(* Title:  Specify/pre-conds.sml

   Author: Walther Neuper 110226

   (c) due to copyrigh,t terms

*)

signature PRE_CONDITIONS =

sig

  type T

  type unchecked

(*RENA unchecked_pos*)

  type unchecked_TEST

  type checked

(*RENA checked_pos*)

  type checked_TEST

  type env_subst

  type env_eval

  type input

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

  val max_variant: Model_Def.i_model -> Model_Def.variant

(*T_TESTold* )

  val environment: Model_Def.i_model -> Env.T

( *T_TEST*)

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

(*T_TEST*)

  (* WRONG ENVS * )

  val check: Proof.context -> Rule_Set.T -> unchecked -> Model_Def.i_model -> 'a -> checked

( **)

(*T_TESTold* )

  val check_from_store: Proof.context -> Rule_Set.T -> unchecked -> env_subst -> env_eval -> checked

( *T_TEST*)

(*RN  check_with_envs*)

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

    -> checked

(*T_TESTnew*)

(**)

  (*T_TESTold* )

  val check_TEST: Proof.context -> Rule_Set.T -> unchecked_TEST  -> env_eval -> checked_TEST

( *T_TEST*)

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

    Model_Pattern.T * Model_Def.i_model_TEST -> checked_TEST

(*T_TESTnew*)

  (*this makes the OLD tests run AFTER introduction of I_Model.T_TEST..*)

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

    Model_Pattern.T * Model_Def.i_model_TEST -> checked

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

(**)

  val feedback_TEST_to_string: Proof.context -> Model_Def.i_model_feedback_TEST -> string

(** )

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

    env_subst -> env_eval -> checked

( **)

(*val sep_variants_envs replaced by of_max_variant       TODO

    for that purpose compare with sep_variants_envs_OLD  TODO* )

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

    ((Model_Def.i_model_TEST * env_subst * env_eval) * Model_Def.variant) list

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

    env_subst * env_eval;

( **)

(*T_TESTold* )

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

    Model_Def.i_model_TEST * env_subst * env_eval

( *T_TEST*)

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

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

(*T_TESTnew*)

(*from isac_test for Minisubpbl*)

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

(** )

  val discern_feedback_subst: Model_Def.descriptor -> Model_Def.i_model_feedback_TEST -> Env.T;

  val discern_type_subst: term * term -> term list -> Env.T;

( **)

(** )

  val mk_env: Model_Def.i_model_feedback_TEST -> Env.T

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

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

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

( **)

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

    Model_Def.variant -> (Model_Pattern.single * Model_Def.i_model_single_TEST) list

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

  val arrange_args1: int list -> int * Model_Def.variant list -> (int * Model_Def.variant) list

  val cnt_corrects: Model_Def.i_model_TEST -> int

(** )

  val handle_descr_ts: term -> term list -> Env.T

  val distinguish_atoms: term list -> Env.T

( **)

(*REN type_repair_env: Env.T -> Env.T*)

  val repair_env: Env.T -> Env.T

  val all_lhs_atoms: term list -> bool

(*from isac_test for Minisubpbl*)

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

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

  val switch_type_TEST: 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

\<^isac_test>\<open>  

  val switch_type: Model_Pattern.descriptor -> typ -> Model_Pattern.descriptor

\<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_TEST = (term * Position.T) list

type checked = bool * (bool * term) list

type checked_TEST = 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;

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_);

(** old code before I_Model.T_TEST **)

(* find most frequent variant v in itms *)

(* ATTENTION

 * spurios old code

 * misses variants with equal number of items, etc

*)

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

(*version without typing problem*)

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

fun max_variant itms = 

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

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

(** )

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 [];

( **)

(** new code for I_Model.T_TEST **)

(** )

fun pen2str ctxt (t, ts) =

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

( **)

fun feedback_TEST_to_string ctxt (Cor_TEST ((d, ts), _)) = 

    "Cor_TEST " ^ UnparseC.term ctxt (Input_Descript.join (d, ts)) ^ " , pen2str"

  | feedback_TEST_to_string _ (Syn_TEST c) =

    "Syn_TEST " ^ c

  | feedback_TEST_to_string ctxt (Inc_TEST ((d, []), _)) = 

    "Inc_TEST " ^ UnparseC.term ctxt (Input_Descript.join (d, [])) ^ " " ^ 

      Model_Pattern.empty_for d

  | feedback_TEST_to_string ctxt (Inc_TEST ((d, ts), _)) =

    "Inc_TEST " ^ UnparseC.term ctxt (Input_Descript.join (d, ts)) ^ " , pen2str"

  | feedback_TEST_to_string ctxt (Sup_TEST (d, ts)) = 

    "Sup_TEST " ^ UnparseC.term ctxt (Input_Descript.join (d, ts))

(** )

fun feedback_TEST_to_string t = feedback_to_string_TEST (ContextC.for_ERROR ()) t;

( **)

(*** make environments for substituting model_pattern+program and for evaluating pre-conditions ***)

(** OLD make environment for substituting model_pattern+program and pre-conditions **)

(* make an Env.T for Prec_Conds.eval * )

fun mk_env (Model_Def.Cor_TEST ((descr, [ts]), _)) =

    let

    (*val ts = TermC.isalist2list ts*)

      val ts = if TermC.is_list ts then TermC.isalist2list ts else [ts]

    in

      (*compare Model_Pattern.empty_for*)

      case type_of descr of

        (Type ("fun", [Type ("List.list", [Type ("HOL.bool", [])]), _])) (*SideConditions \<longrightarrow> (sideconds, [(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2])*)

          => if all_atoms_OLD ts then map (fn t => (TermC.lhs t, TermC.rhs t)) ts else []

      | (Type ("fun", [Type ("List.list", [Type ("Real.real", [])]), _])) (*AdditionalValues [u, v]*)

          => []

      | (Type ("HOL.bool", [])) (*Precision (\<epsilon> = 0.01)*)

          => if all_atoms_OLD ts then map (fn t => (TermC.lhs t, TermC.rhs t)) ts else []

      | _ (*Maximum A*) => [(hd ts, TermC.empty (*dummy rhs*))]

    end

  | mk_env (Model_Def.Inc_TEST ((descr, [ts]), _)) =

    let

    (*val ts = TermC.isalist2list ts*)

      val ts = if TermC.is_list ts then TermC.isalist2list ts else [ts]

    in

      (*compare Model_Pattern.empty_for*)

      case type_of descr of

        (Type ("fun", [Type ("List.list", [Type ("HOL.bool", [])]), _])) (*SideConditions \<longrightarrow> (sideconds, [(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2])*)

          => if all_atoms_OLD ts then map (fn t => (TermC.lhs t, TermC.rhs t)) ts else []

      | (Type ("fun", [Type ("List.list", [Type ("Real.real", [])]), _])) (*AdditionalValues [u, v]*)

          => []

      | (Type ("HOL.bool", [])) (*Precision (\<epsilon> = 0.01)*)

          => if all_atoms_OLD ts then map (fn t => (TermC.lhs t, TermC.rhs t)) ts else []

      | _ (*Maximum A*) => [(hd ts, TermC.empty (*dummy rhs*))]

   end

  | mk_env (Model_Def.Sup_TEST (descr, [ts])) =      

    let

    (*val ts = TermC.isalist2list ts*)

      val ts = if TermC.is_list ts then TermC.isalist2list ts else [ts]

    in

      (*compare Model_Pattern.empty_for*)

      case type_of descr of

        (Type ("fun", [Type ("List.list", [Type ("HOL.bool", [])]), _])) (*SideConditions \<longrightarrow> (sideconds, [(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2])*)

          => if all_atoms_OLD ts then map (fn t => (TermC.lhs t, TermC.rhs t)) ts else []

      | (Type ("fun", [Type ("List.list", [Type ("Real.real", [])]), _])) (*AdditionalValues [u, v]*)

          => []

      | (Type ("HOL.bool", [])) (*Precision (\<epsilon> = 0.01)*)

          => if all_atoms_OLD ts then map (fn t => (TermC.lhs t, TermC.rhs t)) ts else []

      | _ (*Maximum A*) => [(hd ts, TermC.empty (*dummy rhs*))]

    end

  | mk_env feedb =

    raise ERROR ("mk_env not reasonable for " ^  quote (feedback_TEST_to_string feedb))

( ** )

fun mk_env_subst equal_descr_pairs =

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

        => (mk_env feedb) |> map fst (*dummy rhs dropped*)|> map (pair id)) equal_descr_pairs

  |> flat

  |> repair_env

( **)

(*fun mk_env_eval unused? DEL!* )

fun mk_env_eval equal_descr_pairs =

  map (fn (_, (_, _, _, _, (feedb, _))) => mk_env feedb) equal_descr_pairs

  |> flat

  |> filter_out (fn (_, b) => b = TermC.empty) (*drop pairs with dummy rhs*)

( **)

(*  all_atoms: term list -> bool* )

fun all_atoms ts =

  fold (curry and_) (map (fn t => TermC.is_atom t) ts) true

( **)

(*  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

(*T_TESTold* )

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

  if can TermC.lhs t then TermC.is_atom (TermC.lhs t) else false) ts) true

( *T_TEST*)

(*  distinguish_atoms: term list -> Env.T*)

(*T_TESTnew*)

(** )

fun distinguish_atoms (*[(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2], \<epsilon> = 0.01, [L]*) ts =

  if all_atoms ts

  then map (rpair TermC.empty (*dummy rhs*)) ts

  else if all_lhs_atoms ts

    then map (fn t => (TermC.lhs t, TermC.rhs t)) ts

    else []

( ** )

(*  handle_descr_ts: term -> term list -> (term * term) list*)

fun handle_descr_ts descr ts =

  (*compare Model_Pattern.empty_for*)

  case type_of descr of

    (Type ("fun", [Type ("List.list", [Type ("HOL.bool", [])]), _])) (*(SideConds [(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2]), [L]*)

      => distinguish_atoms ts

  | (Type ("fun", [Type ("List.list", [Type ("Real.real", [])]), _])) (*AdditionalValues [u, v]*)

      => if TermC.is_list (hd ts)

         then [(descr, ts |> map TermC.the_single |> TermC.list2isalist HOLogic.realT)]

         else []

  | (Type ("HOL.bool", [])) (*Precision (\<epsilon> = 0.01)*)

      => distinguish_atoms ts

  | _ (*Maximum A*) => [(hd ts, TermC.empty (*dummy rhs*))]

( **)

(** NEW make environment for substituting program and pre-conditions **)

fun switch_type (Free (id, _)) T = Free (id, T)

  | switch_type t _ = raise TERM ("switch_type not for", [t])

(*

  this repair is spurious and indicates the need for considering a separate language for Model-ing.

  E.g. "fixes" is used with 2 different types "bool list" and "real" in the problem-definition

    problem pbl_opti_univ : "univariate_calculus/Optimisation" = ..

      Given: "Constants fixes"

      Where: "0 < fixes"

      ...

     (1) Given: Const ("Input_Descript.Constants", "bool list \<Rightarrow> nam") $ Free ("fixes", "bool list")

     (2) Where: Const ("Orderings.ord_class.less", "real \<Rightarrow> real \<Rightarrow> bool") $

           Const ("Groups.zero_class.zero", "real") $ Free ("fixes", "real")

  The intermediately simplistic solution is to build a pair of environments, type env_pair,

  The simplistic design works for the instantiation of the demo-example

    "Constants [r = (7::real)]"

  but it could be extended to instantiations like

      "Constants [a = (1::real), b = (2::real)]"

    with the same Where: "0 < fixes" in the problem-definition

    if indexing / deletion of found elements from the association list is considered.

  For the purpose of future pimprovements a pair of environments, type env_pair, is built;

  where as key of the "outer" environment Free ("fixes", "real" kept to future improvements

  (by indexing "fixes_1", "fixes_2" in case the are more than one element in 

  "Input_Descript.Constants", "bool list..)

*)

fun repair_env env =

  map (fn (id_inst, val_) => (switch_type id_inst (type_of val_), val_)) env

(*  discern_type_subst: term * term -> term list -> Env.T*)

fun discern_type_subst (descr, id) ts =

  (*..compare Model_Pattern.empty_for*)

  case type_of descr of 

    (Type ("fun", [Type ("List.list", [Type ("HOL.bool", [])]), _])) (*(SideConds [(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2]), [L]*)

      => if TermC.is_list (hd ts)

         then [(id, ts |> map TermC.the_single |> TermC.list2isalist HOLogic.boolT)]

         else if length ts = 1 

           then [(id, Library.the_single ts)]

           else raise error "discern_type_subst list bool DESIGN ERROR"

  | (Type ("fun", [Type ("List.list", [Type ("Real.real", [])]), _])) (*AdditionalValues [u, v]*)

      => if TermC.is_list (hd ts)

         then [(id, ts |> map TermC.the_single |> TermC.list2isalist HOLogic.realT)]

         else if length ts = 1 

           then [(id, Library.the_single ts)]

           else raise error "discern_type_subst list bool DESIGN ERROR"

  | _ (*Maximum A*) => [(id, Library.the_single ts)] (*if length ts = 1 !*)

(** )

(*  discern_feedback_subst: Model_Def.i_model_feedback_TEST -> Env.T*)

fun discern_feedback_subst id (Model_Def.Cor_TEST ((descr, [ts]), _)) =

    discern_type_subst (descr, id) [ts]

  | discern_feedback_subst id (Model_Def.Inc_TEST ((descr, [ts]), _)) =

    discern_type_subst (descr, id) [ts]

  | discern_feedback_subst id (Model_Def.Sup_TEST (descr, [ts])) =

    discern_type_subst (descr, id) [ts]

  | discern_feedback_subst id (Model_Def.Cor_TEST ((descr, (*[*)ts(*]*)), _)) =

    discern_type_subst (descr, id) ts

  | discern_feedback_subst _ feedb =

    raise ERROR ("discern_feedback_subst not reasonable for " ^ quote (feedback_TEST_to_string feedb))

fun mk_env_subst_DEL equal_descr_pairs =

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

        => (discern_feedback_subst id feedb)) equal_descr_pairs

  |> flat

  |> repair_env

( **)

(** NEW make environment for evaluating pre-conditions **)

(** )

(*  all_atoms: term list -> bool*)

fun all_atoms ts =

  fold (curry and_) (map (fn t => TermC.is_atom t) ts) true

(*  discern_atoms: term list -> (term * term) list*)

fun discern_atoms (*[(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2], \<epsilon> = 0.01, [L]*) ts =

  if all_atoms ts

  then map (rpair TermC.empty (*dummy rhs*)) ts

  else if all_lhs_atoms ts

    then map (fn t => (TermC.lhs t, TermC.rhs t)) ts

    else []

fun discern_type_eval descr ts =

  (*..compare Model_Pattern.empty_for*)

  case type_of descr of 

    (Type ("fun", [Type ("List.list", [Type ("HOL.bool", [])]), _])) (*(SideConds [(u / 2) \<up> 2 + (2 / v) \<up> 2 = r \<up> 2]), [L]*)

      => discern_atoms ts

  | (Type ("fun", [Type ("List.list", [Type ("Real.real", [])]), _])) (*AdditionalValues [u, v]*)

      => discern_atoms ts

  | _ (*Maximum A*) => discern_atoms ts

fun discern_feedback_eval (Model_Def.Cor_TEST ((descr, [ts]), _)) = discern_type_eval descr [ts]

  | discern_feedback_eval (Model_Def.Inc_TEST ((descr, [ts]), _)) = discern_type_eval descr [ts]

  | discern_feedback_eval (Model_Def.Sup_TEST (descr, [ts])) = discern_type_eval descr [ts]

  | discern_feedback_eval (Model_Def.Cor_TEST ((descr, ts), _)) = discern_type_eval descr ts

  | discern_feedback_eval feedb =

    raise ERROR ("discern_feedback_eval not defined for " ^  quote (feedback_TEST_to_string feedb))

fun mk_env_eval_DEL i_singles =

  map (fn (_, _, _, _, (feedb, _)) => discern_feedback_eval feedb) i_singles

  |> flat

  |> filter_out (fn (_, b) => b = TermC.empty) (*drop pairs with dummy rhs*)

( **)

(*** old check_variant_envs, sep_variants_envs/_OLD, of_max_variant, check/_TEST/_OLD ***)

(** )

fun check_variant_envs ctxt where_rls pres env_subst env_eval =

  let

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

    val full_subst = map (fn (bool, t) => (bool, subst_atomic env_eval t)) pres_subst

    val evals = map (eval ctxt where_rls) full_subst

  in

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

  end

( **)

(* check_variant_envs for PIDE *)

fun filter_variants pairs i = 

  filter (fn (_, (_, variants, _, _, _)) => member op= variants i) pairs

(*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' _

    (*other feedback cannot contribute to I_Model.mk_env_TEST and Pre_Conds.mk_env_TEST*) = NONE

(*  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

(** )

fun arrange_args2 [] _ _ _(*all have equal length*) = []

  | arrange_args2 (b :: bs) (c :: cs) (d :: ds) (cnt, all) =

    ((b, c, d), nth cnt all) :: (arrange_args2 bs cs ds (cnt + 1, all)) 

  | arrange_args2 _ _ _ _ = raise ERROR "I_Model.arrange_args2 UnequalLengths"

( ** )

fun sep_variants_envs model_patt i_model =

  let

    val equal_descr_pairs =

      map (get_equal_descr i_model) model_patt

      |> flat

    val all_variants =

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

        |> flat

        |> distinct op =

    val variants_separated = map (filter_variants equal_descr_pairs) all_variants

    val i_models = map (map snd) variants_separated

    val restricted_to_given = map (filter (fn ((m_field, (_, _)), (_, _, _, _, (_, _))) =>

      m_field = "#Given")) variants_separated

    val envs_subst = map mk_env_subst restricted_to_given

    val envs_eval =  map mk_env_eval restricted_to_given

  in

    arrange_args2 i_models envs_subst envs_eval (1, all_variants)

  end

( **)

(* smash all environments into one; this works only for old test before Maximum-example *)

(** )

fun sep_variants_envs_OLD model_patt i_model =

  let

    val equal_descr_pairs =

      map (get_equal_descr i_model) model_patt

      |> flat

    val all_variants =

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

        |> flat

        |> distinct op =

    val variants_separated = map (filter_variants equal_descr_pairs) all_variants

    val restricted_to_given = map (filter (fn ((m_field, (_, _)), (_, _, _, _, (_, _))) =>

      m_field = "#Given")) variants_separated

    val envs_subst = map mk_env_subst restricted_to_given

    val envs_eval =  map mk_env_eval restricted_to_given

  in

    (flat envs_subst, flat envs_eval)

  end

( **)

(** of_max_variant **)

(*T_TESTold* )

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 [(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 = ...)*)

( *T_TEST***)

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 = ...)*)

(*T_TESTnew*)

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

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

(*T_TEST.150* )

    if Model_Pattern.is_list_descr descr 

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

    else [(id, hd ts)]

( *T_TEST*)

    handle_lists id (descr, ts)

(*T_TEST.100*)

  | 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), _)) = 

(*T_TEST.150* )

    if Model_Pattern.is_list_descr descr 

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

    else [(id, hd ts)]

( *T_TEST*)

    handle_lists id (descr, ts)

(*T_TEST.100*)

  | 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_TEST descr [] = descr

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

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

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

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

(*T_TESTold* )

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

  | discern_typ id (descr, ts) =

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

    let

      val ts = if Model_Pattern.is_list_descr descr andalso TermC.is_list (hd ts)

        then TermC.isalist2list (hd ts)

        else ts

    in

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

  if Model_Pattern.typ_of_element descr = HOLogic.boolT

    andalso ts |> map TermC.lhs |> all_atoms

  then

    if length ts > 1

    then raise ERROR "model items of type 'bool' in lists with 'lengt ts > 1' NOT YET IMPLEMENTED"

    else [((switch_type_TEST 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_TEST*)

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_TEST 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

(*  filter_variants': Model_Def.i_model_TEST -> Model_Def.variant -> Model_Def.i_model_TEST*)

fun filter_variants' i_singles n = 

  filter (fn (_, variants, _, _, _) => member op= variants n) i_singles

(*arrange_args1: int list -> int * Model_Def.variant list -> (int * Model_Def.variant) list*)

fun arrange_args1 [] _ = []

  | arrange_args1 (sum :: ss) (cnt, all) = (sum, nth cnt all) :: (arrange_args1 ss (cnt + 1, all)) 

(*cnt_corrects: I_Model.T_TEST -> int*)

fun cnt_corrects i_model = 

  fold (curry op +) (map (fn (_, _, _, _, (Cor_TEST _, _)) => 1 | _ => 0) i_model) 0;

(*T_TESTold* )

fun of_max_variant model_patt i_model =

( *T_TEST*)

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

  | of_max_variant model_patt i_model =

(*T_TESTnew*)

 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_args1 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

(*T_TESTold* )

    val env_subst = mk_env_subst_DEL equal_descr_pairs

    val env_eval = mk_env_eval_DEL i_model_max

  in

    (i_model_max, env_subst, env_eval)

  end

( *T_TEST*)

    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

    (i_model_max, env_model, (env_subst, env_eval))

  end

(*T_TESTnew*)

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

(*T_TESTold* )

fun environment itms = 

  let val vt = max_variant itms

  in (flat o (map (mk_en vt))) itms end;

( *T_TEST*)

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

(*T_TEST*)

(** check pre-conditions **)

(* WRONG ENVS expects the precondition from Problem, ie. needs substitution * )

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

  | check ctxt where_rls pres pbl (_ (*I_Model.variants UNNECESSARY: I_Model.T filtered for*)) =

    let

      val env = environment pbl;

      val pres' = map (TermC.subst_atomic_all env) pres;

      val evals = map (eval ctxt where_rls) pres';

    in (foldl and_ (true, map fst evals), evals) end;

( **)

(*T_TESTold* )

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

  | check_TEST ctxt where_rls preconds env_eval =

    let

      val full_subst =

        map (fn (t, pos) => (subst_atomic env_eval t, pos)) preconds

      val evals =

        map (fn (term, pos) => (Rewrite.eval_true ctxt [term] where_rls, (term, pos))) full_subst

    in

      (foldl and_ (true, map fst evals), (map fst evals) ~~ preconds)

    end;

( *T_TEST*)

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;

(*T_TESTnew*)

(*T_TESTold* )

fun check_from_store ctxt where_rls pres env_subst env_eval =

  let

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

    val full_subst = map (fn (bool, t) => (bool, subst_atomic env_eval t)) pres_subst

    val evals = map (eval ctxt where_rls) full_subst

  in

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

  end

( *T_TEST*)

(* takes the envs resulting from of_max_variant *)

fun check_envs_TEST 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

(*T_TESTnew*)

(*  vvv-replaces-^^^*)

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

(* TODO: check_OLD shall call check_envs_TEST *)

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

  | check_OLD ctxt where_rls where_ (model_patt, i_model) =

    let

(*T_TESTold* )

      val (env_subst, env_eval) = sep_variants_envs_OLD model_patt i_model

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

      val full_subst = map (fn (bool, t) => (bool, subst_atomic env_eval t)) pres_subst

      val evals = map (eval ctxt where_rls) full_subst

    in

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

    end;

( *T_TEST*)

      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;

(*T_TESTnew*)

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

(**)end(**)