(* Title:  Specify/solve-step.sml

   Author: Walther Neuper

   (c) due to copyright terms

Code for the solve-phase in analogy to structure Specify_Step for the specify-phase.

*)

signature SOLVE_STEP =

sig

  val check: Tactic.input -> Calc.T -> Applicable.T

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

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

  val s_add_general: State_Steps.T ->

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

  val add_hard:

    theory -> Tactic.T -> Pos.pos' -> Ctree.ctree -> Test_Out.T

  val get_ruleset: 'a -> Pos.pos -> Ctree.ctree ->

    string * ThyC.id * Rewrite_Ord.id * Rule_Def.rule_set * bool

  val get_eval: string -> Pos.pos ->Ctree.ctree ->

    string * ThyC.id * (string * Rule_Def.eval_fn)

\<^isac_test>\<open>

  val rew_info: Rule_Def.rule_set -> string * Rule_Def.rule_set * Rule_Def.calc list

\<close>

end

(**)

structure Solve_Step(**): SOLVE_STEP(**) =

struct

(**)

(** get data from Calc.T **)

(* the source is the parent node, either a problem or a Rule_Set (with inter_steps) *)

fun rew_info (Rule_Def.Repeat {erls, rew_ord = (rew_ord', _), calc = ca, ...}) =

    (rew_ord', erls, ca)

  | rew_info (Rule_Set.Sequence {erls, rew_ord = (rew_ord', _), calc = ca, ...}) =

    (rew_ord', erls, ca)

  | rew_info (Rule_Set.Rrls {erls, rew_ord = (rew_ord', _), calc = ca, ...}) =

    (rew_ord', erls, ca)

  | rew_info rls = raise ERROR ("rew_info called with '" ^ Rule_Set.id rls ^ "'");

fun get_ruleset _ p pt = 

  let 

    val (pbl, p', rls') = Ctree.parent_node pt p

  in                                                      

    if pbl

    then 

      let 

        val thy' = Ctree.get_obj Ctree.g_domID pt p'

        val {rew_ord', erls, ...} = MethodC.from_store (Ctree.get_obj Ctree.g_metID pt p')              

	    in ("OK", thy', rew_ord', erls, false) end

     else 

      let

        val thy' = Ctree.get_obj Ctree.g_domID pt (Ctree.par_pblobj pt p)

		    val (rew_ord', erls, _) = rew_info rls'

		  in ("OK", thy', rew_ord', erls, false) end

  end;

fun get_eval scrop p pt = 

  let

    val (pbl, p', rls') =  Ctree.parent_node pt p

  in

    if pbl

    then

      let

        val thy' = Ctree.get_obj Ctree.g_domID pt p'

        val {calc = scr_isa_fns, ...} = MethodC.from_store (Ctree.get_obj Ctree.g_metID pt p')

        val opt = assoc (scr_isa_fns, scrop)

	    in

	      case opt of

	        SOME isa_fn => ("OK", thy', isa_fn)

	      | NONE => ("applicable_in Calculate: unknown '" ^ scrop ^ "'", "", ("", Eval_Def.e_evalfn))

	    end

    else 

		  let

		    val thy' = Ctree.get_obj Ctree.g_domID pt (Ctree.par_pblobj pt p);

		    val (_, _,(*_,*)scr_isa_fns) = rew_info rls'(*rls*)

		  in

		    case assoc (scr_isa_fns, scrop) of

		      SOME isa_fn => ("OK",thy',isa_fn)

		    | NONE => ("applicable_in Calculate: unknown '" ^ scrop ^ "'", "", ("", Eval_Def.e_evalfn))

		  end

  end;

(** Solve_Step.check **)

(*

  check tactics (input by the user, mostly) for applicability

  and determine as much of the result of the tactic as possible initially.

*)

fun check (Tactic.Apply_Method mI) (pt, (p, _)) =

      let

        val (dI, pI, probl, ctxt) = case Ctree.get_obj I pt p of

          Ctree.PblObj {origin = (_, (dI, pI, _), _), probl, ctxt, ...} => (dI, pI, probl, ctxt)

        | _ => raise ERROR "Specify_Step.check Apply_Method: uncovered case Ctree.get_obj"

        val {where_, ...} = Problem.from_store pI

        val pres = map (I_Model.environment probl |> subst_atomic) where_

        val ctxt = if ContextC.is_empty ctxt (*vvvvvvvvvvvvvv DO THAT EARLIER?!?*)

          then ThyC.get_theory dI |> Proof_Context.init_global |> ContextC.insert_assumptions pres

          else ctxt

      in

        Applicable.Yes (Tactic.Apply_Method' (mI, NONE, Istate_Def.empty (*filled later*), ctxt))

      end

  | check (Tactic.Calculate op_) (cs as (pt, (p, _))) =

      let 

        val (msg, thy', isa_fn) = get_eval op_ p pt;

        val f = Calc.current_formula cs;

      in

        if msg = "OK"

        then

    	    case Rewrite.calculate_ (ThyC.id_to_ctxt thy') isa_fn f of

    	      SOME (f', (id, thm))

    	        => Applicable.Yes (Tactic.Calculate' (thy', op_, f, (f', (id, thm))))

    	    | NONE => Applicable.No ("'calculate " ^ op_ ^ "' not applicable") 

        else Applicable.No msg                                              

      end

  | check (Tactic.Check_Postcond pI) (_, _) = (*TODO: only applicable, if evaluating to True*)

      Applicable.Yes (Tactic.Check_Postcond' (pI, TermC.empty))

  | check (Tactic.Check_elementwise pred) cs =

      let 

        val f = Calc.current_formula cs;

      in

        Applicable.Yes (Tactic.Check_elementwise' (f, pred, (f, [])))

      end

  | check Tactic.Empty_Tac _ = Applicable.No "Empty_Tac is not applicable"

  | check (Tactic.Free_Solve) _ = Applicable.Yes (Tactic.Free_Solve')

  | check Tactic.Or_to_List cs =

       let 

        val f = Calc.current_formula cs;

        val ls = Prog_Expr.or2list f;

      in

        Applicable.Yes (Tactic.Or_to_List' (f, ls))

      end

  | check (Tactic.Rewrite thm) (cs as (pt, (p, _))) = 

      let

        val (msg, thy', ro, rls', _) = get_ruleset thm p pt;

        val thy = ThyC.get_theory thy';

        val ctxt = Proof_Context.init_global thy;

        val f = Calc.current_formula cs;

      in

        if msg = "OK" 

        then

          case Rewrite.rewrite_ ctxt (assoc_rew_ord thy ro) rls' false (snd thm) f of

            SOME (f',asm) => Applicable.Yes (Tactic.Rewrite' (thy', ro, rls', false, thm, f, (f', asm)))

          | NONE => Applicable.No ((thm |> fst |> quote) ^ " not applicable") 

        else Applicable.No msg

      end

  | check (Tactic.Rewrite_Inst (subs, thm)) (cs as (pt, (p, _))) = 

      let 

        val pp = Ctree.par_pblobj pt p;

        val thy' = Ctree.get_obj Ctree.g_domID pt pp;

        val thy = ThyC.get_theory thy';

        val ctxt = Proof_Context.init_global thy;

        val {rew_ord' = ro', erls = erls, ...} = MethodC.from_store (Ctree.get_obj Ctree.g_metID pt pp);

        val f = Calc.current_formula cs;

        val subst = Subst.T_from_input ctxt subs; (*TODO: input requires parse _: _ -> _ option*)

      in 

        case Rewrite.rewrite_inst_ ctxt (assoc_rew_ord thy ro') erls false subst (snd thm) f of

          SOME (f', asm) =>

            Applicable.Yes (Tactic.Rewrite_Inst' (thy', ro', erls, false, subst, thm, f, (f', asm)))

        | NONE => Applicable.No (fst thm ^ " not applicable")

      end

  | check (Tactic.Rewrite_Set rls) (cs as (pt, (p, _))) =

      let 

        val pp = Ctree.par_pblobj pt p; 

        val thy' = Ctree.get_obj Ctree.g_domID pt pp;

        val f = Calc.current_formula cs;

      in

        case Rewrite.rewrite_set_ (ThyC.id_to_ctxt thy') false (assoc_rls rls) f of

          SOME (f', asm)

            => Applicable.Yes (Tactic.Rewrite_Set' (thy', false, assoc_rls rls, f, (f', asm)))

          | NONE => Applicable.No (rls ^ " not applicable")

      end

  | check (Tactic.Rewrite_Set_Inst (subs, rls)) (cs as (pt, (p, _))) =

      let 

        val pp = Ctree.par_pblobj pt p;

        val thy' = Ctree.get_obj Ctree.g_domID pt pp;

        val thy = ThyC.get_theory thy';

        val ctxt = Proof_Context.init_global thy;

        val f = Calc.current_formula cs;

    	  val subst = Subst.T_from_input ctxt subs; (*TODO: input requires parse _: _ -> _ option*)

      in 

        case Rewrite.rewrite_set_inst_ ctxt false subst (assoc_rls rls) f of

          SOME (f', asm)

            => Applicable.Yes (Tactic.Rewrite_Set_Inst' (thy', false, subst, assoc_rls rls, f, (f', asm)))

        | NONE => Applicable.No (rls ^ " not applicable")

      end

  | check (Tactic.Subproblem (domID, pblID)) (_, _) = 

      Applicable.Yes (Tactic.Subproblem' ((domID, pblID, MethodC.id_empty), [], 

			  TermC.empty, [], ContextC.empty, Auto_Prog.subpbl domID pblID))

  | check (Tactic.Substitute sube) (cs as (pt, (p, _))) =

      let

        val pp = Ctree.par_pblobj pt p

        val thy = ThyC.get_theory (Ctree.get_obj Ctree.g_domID pt pp)

        val ctxt = Proof_Context.init_global thy;

        val f = Calc.current_formula cs;

		    val {rew_ord', erls, ...} = MethodC.from_store (Ctree.get_obj Ctree.g_metID pt pp)

		    val subte = Subst.input_to_terms sube (*TODO: input requires parse _: _ -> _ option*)

		    val subst = Subst.T_from_string_eqs thy sube

		    val ro = assoc_rew_ord thy rew_ord'

		  in

		    if foldl and_ (true, map TermC.contains_Var subte)

		    then (*1*)

		      let val f' = subst_atomic subst f

		      in if f = f'

		        then Applicable.No (Subst.string_eqs_to_string sube ^ " not applicable")

		        else Applicable.Yes (Tactic.Substitute' (ro, erls, subte, f, f'))

		      end

		    else (*2*)

		      case Rewrite.rewrite_terms_ ctxt ro erls subte f of

		        SOME (f', _) =>  Applicable.Yes (Tactic.Substitute' (ro, erls, subte, f, f'))

		      | NONE => Applicable.No (Subst.string_eqs_to_string sube ^ " not applicable")

		  end

  | check (Tactic.Tac id) (cs as (pt, (p, _))) =

      let 

        val pp = Ctree.par_pblobj pt p; 

        val thy' = Ctree.get_obj Ctree.g_domID pt pp;

        val thy = ThyC.get_theory thy';

        val f = Calc.current_formula cs;

      in

        Applicable.Yes (Tactic.Tac_ (thy, UnparseC.term f, id, UnparseC.term f))

      end

  | check (Tactic.Take str) _ = Applicable.Yes (Tactic.Take' (TermC.str2term str)) (* always applicable ?*)

  | check (Tactic.Begin_Trans) cs =

      Applicable.Yes (Tactic.Begin_Trans' (Calc.current_formula cs))

  | check (Tactic.End_Trans) (pt, (p, p_)) = (*TODO: check parent branches*)

    if p_ = Pos.Res 

	  then Applicable.Yes (Tactic.End_Trans' (Ctree.get_obj Ctree.g_result pt p))

    else Applicable.No "'End_Trans' is not applicable at the beginning of a transitive sequence"

  | check Tactic.End_Proof' _ = Applicable.Yes Tactic.End_Proof''

  | check m _ = raise ERROR ("Solve_Step.check called for " ^ Tactic.input_to_string m);

(** Solve_Step.add **)

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

    (case topt of 

      SOME t => 

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

        in (pos, c, Test_Out.EmptyMout, pt) end

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

  | add (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) = Ctree.cappend_form pt p l t

    in

      ((p, Pos.Frm), c, Test_Out.FormKF (UnparseC.term t), pt)

    end

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

    let

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

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

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

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

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

    in

      ((p, Pos.Frm), c @ c', Test_Out.FormKF (UnparseC.term t), pt)

    end

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

    (*append after existing PrfObj    vvvvvvvvvvvvv*)

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

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

    let

      val p' = Pos.lev_up p

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

    in

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

    end

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

    let

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

        (Tactic.Rewrite_Inst (Subst.T_to_input subs', thm')) (f',asm) Ctree.Complete;

      val pt = Ctree.update_branch pt p Ctree.TransitiveB

    in

      ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term f'), pt)

    end

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

   let

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

     val pt = Ctree.update_branch pt p Ctree.TransitiveB

   in

    ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term f'), pt)

   end

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

    let

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

        (Tactic.Rewrite_Set_Inst (Subst.T_to_input subs', Rule_Set.id rls')) (f', asm) Ctree.Complete

      val pt = Ctree.update_branch pt p Ctree.TransitiveB

    in

      ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term f'), pt)

    end

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

    let

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

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

      val pt = Ctree.update_branch pt p Ctree.TransitiveB

    in

      ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term f'), pt)

    end

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

      let

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

      in

        ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term scval), pt)

      end

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

      let

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

      in

        ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term f'), pt)

      end

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

      let

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

      in

        ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term f'), pt)

      end

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

      let

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

      in

        ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term list), pt)

      end

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

      let

        val (pt,c) =

          Ctree.cappend_atomic pt p l t (Tactic.Substitute (Subst.eqs_to_input subte)) (t',[]) Ctree.Complete

        in ((p, Pos.Res), c, Test_Out.FormKF (UnparseC.term t'), pt) 

        end

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

      let

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

      in

        ((p,Pos.Res), c, Test_Out.FormKF f', pt)

      end

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

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

      let

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

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

  	    val f = Syntax.string_of_term ctxt f

      in

        ((p, Pos.Pbl), c, Test_Out.FormKF f, pt)

      end

  | add m' _ (_, pos) =

      raise ERROR ("Solve_Step.add: not impl.for " ^ Tactic.string_of m' ^ " at " ^ Pos.pos'2str pos)

(* LI switches between solve-phase and specify-phase *)

fun add_general tac ic cs =

  if Tactic.for_specify' tac

  then Specify_Step.add tac ic cs

  else add tac ic cs

(* the order of State_Steps is reversed: insert last element first  *)

fun s_add_general [] ptp = ptp

  | s_add_general tacis (pt, c, _) = 

    let

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

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

    in

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

    end

(* a still undeveloped concept: do a calculation without LI *)

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

  let  

    val p = case p_ of

      Pos.Frm => p | Pos.Res => Pos.lev_on p

    | _ => raise ERROR ("generate_hard: call by " ^ Pos.pos'2str (p,p_))

  in

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

  end

(**)end(**);