(* Title:  Specify/pre-conds.sml

    Author: Walther Neuper 110226

    (c) due to copyrigh,t terms

 *)

 signature PRE_CONDITIONS =

 sig

   type T

   type unchecked

   type unchecked_pos

   type checked

   type checked_pos

   type env_subst

   type env_eval

   type input

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

   val eval: Proof.context -> Rule_Set.T -> bool * term -> bool * term

   val max_variant: Model_Def.i_model -> Model_Def.variant

   val environment_TEST: Model_Pattern.T -> Model_Def.i_model_TEST -> Env.T

 (*TODO: replace in pre-conditions.m, see fun max_variants + make_envs_preconds,

   see i-model.sml (** complete I_Model.T **) *)

   val of_max_variant: Model_Pattern.T -> Model_Def.i_model_TEST ->

        (bool * Model_Def.variant * Model_Def.i_model_TEST) * Env.T * (env_subst * env_eval)

   val make_envs_preconds: (Model_Pattern.single * Model_Def.i_model_single_TEST) list ->

     ((term * term) * (term * term)) list

   val check_pos: Proof.context -> Rule_Set.T -> unchecked_pos -> 

     Model_Pattern.T * Model_Def.i_model_TEST -> checked_pos

   val check_envs: Proof.context -> Rule_Set.T -> unchecked -> Env.T * (env_subst * env_eval)

     -> checked

   val check: Proof.context -> Rule_Set.T -> unchecked ->

     Model_Pattern.T * Model_Def.i_model_TEST -> checked

 (*from isac_test for Minisubpbl*)

   val get_equal_descr: Model_Def.i_model_TEST -> Model_Pattern.single ->

     (Model_Pattern.single * Model_Def.i_model_single_TEST) list

   val unchecked_OLD_to_TEST: term list -> (term * Position.T) list

   val all_lhs_atoms: term list -> bool

   val handle_lists: term -> Model_Def.descriptor * term list -> Env.T;

   val filter_variants': Model_Def.i_model_TEST -> Model_Def.variant -> Model_Def.i_model_TEST

   val switch_type: Model_Def.descriptor -> term list -> Model_Def.descriptor;

   val discern_feedback: term -> Model_Def.i_model_feedback_TEST ->

     ((term * term) * (term * term)) list

   val discern_typ: term -> Model_Pattern.descriptor * term list ->

     ((term * term) * (term * term)) list

   val mk_env_model: term -> Model_Def.i_model_feedback_TEST -> Env.T

   val make_env_model: (Model_Pattern.single * Model_Def.i_model_single_TEST) list -> Env.T

   val get_descr: Model_Def.i_model_single_TEST -> Model_Def.descriptor option;

   val get_dscr': Model_Def.i_model_feedback_TEST -> Model_Def.descriptor option

   val get_descr_vnt: Model_Def.descriptor -> Model_Def.variants -> Model_Def.i_model_TEST ->

     Model_Def.i_model_single_TEST

   val get_descr_vnt': Model_Def.i_model_feedback_TEST -> Model_Def.variants -> O_Model.T ->

     O_Model.T

 \<^isac_test>\<open>

 (**)

 \<close>

 end

 (**)

 structure Pre_Conds(**) : PRE_CONDITIONS(**) =

 struct

 (**)

 open Model_Def

 type T = Pre_Conds_Def.T;  (*= (bool * term) list;*)

 type unchecked = term list

 type unchecked_pos = (term * Position.T) list

 type checked = bool * (bool * term) list

 type checked_pos = bool * ((bool * (term * Position.T)) list)

 (* 

   we have three kinds of Env.T in the specification-phase:

 (*1*) Env.T produced by I_Model.of_max_variant and required to create O_Model.T, I_Model.T from

     Model_Pattern.T.

                        Env.T                  / (Constants, fixes)  in Model_Pattern.T

                        e.g.[(fixes, [r = 7])] |

                                               > (Constants, [<r = 7>]) in O/I_Model.T       *)

 (*2*) type env_subst = Env.T (*               / 0 < fixes           in Problem.{where_, ...}

                        eg. [(fixes, r)]       |

                                               > 0 < r *)

 (*3*) type env_eval =  Env.T (*               |

                        eg. [(r, 7)]           |

                                               > 0 < 7 \<longrightarrow> true

   (*1*) is required to produce (*2*) and (*3*); thus respective code is shifted to Pre_Conds.

   (*2*) and (*3*) is produced from I_Model.of_max_variant by restricting to "#Given".

   There is a typing problem, probably to be solved by a language for Specification in the future:

   term <fixes> in (*1*) has type "bool list"

   term <fixes> in (*2*) has type "real". So for the transition from (*1*) to (*2..3*)

     fun switch_type is required.

   The transition requires better modelling by a novel language for Specification.

 *)

 type input = TermC.as_string list;

 (** tools **)

 fun to_str ctxt (b, t) = pair2str (bool2str b, UnparseC.term ctxt t);

 fun to_string ctxt pres = strs2str' (map (linefeed o (to_str ctxt)) pres);

 fun eval _ _ (false, where_) = (false, where_) (*NOT ALL Free's have been substituted*)

   | eval ctxt where_rls (true, where_) =

     if Rewrite.eval_true ctxt [where_] where_rls

     then (true, where_)

     else (false, where_);

 (** find the maximal variant within an I_Model.T **)

 (* old code before I_Model.T_TEST *)

 (*ATTENTION: misses variants with equal number of items, etc*)

 fun cnt itms v = (v, (length o (filter (curry op = v)) o flat o (map (fn (_, vrs, _, _, _) => vrs))) itms);

 fun count_variants vts itms = map (cnt itms) vts;

 fun max_list [] = raise ERROR "max_list of []"

   | max_list (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;

 (*find most frequent variant v in itms*)

 fun variants itms = ((distinct op =) o flat o (map (fn (_, vrs, _, _, _) => vrs))) itms;

 (*find the variant with most items already input, without Pre_Conds (of_max_variant)*)

 (*T_TESTold \<rightarrow> fun max_variants*)

 fun max_variant itms = 

     let val vts = (count_variants (variants itms)) itms;

     in if vts = [] then 0 else (fst o max_list) vts end;

 (* new code with I_Model.T_TEST proper handling variants *)

 (*get descriptor of those items which can contribute to Subst.T and Env.T*)

 (*  get_dscr: feedback_TEST -> descriptor option*)

 fun get_dscr' (Cor_TEST (descr, _)) = SOME descr

   | get_dscr' (Inc_TEST (descr, _)) = SOME descr

   | get_dscr' (Sup_TEST (descr, _)) = SOME descr

   | get_dscr' _ = NONE

     (*other feedback cannot contribute to I_Model.mk_env_TEST and Pre_Conds.mk_env_TEST*)

 (*  get_descr: I_Model.single_TEST -> descriptor option*)

 fun get_descr (_, _, _, _, (feedb, _)) =

   case get_dscr' feedb of NONE => NONE | some_descr => some_descr

 (*  get_equal_descr: I_Model.T_TEST -> Model_Pattern.single -> (Model_Pattern.single * I_Model.single_TEST) list*)

 fun get_equal_descr i_model (m_patt_single as (_, (descr, _))) =

   let

     val equal_variants = 

       filter (fn i_single => case get_descr i_single of

           NONE => false (*--------vvvvv*)

         | SOME descr' => descr' = descr) (*probl_POS*) i_model

     in

       (map (pair m_patt_single) equal_variants)

     end

 (*get an appropriate (description, variant) item from pbl_imod, otherwise return empty item*)

 fun get_descr_vnt descr vnts i_model =

   let

     val equal_descr = filter (fn (_, _, _, _, (feedb, _)) => case get_dscr' feedb of NONE => false

       | SOME descr' => if descr = descr' then true else false) i_model 

   in

     case filter (fn (_, vnts', _, _, _) => inter op= vnts' vnts <> []) equal_descr of

       [] => (0, [], false, "i_model_empty", (Sup_TEST (descr, []), Position.none))

     | items => Library.the_single items (*only applied to model_patt, which has each descr once*)

   end

 (*

   get an appropriate (description, variant) item from o_model;

   called in case of item in met_imod is_empty_single_TEST

   (i.e. was not transferred pbl_mod by \<open>fun get_descr_vnt\<close>).

 *)

 fun get_descr_vnt' feedb vnts o_model =

   filter (fn (_, vnts', _, descr', _) =>

     case get_dscr' feedb of

       SOME descr => if descr' = descr andalso inter op= vnts' vnts <> [] then true else false

     | NONE => false) o_model

 (*  all_lhs_atoms: term list -> bool*)

 fun all_lhs_atoms ts = fold (curry and_) (map (fn t =>

   if can TermC.lhs t andalso not (TermC.is_num (TermC.lhs t))

   then TermC.is_atom (TermC.lhs t)

   else false) ts) true

 fun handle_lists id (descr, ts) =

   if Model_Pattern.is_list_descr descr

   then if length ts > 1         (*list with more than 1 element needs to collect by [.., .., ..]*)

     then if TermC.is_list (hd ts) (*---broken elementwise input to lists---*)

       then [(id, TermC.list2isalist (Model_Pattern.typ_of_element descr) (map TermC.the_single ts))]

       else [(id, TermC.list2isalist (Model_Pattern.typ_of_element descr) ts)] (*AdditValues [u, v]*)

     else if TermC.is_atom (Library.the_single ts)

       then [(id, Library.the_single ts)]                                     (* solutions L, ...*)

       else [(id, TermC.list2isalist (Model_Pattern.typ_of_element descr) ts)](*Constants [r = 7]*)

   else [(id, Library.the_single ts)]                           (* solveFor x, Extremum (A = ...)*)

 fun mk_env_model _ (Model_Def.Cor_TEST (_, [])) = []

   | mk_env_model id (Model_Def.Cor_TEST (descr, ts)) = 

     handle_lists id (descr, ts)

   | mk_env_model _ (Model_Def.Syn_TEST _) = [] (*TODO handle correct list elements*)

   | mk_env_model _ (Model_Def.Inc_TEST (_, [])) = []

   | mk_env_model id (Model_Def.Inc_TEST (descr, ts)) = 

     handle_lists id (descr, ts)

   | mk_env_model _ (Model_Def.Sup_TEST _) = []

 fun make_env_model equal_descr_pairs =

   map (fn ((_, (_, id)), (_, _, _, _, (feedb, _)))

         => (mk_env_model id feedb)) equal_descr_pairs

   |> flat

 fun switch_type descr [] = descr

   | switch_type (Free (id_string, _)) ts =

     Free (id_string, ts |> hd |> TermC.lhs |> type_of)

   | switch_type descr _ = raise ERROR ("switch_type undefined argument " ^

       quote (UnparseC.term (ContextC.for_ERROR ()) descr))

 fun discern_typ _ (_, []) = []

   | discern_typ id (descr, ts) =

 (*TODO.md "review (descriptor, ts)" REMOVE--------------------------------------\*)

     let

       val ts = if Model_Pattern.is_list_descr descr

         then if TermC.is_list (hd ts)

           then ts |> map TermC.isalist2list |> flat

           else ts

         else ts

     in

 (*TODO.md "review (descriptor, ts)" REMOVE--------------------------------------/*)

   if Model_Pattern.typ_of_element descr = HOLogic.boolT andalso all_lhs_atoms ts

   then

     if length ts > 1

     then (writeln "model items of type 'bool' in lists with 'lengt ts > 1' NOT YET IMPLEMENTED";

       [])

     else [((switch_type id ts, TermC.lhs (hd ts)), 

            (TermC.lhs (hd ts), TermC.rhs (hd ts)))]

   else []

 (*TODO.md "review (descriptor, ts)" REMOVE--------------------------------------\*)

     end

 (*TODO.md "review (descriptor, ts)" REMOVE--------------------------------------/*)

 (*T_TESTnew*)

 fun discern_feedback id (Model_Def.Cor_TEST (descr, ts)) = discern_typ id (descr, ts)

   | discern_feedback _ (Model_Def.Syn_TEST _) = [] (*TODO: handle correct elements*)

   | discern_feedback id (Model_Def.Inc_TEST (descr, ts)) = discern_typ id (descr, ts)

   | discern_feedback _ (Model_Def.Sup_TEST _) = []

 fun make_envs_preconds equal_givens =

   map (fn ((_, (_, id)), (_, _, _, _, (feedb, _))) => discern_feedback id feedb) equal_givens

   |> flat

 (*T_TESTold*)

 fun of_max_variant _ [] = ((false, 0, []), [], ([], []))

   | of_max_variant model_patt i_model =

  let

     val all_variants =

         map (fn (_, variants, _, _, _) => variants) i_model

         |> flat

         |> distinct op =

     val variants_separated = map (filter_variants' i_model) all_variants

     val sums_corr = map (cnt_corrects) variants_separated

     val sum_variant_s = arrange_args sums_corr (1, all_variants)

     val (_, max_variant) = hd (*..crude decision, up to improvement *)

       (sort (fn ((i, _), (j, _)) => int_ord (i, j)) sum_variant_s)

     val i_model_max =

       filter (fn (_, variants, _ , _ ,_) => member (op =) variants max_variant) i_model

     val equal_descr_pairs = map (get_equal_descr i_model) model_patt |> flat

     val env_model = make_env_model equal_descr_pairs

     val equal_givens = filter (fn ((m_field, _), _) => m_field = "#Given") equal_descr_pairs

     val subst_eval_list = make_envs_preconds equal_givens

     val (env_subst, env_eval) = split_list subst_eval_list

   in

     ((length (filter (fn (_, _, _, _, (Cor_TEST _, _)) => true | _ => false) i_model_max)

         = length model_patt, max_variant, i_model_max),

       env_model, (env_subst, env_eval))

   end

 (*T_TEST* \<longrightarrow> Model_Def)

 fun max_variants model_patt i_model =

     let

       val all_variants =

           map (fn (_, variants, _, _, _) => variants) i_model

           |> flat

           |> distinct op =

       val variants_separated = map (filter_variants' i_model) all_variants

       val sums_corr = map (cnt_corrects) variants_separated

       val sum_variant_s = arrange_args sums_corr (1, all_variants)

       val max_first = rev (sort (fn ((i, _), (j, _)) => int_ord (i, j)) sum_variant_s)

       val maxes = filter (fn (cnt, _) => curry op = (fst (hd max_first)) cnt) max_first

         |> map snd

       val option_sequence = map 

         (fn (_, vnt) => if (member (op =) maxes vnt) then SOME vnt else NONE) sum_variant_s

 (*THAT IS NONSENSE, SEE Test_Theory (*+*)if (pbl_max_imos*)

       val max_i_models = map (fn (pos_in_sum_variant_s, i_model) =>

             if is_some pos_in_sum_variant_s then i_model else [])

           (option_sequence ~~ variants_separated)

         |> filter_out (fn place_holder => place_holder = []);

 (*/-- fun make_envs_preconds: 1 max_i_model can be determined only together with meth --------\ * )

       PROBALBY FOR RE-USE:

       val option_sequence = map 

         (fn (_, vnt) => if (member (op =) maxes vnt) then SOME vnt else NONE) sum_variant_s

       val max_i_models = map (fn (pos_in_sum_variant_s, i_model) =>

             if is_some pos_in_sum_variant_s then i_model else [])

           (option_sequence ~~ variants_separated)

         |> filter_out (fn place_holder => place_holder = []);

       \<longrightarrow> [

            [(1, [1, 2, 3]), (2, [1, 2, 3]), (3, [1, 2, 3]), (4, [1, 2, 3]), (5, [1, 2])], 

            [(1, [1, 2, 3]), (2, [1, 2, 3]), (3, [1, 2, 3]), (4, [1, 2, 3]), (5, [1, 2])]]

 ------   ----------------------------------------------------------------------------------------

       val equal_descr_pairs = map (get_equal_descr (hd max_i_models)) model_patt

         |> flat (*a hack for continuing ------------^^--  "turn to PIDE", works for test example*)

       val env_model = make_env_model equal_descr_pairs

       val equal_givens = filter (fn ((m_field, _), _) => m_field = "#Given") equal_descr_pairs

       val subst_eval_list = make_envs_preconds equal_givens

       val (env_subst, env_eval) = split_list subst_eval_list

 ( *\-- fun make_envs_preconds: 1 max_i_model can be determined only together with meth --------/ *)

     in

       ((maxes, max_i_models)(*, env_model, (env_subst, env_eval)*))

 (*     (maxes, max_i_models)*)

 (*/-- fun make_envs_preconds: 1 max_i_model can be determined only together with meth --------\ * )

                              (env_model, (env_subst, env_eval)

 ( *\--fun make_envs_preconds: 1 max_i_model can be determined only together with meth --------/ *)

     end 

 ( *T_TESTnew*)

 (*extract the environment from an I_Model.of_max_variant*)

 fun environment_TEST model_patt i_model = of_max_variant model_patt i_model |> #2

 (** check pre-conditions **)

 fun check_pos ctxt where_rls where_POS (model_patt, i_model) =

     let

       val (_, _, (_, env_eval)) = of_max_variant model_patt 

         (filter (fn (_, _, _, m_field ,_) => m_field = "#Given") i_model)

       val full_subst = if env_eval = []

         then map (fn (t, pos) => ((true, t), pos)) where_POS

         else map (fn (t, pos) => (TermC.subst_atomic_all env_eval t, pos)) where_POS;

       val evals = map (fn ((bool_t), pos) => (eval ctxt where_rls bool_t, pos)) full_subst;

       val display = map (fn ((t, pos), ((bool, _), _)) => (bool, (t, pos))) (where_POS ~~ evals)

     in

       (foldl and_ (true, map (fn ((bool, _: term), _: Position.T) => bool) evals), display)

     end;

 (*takes the envs resulting from of_max_variant*)

 fun check_envs ctxt where_rls where_ (env_model, (env_subst, env_eval)) =

   let

       val pres_subst = map (TermC.subst_atomic_all env_subst) where_;

       val pres_subst_other = map (TermC.subst_atomic_all env_model) (map #2 pres_subst);

       val full_subst = if env_eval = [] then pres_subst_other

         else map (TermC.subst_atomic_all env_eval) (map #2 pres_subst_other)

       val evals = map (eval ctxt where_rls) full_subst

   in

       (foldl and_ (true, map fst evals), pres_subst_other)

   end

 (*expects the precondition from Problem, ie. needs substitution by env_model*)

 (*TODO: check shall call check_envs*)

 fun check _ _ [] _  = (true, [])

   | check ctxt where_rls where_ (model_patt, i_model) =

     let

       val (_, env_model, (env_subst, env_eval)) = of_max_variant model_patt i_model

       val pres_subst = map (TermC.subst_atomic_all env_subst) where_;

       val pres_subst_other = map (TermC.subst_atomic_all env_model) (map #2 pres_subst);

       val full_subst = if env_eval = [] then pres_subst_other

         else map (TermC.subst_atomic_all env_eval) (map #2 pres_subst_other)

       val evals = map (eval ctxt where_rls) full_subst

     in

       (foldl and_ (true, map fst evals), pres_subst_other)

     end;

 fun unchecked_OLD_to_TEST pres = map (fn t => (t, Position.none)) pres

 (**)end(**)