(* 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 environment: Model_Pattern.T -> Model_Def.i_model -> Env.T

   val make_environments: Model_Pattern.T -> Model_Def.i_model -> Env.T * (env_subst * env_eval)

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

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

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

     Model_Pattern.T * Model_Def.i_model -> checked_pos

   val check_internal: Proof.context -> Model_Def.i_model -> (Pos.pos_ * References_Def.id)

     -> checked

   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 -> checked

 (*/----- from isac_test for Minisubpbl*)

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

     (Model_Pattern.single * Model_Def.i_model_single) list

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

   val all_lhs_atoms: term list -> bool

   val handle_lists: term -> Model_Def.values -> Env.T

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

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

   val discern_feedback: term -> Model_Def.i_model_feedback ->

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

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

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

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

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

   val get_values: Model_Def.i_model_feedback -> Model_Def.values

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

     Model_Def.i_model_single

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

     O_Model.T

 (*\----- from isac_test for Minisubpbl*)

 \<^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 Pre_Conds.make_environments and required to create 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*) are produced from Pre_Conds.make_environments 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 **)

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

   let

     val equal_descr = 

       filter (fn i_single => case get_descr_opt i_single of

           NONE => false

         | SOME descr' => descr' = descr) i_model

     in

       (map (pair m_patt_single) equal_descr)

     end

 fun get_values (Cor (_, values)) = values

   | get_values (Syn _) = raise ERROR "Pre_Conds.get_values not for Syn"

   | get_values (Inc (_, values)) = values

   | get_values (Sup (_, values)) = values

 (*

   get an appropriate (description, variant)-item from i_model, otherwise return empty item,

   i.e. this function produces items with Sup.

 *)

 fun get_descr_vnt descr vnts i_model =

   let

     val equal_descr = filter (fn (_, _, _, _, (feedb, _)) => case get_dscr_opt 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 (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

   (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_opt 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 values = [(id, values_to_present values)]

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

   | mk_env_model id (Model_Def.Cor (_, ts)) = handle_lists id ts

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

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

   | mk_env_model id (Model_Def.Inc (_, ts)) = handle_lists id ts

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

 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_Def.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--------------------------------------/*)

 (*Tnew*)

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

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

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

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

 fun make_envs_preconds equal_givens =

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

   |> flat

 fun make_environments model_patt i_model =

   let

     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

     (env_model, (env_subst, env_eval))

   end 

 fun check_internal ctxt i_model (pbl_met, id) =

   let

     val (model, where_rls, where_) = case pbl_met of

         Pos.Pbl => let val {model, where_rls, where_, ...} = Problem.from_store ctxt id

           in (model, where_rls, where_) end

       | Pos.Met => let val {model, where_rls, where_, ...} = MethodC.from_store ctxt id

           in (model, where_rls, where_) end

       | _ => raise ERROR ("Pre_Conds.check_internal calles with " ^ Pos.pos_2str pbl_met)

     val (env_model, (env_subst, env_eval)) = make_environments model

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

 (*extract one environment rom make_environments *)

 fun environment model_patt i_model = make_environments model_patt i_model |> #1

 (** check pre-conditions **)

 fun check_pos ctxt where_rls where_ (model_patt, i_model) =

     let

       val (_, (_, env_eval)) = make_environments 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_

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

       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_ ~~ evals)

     in

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

     end;

 (*takes the envs resulting from make_environments*)

 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*)

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

   | check ctxt where_rls where_ (model_patt, i_model) =

     let

       val (env_model, (env_subst, env_eval)) = make_environments 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 pres = map (fn t => (t, Position.none)) pres

 (**)end(**)