Tactic.Rewrite_Set rls) t =

    let

      val thy = Celem.assoc_thy "Isac_Knowledge"

      val args = Auto_Prog.gen thy t (assoc_rls rls) |> Program.formal_args

    in

      Istate_Def.Pstate (Istate_Def.e_pstate |> Istate_Def.set_env_true [(hd args, t)])

    end

  | init_istate (Tactic.Rewrite_Set_Inst (subs, rls)) t =

    let

      val thy = Celem.assoc_thy "Isac_Knowledge"

      val rls' = assoc_rls rls

      val v = case Selem.subs2subst thy subs of

        (_, v) :: _ => v (*...we suppose the substitution of only ONE bound variable*)

      | _ => raise ERROR "init_istate: uncovered case"

      val prog = Auto_Prog.gen thy t rls'

      val args = Program.formal_args prog

    in

      Istate_Def.Pstate (Istate_Def.e_pstate |> Istate_Def.set_env_true (args ~~ [t, v]))

    end

  | init_istate tac _ = error ("init_istate: uncovered definition for " ^ Tactic.input_to_string tac)

(* a taci holds alle information required to build a node in the calc-tree;

   a taci is assumed to be used efficiently such that the calc-tree

   resulting from applying a taci need not be stored separately;

   see "type calcstate" *)

(*TODO.WN0504 redesign ??? or redesign generate ?? see "fun generate"

  TODO.WN0512 ? redesign this _list_:

  # only used for [Apply_Method + (Take or Subproblem)], i.e. for initacs

  # the latter problem may be resolved automatically if "fun autocalc" is 

    not any more used for the specify-phase and for changing the phases*)

type taci = 

  (Tactic.input *                     (* for comparison with input tac             *)      

   Tactic.T *                         (* for ctree generation                      *)

   (pos' *                            (* after applying tac_, for ctree generation *)

    (Istate_Def.T * Proof.context)))  (* after applying tac_, for ctree generation *)

val e_taci = (Tactic.Empty_Tac, Tactic.Empty_Tac_, (e_pos', (Istate_Def.empty, ContextC.empty))): taci

fun taci2str ((tac, tac_, (pos', (istate, _))):taci) =

  "( " ^ Tactic.input_to_string tac ^ ", " ^ Tactic.string_of tac_ ^ ", ( " ^ pos'2str pos' ^ ", " ^

  Istate_Def.string_of istate ^ " ))"

fun tacis2str tacis = (strs2str o (map (Celem.linefeed o taci2str))) tacis

datatype pblmet =           (*%^%*)

  Upblmet                   (*undefined*)

| Problem of Celem.pblID    (*%^%*)

| Method of Celem.metID;    (*%^%*)

fun pblmet2str (Problem pblID) = "Problem " ^ strs2str pblID (*%^%*)

  | pblmet2str (Method metID) = "Method " ^ Celem.metID2str metID (*%^%*)

  | pblmet2str x = error ("pblmet2str: uncovered definition " ^ pblmet2str x)

(*3.5.00: TODO: foppFK eliminated in interface FE-KE !!!*)

datatype foppFK =                  (* in DG cases div 2 *)

  EmptyFoppFK         (*DG internal*)

| FormFK of UnparseC.cterm'

| PpcFK of UnparseC.cterm' Model.ppc

fun foppFK2str (FormFK ct') ="FormFK " ^ ct'

  | foppFK2str (PpcFK  ppc) ="PpcFK " ^ Model.ppc2str ppc

  | foppFK2str EmptyFoppFK  ="EmptyFoppFK"

datatype nest = Open | Closed | Nundef;

fun nest2str Open = "Open"

  | nest2str Closed = "Closed"

  | nest2str Nundef = "Nundef"

type indent = int;

datatype edit = EdUndef | Write | Protect;

                                   (* bridge --> kernel *)

                                   (* bridge <-> kernel *)

(* needed in dialog.sml *)         (* bridge <-- kernel *)

fun edit2str EdUndef = "EdUndef"

  | edit2str Write = "Write"

  | edit2str Protect = "Protect";

datatype inout = (*FIXME.WN1105 drop this: was required for proto0 with dialog in sml*)

  Error_ of string                                                         (*<--*)

| FormKF of cellID * edit * indent * nest * UnparseC.cterm'                   (*<--*)

| PpcKF of cellID * edit * indent * nest * (pblmet * Model.item Model.ppc) (*<--*)

| RefineKF of Stool.match list                                             (*<--*)

| RefinedKF of (Celem.pblID * ((Model.itm list) * ((bool * term) list)))   (*<--*)

(*

  datatype mout = EmptyMout | Error' of inout | Form' of inout | Problems of inout

*)

datatype mout =

  FormKF of UnparseC.cterm'

| PpcKF of (pblmet * Model.item Model.ppc) 

| RefinedKF of Celem.pblID * (Model.itm list * (bool * term) list)

| Error' of string

| EmptyMout

fun mout2str (FormKF cterm') = "FormKF " ^ cterm'

  | mout2str (PpcKF  (pm, itemppc)) = "PpcKF (" ^ pblmet2str pm ^ "," ^ Model.itemppc2str itemppc ^ ")"

  | mout2str (RefinedKF  (_, _)) = "mout2str: RefinedKF not impl."

  | mout2str (Error'  str) = "Error' " ^ str

  | mout2str (EmptyMout    ) = "EmptyMout"

(* init pbl with ...,dsc,empty | [] *)

fun init_pbl pbt = 

  let

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

  in map pbt2itm pbt end

(* take formal parameters from pbt, for transfer from pbl/met-hierarchy *)

fun init_pbl' pbt = 

  let 

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

  in map pbt2itm pbt end

(* generate 1 ppobj in Ctree *)

fun generate1 (Tactic.Model_Problem' (_, itms, met)) (_, ctxt) (pt, pos as (p, _)) =

    let

      val pt = update_pbl pt p itms

	    val pt = update_met pt p met

    in

      (pos, [], PpcKF (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [] []), pt)

    end

  | generate1 (Tactic.Add_Given' (_, itmlist)) (_, ctxt) (pt, pos as (p, p_)) = 

    (pos: pos', [], PpcKF (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [][]),

       case p_ of

         Pbl => update_pbl pt p itmlist

	     | Met => update_met pt p itmlist

       | _ => error ("uncovered case " ^ pos_2str p_))

    (* WN110515 probably declare_constraints with input item (without dsc) --

      -- important when specifying without formalisation *)

  | generate1 (Tactic.Add_Find' (_, itmlist)) (_, ctxt) (pt, pos as (p, p_)) = 

    (pos, [], (PpcKF (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [] [])),

       case p_ of

         Pbl => update_pbl pt p itmlist

	     | Met => update_met pt p itmlist

       | _ => error ("uncovered case " ^ pos_2str p_))

    (*WN110515 probably declare_constraints with input item (without dsc)*)

  | generate1 (Tactic.Add_Relation' (_, itmlist)) (_, ctxt) (pt, pos as (p, p_)) = 

    (pos, [],  PpcKF (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [] []),

       case p_ of

         Pbl => update_pbl pt p itmlist

	     | Met => update_met pt p itmlist

       | _ => error ("uncovered case " ^ pos_2str p_))

  | generate1 (Tactic.Specify_Theory' domID) (_, ctxt) (pt, pos as (p,_)) = 

    (pos, [] , PpcKF  (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [] []),

      update_domID pt p domID)

  | generate1 (Tactic.Specify_Problem' (pI, (_, (itms, _)))) (_, ctxt) (pt, (p, _)) =

    let

      val pt = update_pbl pt p itms

      val pt = update_pblID pt p pI

    in

      ((p, Pbl), [], PpcKF (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [] []), pt)

    end

  | generate1 (Tactic.Specify_Method' (mID, oris, itms)) (_, ctxt) (pt, (p, _)) =

    let

      val pt = update_oris pt p oris

      val pt = update_met pt p itms

      val pt = update_metID pt p mID

    in

      ((p, Met), [], PpcKF (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [] []), pt)

    end

  | generate1 (Tactic.Refine_Tacitly' (_, pIre, domID, metID, pbl)) (_, ctxt) (pt, pos as (p, _)) = 

    let

      val pt = update_pbl pt p pbl

      val pt = update_orispec pt p (domID, pIre, metID)

    in

      (pos, [], PpcKF (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [] []), pt)

    end

  | generate1 (Tactic.Refine_Problem' (pI, _)) (_, ctxt) (pt, pos as (p, _)) =

    let

      val (dI, _, mI) = get_obj g_spec pt p

      val pt = update_spec pt p (dI, pI, mI)

    in

      (pos, [], PpcKF (Upblmet, Specify.itms2itemppc (Proof_Context.theory_of ctxt) [] []), pt)

    end

  | generate1 (Tactic.Apply_Method' (_, topt, is, _)) (_, ctxt) (pt, pos as (p, _)) = 

    (case topt of 

      SOME t => 

        let val (pt, c) = cappend_form pt p (is, ctxt) t

        in (pos, c, EmptyMout, pt) end

    | NONE => (pos, [], EmptyMout, pt))

  | generate1 (Tactic.Take' t) l (pt, (p, _)) = (* val (Take' t) = m; *)

    let

      val p =

        let val (ps, p') = split_last p (* no connex to prev.ppobj *)

	      in if p' = 0 then ps @ [1] else p end

      val (pt, c) = cappend_form pt p l t

    in

      ((p, Frm): pos', c, FormKF (UnparseC.term2str t), pt)

    end

  | generate1 (Tactic.Begin_Trans' t) l (pt, (p, Frm)) =

    let

      val (pt, c) = cappend_form pt p l t

      val pt = update_branch pt p TransitiveB (*040312*)

      (* replace the old PrfOjb ~~~~~ *)

      val p = (lev_on o lev_dn (* starts with [...,0] *)) p

      val (pt, c') = cappend_form pt p l t (*FIXME.0402 same istate ???*)

    in

      ((p, Frm), c @ c', FormKF (UnparseC.term2str t), pt)

    end

  | generate1 (Tactic.Begin_Trans' t) l (pt, (p, Res)) = 

    (*append after existing PrfObj    vvvvvvvvvvvvv*)

    generate1 (Tactic.Begin_Trans' t) l (pt, (lev_on p, Frm))

  | generate1 (Tactic.End_Trans' tasm) l (pt, (p, _)) =

    let

      val p' = lev_up p

      val (pt, c) = append_result pt p' l tasm Complete

    in

      ((p', Res), c, FormKF "DUMMY" (*term2str t ..ERROR (t) has not been declared*), pt)

    end

  | generate1 (Tactic.Rewrite_Inst' (_, _, _, _, subs', thm', f, (f', asm))) (is, ctxt) (pt, (p, _)) =

    let

      val (pt, c) = cappend_atomic pt p (is, ctxt) f

        (Tactic.Rewrite_Inst (Selem.subst2subs subs', thm')) (f',asm) Complete;

      val pt = update_branch pt p TransitiveB

    in

      ((p, Res), c, FormKF (UnparseC.term2str f'), pt)

    end

 | generate1 (Tactic.Rewrite' (_, _, _, _, thm', f, (f', asm))) (is, ctxt) (pt, (p, _)) =

   let

     val (pt, c) = cappend_atomic pt p (is, ctxt) f (Tactic.Rewrite thm') (f', asm) Complete

     val pt = update_branch pt p TransitiveB

   in

    ((p, Res), c, FormKF (UnparseC.term2str f'), pt)

   end

  | generate1 (Tactic.Rewrite_Set_Inst' (_, _, subs', rls', f, (f', asm))) (is, ctxt) (pt, (p, _)) =

    let

      val (pt, c) = cappend_atomic pt p (is, ctxt) f 

        (Tactic.Rewrite_Set_Inst (Selem.subst2subs subs', Rule_Set.rls2str rls')) (f', asm) Complete

      val pt = update_branch pt p TransitiveB

    in

      ((p, Res), c, FormKF (UnparseC.term2str f'), pt)

    end

  | generate1 (Tactic.Detail_Set_Inst' (_, _, subs, rls, f, _)) (is, ctxt) (pt, (p, _)) =

    let

      val (pt, _) = cappend_form pt p (is, ctxt) f 

      val pt = update_branch pt p TransitiveB

      val is = init_istate (Tactic.Rewrite_Set_Inst (Selem.subst2subs subs, Rule_Set.rls2str rls)) f 

      val tac_ = Tactic.Apply_Method' (Celem.e_metID, SOME TermC.empty (*t ..has not been declared*), is, ctxt)

      val pos' = ((lev_on o lev_dn) p, Frm)

    in

      generate1 tac_ (is, ctxt) (pt, pos') (*implicit Take*)

    end

  | generate1 (Tactic.Rewrite_Set' (_, _, rls', f, (f', asm))) (is, ctxt) (pt, (p, _)) =

    let

      val (pt, c) = cappend_atomic pt p (is, ctxt) f 

        (Tactic.Rewrite_Set (Rule_Set.rls2str rls')) (f', asm) Complete

      val pt = update_branch pt p TransitiveB

    in

      ((p, Res), c, FormKF (UnparseC.term2str f'), pt)

    end

  | generate1 (Tactic.Detail_Set' (_, _, rls, f, _)) (is, ctxt) (pt, (p, _)) =

    let

      val (pt, _) = cappend_form pt p (is, ctxt) f 

      val pt = update_branch pt p TransitiveB

      val is = init_istate (Tactic.Rewrite_Set (Rule_Set.rls2str rls)) f

      val tac_ = Tactic.Apply_Method' (Celem.e_metID, SOME TermC.empty (*t ..has not been declared*), is, ctxt)

      val pos' = ((lev_on o lev_dn) p, Frm)

    in

      generate1 tac_ (is, ctxt) (pt, pos') (*implicit Take*)

    end

  | generate1 (Tactic.Check_Postcond' (_, scval)) l (pt, (p, _)) =

      let

        val (pt, c) = append_result pt p l (scval, []) Complete

      in

        ((p, Res), c, FormKF (UnparseC.term2str scval), pt)

      end

  | generate1 (Tactic.Calculate' (_, op_, f, (f', _))) l (pt, (p, _)) =

      let

        val (pt,c) = cappend_atomic pt p l f (Tactic.Calculate op_) (f', []) Complete

      in

        ((p, Res), c, FormKF (UnparseC.term2str f'), pt)

      end

  | generate1 (Tactic.Check_elementwise' (consts, pred, (f', asm))) l (pt, (p, _)) =

      let

        val (pt,c) = cappend_atomic pt p l consts (Tactic.Check_elementwise pred) (f', asm) Complete

      in

        ((p, Res), c, FormKF (UnparseC.term2str f'), pt)

      end

  | generate1 (Tactic.Or_to_List' (ors, list)) l (pt, (p, _)) =

      let

        val (pt,c) = cappend_atomic pt p l ors Tactic.Or_to_List (list, []) Complete

      in

        ((p, Res), c, FormKF (UnparseC.term2str list), pt)

      end

  | generate1 (Tactic.Substitute' (_, _, subte, t, t')) l (pt, (p, _)) =

      let

        val (pt,c) =

          cappend_atomic pt p l t (Tactic.Substitute (Selem.subte2sube subte)) (t',[]) Complete

        in ((p, Res), c, FormKF (UnparseC.term2str t'), pt) 

        end

  | generate1 (Tactic.Tac_ (_, f, id, f')) l (pt, (p, _)) =

      let

        val (pt, c) = cappend_atomic pt p l (TermC.str2term f) (Tactic.Tac id) (TermC.str2term f', []) Complete

      in

        ((p,Res), c, FormKF f', pt)

      end

  | generate1 (Tactic.Subproblem' ((domID, pblID, metID), oris, hdl, fmz_, ctxt_specify, f))

      (l as (_, ctxt)) (pt, (p, _)) =

    let

	    val (pt, c) = cappend_problem pt p l (fmz_, (domID, pblID, metID))

	      (oris, (domID, pblID, metID), hdl, ctxt_specify)

	    val f = Syntax.string_of_term (ThyC.thy2ctxt (Proof_Context.theory_of ctxt)) f

    in

      ((p, Pbl), c, FormKF f, pt)

    end

  | generate1 m' _ _ = error ("generate1: not impl.for " ^ Tactic.string_of m')

fun generate_inconsistent_rew (subs_opt, thm') f' (is, ctxt) (pos as (p,_)) pt =

  let

    val f = get_curr_formula (pt, pos)

    val pos' as (p', _) = (lev_on p, Res)

    val (pt, _) = case subs_opt of

      NONE => cappend_atomic pt p' (is, ctxt) f

        (Tactic.Rewrite thm') (f', []) Inconsistent

    | SOME subs => cappend_atomic pt p' (is, ctxt) f

        (Tactic.Rewrite_Inst (subs, thm')) (f', []) Inconsistent

    val pt = update_branch pt p' TransitiveB

  in (pt, pos') end

fun generate_hard _(*thy*) m' (p,p_) pt =

  let  

    val p = case p_ of

      Frm => p | Res => lev_on p

    | _ => error ("generate_hard: call by " ^ pos'2str (p,p_))

  in

    generate1 m' (Istate_Def.empty, ContextC.empty) (pt, (p, p_))

  end

(* tacis are in reverse order from do_next/specify_: last = fst to insert *)

fun generate ([]: taci list) ptp = ptp

  | generate tacis (pt, c, _: pos'(*!dropped!WN0504redesign generate/tacis?*)) = 

    let

      val (tacis', (_, tac_, (p, is))) = split_last tacis

	    val (p',c',_,pt') = generate1 tac_ is (pt, p)

    in

      generate tacis' (pt', c@c', p')

    end

(* update pos in tacis for embedding by generate *)

fun insert_pos (_: pos) [] = []

  | insert_pos (p: pos) (((tac, tac_, (_, ist)): taci) :: tacis) = 

    ((tac, tac_, ((p, Res), ist)): taci) :: (insert_pos (lev_on p) tacis)

fun res_from_taci (_, Tactic.Rewrite' (_, _, _, _, _, _,(res, asm)), _) = (res, asm)

  | res_from_taci (_, Tactic.Rewrite_Set' (_, _, _, _, (res, asm)), _) = (res, asm)

  | res_from_taci (_, tac_, _) = error ("res_from_taci: called with" ^ Tactic.string_of tac_)

(* embed the tacis created by a '_deriv'ation; sys.form <> input.form

  tacis are in order, thus are reverted for generate *)

fun embed_deriv tacis (pt, pos as (p, Frm)) =

  (*inform at Frm: replace the whole PrfObj by a Transitive-ProfObj FIXME?0402

    and transfer the istate (from _after_ compare_deriv) from Frm to Res*)

    let

      val (res, asm) = (res_from_taci o last_elem) tacis

    	val (ist, ctxt) = case get_obj g_loc pt p of

    	  (SOME (ist, ctxt), _) => (ist, ctxt)

      | (NONE, _) => error "embed_deriv Frm: uncovered case get_obj"

    	val form = get_obj g_form pt p

      (*val p = lev_on p; ---------------only difference to (..,Res) below*)

    	val tacis = (Tactic.Begin_Trans, Tactic.Begin_Trans' form, (pos, (Istate_Def.Uistate, ctxt))) ::

    		(insert_pos ((lev_on o lev_dn) p) tacis) @ [(Tactic.End_Trans, Tactic.End_Trans' (res, asm),

    			(pos_plus (length tacis) (lev_dn p, Res), (new_val res ist, ctxt)))]

    	val {nrls, ...} = Specify.get_met (get_obj g_metID pt (par_pblobj pt p))

    	val (pt, c, pos as (p, _)) = generate (rev tacis) (pt, [], (p, Res))

    	val pt = update_tac pt p (Tactic.Derive (Rule_Set.rls2str nrls))

    	val pt = update_branch pt p TransitiveB

    in (c, (pt, pos: pos')) end

  | embed_deriv tacis (pt, (p, Res)) =

    (*inform at Res: append a Transitive-PrfObj FIXME?0402 other branch-types ?

      and transfer the istate (from _after_ compare_deriv) from Res to new Res*)

    let val (res, asm) = (res_from_taci o last_elem) tacis

    	val (ist, ctxt) = case get_obj g_loc pt p of

    	  (_, SOME (ist, ctxt)) => (ist, ctxt)

      | (_, NONE) => error "embed_deriv Frm: uncovered case get_obj"

    	val (f, _) = get_obj g_result pt p

    	val p = lev_on p(*---------------only difference to (..,Frm) above*);

    	val tacis = (Tactic.Begin_Trans, Tactic.Begin_Trans' f, ((p, Frm), (Istate_Def.Uistate, ctxt))) ::

    		(insert_pos ((lev_on o lev_dn) p) tacis) @ [(Tactic.End_Trans, Tactic.End_Trans' (res, asm), 

    			(pos_plus (length tacis) (lev_dn p, Res), (new_val res ist, ctxt)))];

    	val {nrls, ...} = Specify.get_met (get_obj g_metID pt (par_pblobj pt p))

    	val (pt, c, pos as (p, _)) = generate (rev tacis) (pt, [], (p, Res))

    	val pt = update_tac pt p (Tactic.Derive (Rule_Set.rls2str nrls))

    	val pt = update_branch pt p TransitiveB

    in (c, (pt, pos)) end

  | embed_deriv _ _ = error "embed_deriv: uncovered definition"

end