Quelle predicate_compile_core.ML Sprache: SML

(*  Title:      HOL/Tools/Predicate_Compile/predicate_compile_core.ML
    Author:     Lukas Bulwahn, TU Muenchen

A compiler from predicates specified by intro/elim rules to equations.
*)

signature PREDICATE_COMPILE_CORE =
sig
  type seed = Random_Engine.seed
  type mode = Predicate_Compile_Aux.mode
  type options = Predicate_Compile_Aux.options
  type compilation = Predicate_Compile_Aux.compilation
  type compilation_funs = Predicate_Compile_Aux.compilation_funs

  val code_pred : options -> string -> Proof.context -> Proof.state
  val code_pred_cmd : options -> string -> Proof.context -> Proof.state
  val values_cmd : string list -> mode option list option ->
    ((string option * bool) * (compilation * int list)) -> int -> string -> Toplevel.state -> unit

  val values_timeout : real Config.T

  val print_stored_rules : Proof.context -> unit
  val print_all_modes : compilation -> Proof.context -> unit

  val put_pred_result : (unit -> term Predicate.pred) -> Proof.context -> Proof.context
  val put_pred_random_result : (unit -> seed -> term Predicate.pred * seed) ->
    Proof.context -> Proof.context
  val put_dseq_result : (unit -> term Limited_Sequence.dseq) -> Proof.context -> Proof.context
  val put_dseq_random_result :
    (unit -> Code_Numeral.natural -> Code_Numeral.natural -> seed ->
      term Limited_Sequence.dseq * seed) ->
    Proof.context -> Proof.context
  val put_new_dseq_result : (unit -> Code_Numeral.natural -> term Lazy_Sequence.lazy_sequence) ->
    Proof.context -> Proof.context
  val put_lseq_random_result :
    (unit -> Code_Numeral.natural -> Code_Numeral.natural -> seed -> Code_Numeral.natural ->
      term Lazy_Sequence.lazy_sequence) ->
    Proof.context -> Proof.context
  val put_lseq_random_stats_result :
    (unit -> Code_Numeral.natural -> Code_Numeral.natural -> seed -> Code_Numeral.natural ->
      (term * Code_Numeral.natural) Lazy_Sequence.lazy_sequence) ->
    Proof.context -> Proof.context

  val code_pred_intro_attrib : attribute
  (* used by Quickcheck_Generator *)
  (* temporary for testing of the compilation *)
  val add_equations : options -> string list -> theory -> theory
  val add_depth_limited_random_equations : options -> string list -> theory -> theory
  val add_random_dseq_equations : options -> string list -> theory -> theory
  val add_new_random_dseq_equations : options -> string list -> theory -> theory
  val add_generator_dseq_equations : options -> string list -> theory -> theory
  val add_generator_cps_equations : options -> string list -> theory -> theory
  val mk_tracing : string -> term -> term
  val prepare_intrs : options -> Proof.context -> string list -> thm list ->
    ((string * typ) list * string list * string list * (string * mode list) list *
      (string *  (Term.term list * Predicate_Compile_Aux.indprem list) list) list)
  type mode_analysis_options =
   {use_generators : bool,
    reorder_premises : bool,
    infer_pos_and_neg_modes : bool}
  datatype mode_derivation = Mode_App of mode_derivation * mode_derivation | Context of mode
    | Mode_Pair of mode_derivation * mode_derivation | Term of mode
  val head_mode_of : mode_derivation -> mode
  type moded_clause = term list * (Predicate_Compile_Aux.indprem * mode_derivation) list
  type 'a pred_mode_table = (string * ((bool * mode) * 'a) list) list

end;

structure Predicate_Compile_Core : PREDICATE_COMPILE_CORE =
struct

type random_seed = Random_Engine.seed

open Predicate_Compile_Aux;
open Mode_Inference;
open Predicate_Compile_Proof;

type seed = Random_Engine.seed;

(** fundamentals **)

(* syntactic operations *)

fun mk_eq (x, xs) =
  let fun mk_eqs _ [] = []
        | mk_eqs a (b::cs) =
            HOLogic.mk_eq (Free (a, fastype_of b), b) :: mk_eqs a cs
  in mk_eqs x xs end;

fun mk_tracing s t =
  Const(\<^const_name>\<open>Code_Evaluation.tracing\<close>,
    \<^typ>\<open>String.literal\<close> --> (fastype_of t) --> (fastype_of t)) $ (HOLogic.mk_literal s) $ t

(* representation of inferred clauses with modes *)

type moded_clause = term list * (indprem * mode_derivation) list

type 'a pred_mode_table = (string * ((bool * mode) * 'a) list) list

(* diagnostic display functions *)

fun print_modes options modes =
  if show_modes options then
    tracing ("Inferred modes:\n" ^
      cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
        (fn (p, m) => string_of_mode m ^ (if p then "pos" else "neg")) ms)) modes))
  else ()

fun print_pred_mode_table string_of_entry pred_mode_table =
  let
    fun print_mode pred ((_, mode), entry) =  "mode : " ^ string_of_mode mode
      ^ string_of_entry pred mode entry
    fun print_pred (pred, modes) =
      "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes)
    val _ = tracing (cat_lines (map print_pred pred_mode_table))
  in () end;

fun print_compiled_terms options ctxt =
  if show_compilation options then
    print_pred_mode_table (fn _ => fn _ => Syntax.string_of_term ctxt)
  else K ()

fun print_stored_rules ctxt =
  let
    val preds = Graph.keys (Core_Data.PredData.get (Proof_Context.theory_of ctxt))
    fun print pred () =
      let
        val _ = writeln ("predicate: " ^ pred)
        val _ = writeln ("introrules: ")
        val _ = fold (fn thm => fn _ => writeln (Thm.string_of_thm ctxt thm))
          (rev (Core_Data.intros_of ctxt pred)) ()
      in
        if Core_Data.has_elim ctxt pred then
          writeln ("elimrule: " ^ Thm.string_of_thm ctxt (Core_Data.the_elim_of ctxt pred))
        else
          writeln ("no elimrule defined")
      end
  in
    fold print preds ()
  end;

fun print_all_modes compilation ctxt =
  let
    val _ = writeln ("Inferred modes:")
    fun print (pred, modes) u =
      let
        val _ = writeln ("predicate: " ^ pred)
        val _ = writeln ("modes: " ^ (commas (map string_of_mode modes)))
      in u end
  in
    fold print (Core_Data.all_modes_of compilation ctxt) ()
  end

(* validity checks *)

fun check_expected_modes options _ modes =
  (case expected_modes options of
    SOME (s, ms) =>
      (case AList.lookup (op =) modes s of
        SOME modes =>
          let
            val modes' = map snd modes
          in
            if not (eq_set eq_mode (ms, modes')) then
              error ("expected modes were not inferred:\n"
              ^ " inferred modes for " ^ s ^ ": " ^ commas (map string_of_mode modes') ^ "\n"
              ^ " expected modes for " ^ s ^ ": " ^ commas (map string_of_mode ms))
            else ()
          end
        | NONE => ())
  | NONE => ())

fun check_proposed_modes options preds modes errors =
  map (fn (s, _) =>
    case proposed_modes options s of
      SOME ms =>
        (case AList.lookup (op =) modes s of
          SOME inferred_ms =>
            let
              val preds_without_modes = map fst (filter (null o snd) modes)
              val modes' = map snd inferred_ms
            in
              if not (eq_set eq_mode (ms, modes')) then
                error ("expected modes were not inferred:\n"
                ^ " inferred modes for " ^ s ^ ": " ^ commas (map string_of_mode modes') ^ "\n"
                ^ " expected modes for " ^ s ^ ": " ^ commas (map string_of_mode ms) ^ "\n"
                ^ (if show_invalid_clauses options then
                ("For the following clauses, the following modes could not be inferred: " ^ "\n"
                ^ cat_lines errors) else "") ^
                (if not (null preds_without_modes) then
                  "\n" ^ "No mode inferred for the predicates " ^ commas preds_without_modes
                else ""))
              else ()
            end
        | NONE => ())
    | NONE => ()) preds

fun check_matches_type ctxt predname T ms =
  let
    fun check (Fun (m1, m2)) (Type("fun", [T1,T2])) = check m1 T1 andalso check m2 T2
      | check m (Type("fun", _)) = (m = Input orelse m = Output)
      | check (Pair (m1, m2)) (Type (\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2])) =
          check m1 T1 andalso check m2 T2
      | check Input _ = true
      | check Output _ = true
      | check Bool \<^typ>\<open>bool\<close> = true
      | check _ _ = false
    fun check_consistent_modes ms =
      if forall (fn Fun _ => true | _ => false) ms then
        apply2 check_consistent_modes (split_list (map (fn Fun (m1, m2) => (m1, m2)) ms))
        |> (fn (res1, res2) => res1 andalso res2)
      else if forall (fn Input => true | Output => true | Pair _ => true | _ => false) ms then
        true
      else if forall (fn Bool => true | _ => false) ms then
        true
      else
        false
    val _ =
      map (fn mode =>
        if length (strip_fun_mode mode) = length (binder_types T)
          andalso (forall (uncurry check) (strip_fun_mode mode ~~ binder_types T)) then ()
        else
          error (string_of_mode mode ^ " is not a valid mode for " ^
            Syntax.string_of_typ ctxt T ^ " at predicate " ^ predname)) ms
    val _ =
      if check_consistent_modes ms then ()
      else
        error (commas (map string_of_mode ms) ^ " are inconsistent modes for predicate " ^ predname)
  in
    ms
  end

(* compilation modifiers *)

structure Comp_Mod =  (* FIXME proper signature *)
struct

datatype comp_modifiers = Comp_Modifiers of
{
  compilation : compilation,
  function_name_prefix : string,
  compfuns : compilation_funs,
  mk_random : typ -> term list -> term,
  modify_funT : typ -> typ,
  additional_arguments : string list -> term list,
  wrap_compilation : compilation_funs -> string -> typ -> mode -> term list -> term -> term,
  transform_additional_arguments : indprem -> term list -> term list
}

fun dest_comp_modifiers (Comp_Modifiers c) = c

val compilation = #compilation o dest_comp_modifiers
val function_name_prefix = #function_name_prefix o dest_comp_modifiers
val compfuns = #compfuns o dest_comp_modifiers

val mk_random = #mk_random o dest_comp_modifiers
val funT_of' = funT_of o compfuns
val modify_funT = #modify_funT o dest_comp_modifiers
fun funT_of comp mode = modify_funT comp o funT_of' comp mode

val additional_arguments = #additional_arguments o dest_comp_modifiers
val wrap_compilation = #wrap_compilation o dest_comp_modifiers
val transform_additional_arguments = #transform_additional_arguments o dest_comp_modifiers

fun set_compfuns compfuns' (Comp_Modifiers {compilation, function_name_prefix, compfuns, mk_random,
    modify_funT, additional_arguments, wrap_compilation, transform_additional_arguments}) =
    (Comp_Modifiers {compilation = compilation, function_name_prefix = function_name_prefix,
    compfuns = compfuns', mk_random = mk_random, modify_funT = modify_funT,
    additional_arguments = additional_arguments, wrap_compilation = wrap_compilation,
    transform_additional_arguments = transform_additional_arguments})

end

fun unlimited_compfuns_of true New_Pos_Random_DSeq =
      New_Pos_Random_Sequence_CompFuns.depth_unlimited_compfuns
  | unlimited_compfuns_of false New_Pos_Random_DSeq =
      New_Neg_Random_Sequence_CompFuns.depth_unlimited_compfuns
  | unlimited_compfuns_of true Pos_Generator_DSeq =
      New_Pos_DSequence_CompFuns.depth_unlimited_compfuns
  | unlimited_compfuns_of false Pos_Generator_DSeq =
      New_Neg_DSequence_CompFuns.depth_unlimited_compfuns
  | unlimited_compfuns_of _ c =
      raise Fail ("No unlimited compfuns for compilation " ^ string_of_compilation c)

fun limited_compfuns_of true Predicate_Compile_Aux.New_Pos_Random_DSeq =
      New_Pos_Random_Sequence_CompFuns.depth_limited_compfuns
  | limited_compfuns_of false Predicate_Compile_Aux.New_Pos_Random_DSeq =
      New_Neg_Random_Sequence_CompFuns.depth_limited_compfuns
  | limited_compfuns_of true Pos_Generator_DSeq =
      New_Pos_DSequence_CompFuns.depth_limited_compfuns
  | limited_compfuns_of false Pos_Generator_DSeq =
      New_Neg_DSequence_CompFuns.depth_limited_compfuns
  | limited_compfuns_of _ c =
      raise Fail ("No limited compfuns for compilation " ^ string_of_compilation c)

val depth_limited_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Depth_Limited,
  function_name_prefix = "depth_limited_",
  compfuns = Predicate_Comp_Funs.compfuns,
  mk_random = (fn _ => error "no random generation"),
  additional_arguments = fn names =>
    let
      val depth_name = singleton (Name.variant_list names) "depth"
    in [Free (depth_name, \<^typ>\<open>natural\<close>)] end,
  modify_funT = (fn T => let val (Ts, U) = strip_type T
  val Ts' = [\<^typ>\natural\] in (Ts @ Ts') ---> U end),
  wrap_compilation =
    fn compfuns => fn s => fn T => fn mode => fn additional_arguments => fn compilation =>
    let
      val [depth] = additional_arguments
      val (_, Ts) = split_modeT mode (binder_types T)
      val T' = mk_monadT compfuns (HOLogic.mk_tupleT Ts)
      val if_const = Const (\<^const_name>\<open>If\<close>, \<^typ>\<open>bool\<close> --> T' --> T' --> T')
    in
      if_const $ HOLogic.mk_eq (depth, \<^term>\<open>0 :: natural\<close>)
        $ mk_empty compfuns (dest_monadT compfuns T')
        $ compilation
    end,
  transform_additional_arguments =
    fn _ => fn additional_arguments =>
    let
      val [depth] = additional_arguments
      val depth' =
        Const (\<^const_name>\<open>Groups.minus\<close>, \<^typ>\<open>natural => natural => natural\<close>)
          $ depth $ Const (\<^const_name>\<open>Groups.one\<close>, \<^typ>\<open>natural\<close>)
    in [depth'] end
  }

val random_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Random,
  function_name_prefix = "random_",
  compfuns = Predicate_Comp_Funs.compfuns,
  mk_random = (fn T => fn additional_arguments =>
  list_comb (Const(\<^const_name>\<open>Random_Pred.iter\<close>,
  [\<^typ>\<open>natural\<close>, \<^typ>\<open>natural\<close>, \<^typ>\<open>Random.seed\<close>] --->
    Predicate_Comp_Funs.mk_monadT T), additional_arguments)),
  modify_funT = (fn T =>
    let
      val (Ts, U) = strip_type T
      val Ts' = [\<^typ>\natural\, \<^typ>\natural\, \<^typ>\Random.seed\]
    in (Ts @ Ts') ---> U end),
  additional_arguments = (fn names =>
    let
      val [nrandom, size, seed] = Name.variant_list names ["nrandom", "size", "seed"]
    in
      [Free (nrandom, \<^typ>\<open>natural\<close>), Free (size, \<^typ>\<open>natural\<close>),
        Free (seed, \<^typ>\<open>Random.seed\<close>)]
    end),
  wrap_compilation = K (K (K (K (K I))))
    : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val depth_limited_random_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Depth_Limited_Random,
  function_name_prefix = "depth_limited_random_",
  compfuns = Predicate_Comp_Funs.compfuns,
  mk_random = (fn T => fn additional_arguments =>
  list_comb (Const(\<^const_name>\<open>Random_Pred.iter\<close>,
  [\<^typ>\<open>natural\<close>, \<^typ>\<open>natural\<close>, \<^typ>\<open>Random.seed\<close>] --->
    Predicate_Comp_Funs.mk_monadT T), tl additional_arguments)),
  modify_funT = (fn T =>
    let
      val (Ts, U) = strip_type T
      val Ts' = [\<^typ>\natural\, \<^typ>\natural\, \<^typ>\natural\,
        \<^typ>\<open>Random.seed\<close>]
    in (Ts @ Ts') ---> U end),
  additional_arguments = (fn names =>
    let
      val [depth, nrandom, size, seed] = Name.variant_list names ["depth", "nrandom", "size", "seed"]
    in
      [Free (depth, \<^typ>\<open>natural\<close>), Free (nrandom, \<^typ>\<open>natural\<close>),
        Free (size, \<^typ>\<open>natural\<close>), Free (seed, \<^typ>\<open>Random.seed\<close>)]
    end),
  wrap_compilation =
  fn compfuns => fn _ => fn T => fn mode => fn additional_arguments => fn compilation =>
    let
      val depth = hd (additional_arguments)
      val (_, Ts) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE))
        mode (binder_types T)
      val T' = mk_monadT compfuns (HOLogic.mk_tupleT Ts)
      val if_const = Const (\<^const_name>\<open>If\<close>, \<^typ>\<open>bool\<close> --> T' --> T' --> T')
    in
      if_const $ HOLogic.mk_eq (depth, \<^term>\<open>0 :: natural\<close>)
        $ mk_empty compfuns (dest_monadT compfuns T')
        $ compilation
    end,
  transform_additional_arguments =
    fn _ => fn additional_arguments =>
    let
      val [depth, nrandom, size, seed] = additional_arguments
      val depth' =
        Const (\<^const_name>\<open>Groups.minus\<close>, \<^typ>\<open>natural => natural => natural\<close>)
          $ depth $ Const (\<^const_name>\<open>Groups.one\<close>, \<^typ>\<open>natural\<close>)
    in [depth', nrandom, size, seed] end
}

val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Pred,
  function_name_prefix = "",
  compfuns = Predicate_Comp_Funs.compfuns,
  mk_random = (fn _ => error "no random generation"),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = DSeq,
  function_name_prefix = "dseq_",
  compfuns = DSequence_CompFuns.compfuns,
  mk_random = (fn _ => error "no random generation in dseq"),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val pos_random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Pos_Random_DSeq,
  function_name_prefix = "random_dseq_",
  compfuns = Random_Sequence_CompFuns.compfuns,
  mk_random = (fn T => fn _ =>
  let
    val random = Const (\<^const_name>\<open>Quickcheck_Random.random\<close>,
      \<^typ>\<open>natural\<close> --> \<^typ>\<open>Random.seed\<close> -->
        HOLogic.mk_prodT (HOLogic.mk_prodT (T, \<^typ>\<open>unit => term\<close>), \<^typ>\<open>Random.seed\<close>))
  in
    Const (\<^const_name>\<open>Random_Sequence.Random\<close>, (\<^typ>\<open>natural\<close> --> \<^typ>\<open>Random.seed\<close> -->
      HOLogic.mk_prodT (HOLogic.mk_prodT (T, \<^typ>\<open>unit => term\<close>), \<^typ>\<open>Random.seed\<close>)) -->
      Random_Sequence_CompFuns.mk_random_dseqT T) $ random
  end),

  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val neg_random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Neg_Random_DSeq,
  function_name_prefix = "random_dseq_neg_",
  compfuns = Random_Sequence_CompFuns.compfuns,
  mk_random = (fn _ => error "no random generation"),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val new_pos_random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = New_Pos_Random_DSeq,
  function_name_prefix = "new_random_dseq_",
  compfuns = New_Pos_Random_Sequence_CompFuns.depth_limited_compfuns,
  mk_random = (fn T => fn _ =>
  let
    val random = Const (\<^const_name>\<open>Quickcheck_Random.random\<close>,
      \<^typ>\<open>natural\<close> --> \<^typ>\<open>Random.seed\<close> -->
        HOLogic.mk_prodT (HOLogic.mk_prodT (T, \<^typ>\<open>unit => term\<close>), \<^typ>\<open>Random.seed\<close>))
  in
    Const (\<^const_name>\<open>Random_Sequence.pos_Random\<close>, (\<^typ>\<open>natural\<close> --> \<^typ>\<open>Random.seed\<close> -->
      HOLogic.mk_prodT (HOLogic.mk_prodT (T, \<^typ>\<open>unit => term\<close>), \<^typ>\<open>Random.seed\<close>)) -->
      New_Pos_Random_Sequence_CompFuns.mk_pos_random_dseqT T) $ random
  end),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val new_neg_random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = New_Neg_Random_DSeq,
  function_name_prefix = "new_random_dseq_neg_",
  compfuns = New_Neg_Random_Sequence_CompFuns.depth_limited_compfuns,
  mk_random = (fn _ => error "no random generation"),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val pos_generator_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Pos_Generator_DSeq,
  function_name_prefix = "generator_dseq_",
  compfuns = New_Pos_DSequence_CompFuns.depth_limited_compfuns,
  mk_random =
    (fn T => fn _ =>
      Const (\<^const_name>\<open>Lazy_Sequence.small_lazy_class.small_lazy\<close>,
        \<^typ>\<open>natural\<close> --> Type (\<^type_name>\<open>Lazy_Sequence.lazy_sequence\<close>, [T]))),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val neg_generator_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Neg_Generator_DSeq,
  function_name_prefix = "generator_dseq_neg_",
  compfuns = New_Neg_DSequence_CompFuns.depth_limited_compfuns,
  mk_random = (fn _ => error "no random generation"),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val pos_generator_cps_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Pos_Generator_CPS,
  function_name_prefix = "generator_cps_pos_",
  compfuns = Pos_Bounded_CPS_Comp_Funs.compfuns,
  mk_random =
    (fn T => fn _ =>
       Const (\<^const_name>\<open>Quickcheck_Exhaustive.exhaustive\<close>,
       (T --> \<^typ>\<open>(bool * term list) option\<close>) -->
         \<^typ>\<open>natural => (bool * term list) option\<close>)),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

val neg_generator_cps_comp_modifiers = Comp_Mod.Comp_Modifiers
  {
  compilation = Neg_Generator_CPS,
  function_name_prefix = "generator_cps_neg_",
  compfuns = Neg_Bounded_CPS_Comp_Funs.compfuns,
  mk_random = (fn _ => error "No enumerators"),
  modify_funT = I,
  additional_arguments = K [],
  wrap_compilation = K (K (K (K (K I))))
   : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
  transform_additional_arguments = K I : (indprem -> term list -> term list)
  }

fun negative_comp_modifiers_of comp_modifiers =
  (case Comp_Mod.compilation comp_modifiers of
    Pos_Random_DSeq => neg_random_dseq_comp_modifiers
  | Neg_Random_DSeq => pos_random_dseq_comp_modifiers
  | New_Pos_Random_DSeq => new_neg_random_dseq_comp_modifiers
  | New_Neg_Random_DSeq => new_pos_random_dseq_comp_modifiers
  | Pos_Generator_DSeq => neg_generator_dseq_comp_modifiers
  | Neg_Generator_DSeq => pos_generator_dseq_comp_modifiers
  | Pos_Generator_CPS => neg_generator_cps_comp_modifiers
  | Neg_Generator_CPS => pos_generator_cps_comp_modifiers
  | _ => comp_modifiers)

(* term construction *)

fun mk_v (names, vs) s T =
  (case AList.lookup (op =) vs s of
    NONE => (Free (s, T), (names, (s, [])::vs))
  | SOME xs =>
      let
        val s' = singleton (Name.variant_list names) s;
        val v = Free (s', T)
      in
        (v, (s'::names, AList.update (op =) (s, v::xs) vs))
      end);

fun distinct_v (Free (s, T)) nvs = mk_v nvs s T
  | distinct_v (t $ u) nvs =
      let
        val (t', nvs') = distinct_v t nvs;
        val (u', nvs'') = distinct_v u nvs';
      in (t' $ u', nvs'') end
  | distinct_v x nvs = (x, nvs);

(** specific rpred functions -- move them to the correct place in this file *)
fun mk_Eval_of (P as (Free _), T) mode =
  let
    fun mk_bounds (Type (\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2])) i =
          let
            val (bs2, i') = mk_bounds T2 i
            val (bs1, i'') = mk_bounds T1 i'
          in
            (HOLogic.pair_const T1 T2 $ bs1 $ bs2, i'' + 1)
          end
      | mk_bounds _ i = (Bound i, i + 1)
    fun mk_prod ((t1, T1), (t2, T2)) = (HOLogic.pair_const T1 T2 $ t1 $ t2, HOLogic.mk_prodT (T1, T2))
    fun mk_tuple [] = (HOLogic.unit, HOLogic.unitT)
      | mk_tuple tTs = foldr1 mk_prod tTs
    fun mk_split_abs (T as Type (\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2])) t =
          absdummy T
            (HOLogic.case_prod_const (T1, T2, \<^typ>\<open>bool\<close>) $ (mk_split_abs T1 (mk_split_abs T2 t)))
      | mk_split_abs T t = absdummy T t
    val args = rev (fst (fold_map mk_bounds (rev (binder_types T)) 0))
    val (inargs, outargs) = split_mode mode args
    val (_, outTs) = split_map_modeT (fn _ => fn T => (SOME T, NONE)) mode (binder_types T)
    val inner_term = Predicate_Comp_Funs.mk_Eval (list_comb (P, inargs), fst (mk_tuple (outargs ~~ outTs)))
  in
    fold_rev mk_split_abs (binder_types T) inner_term
  end

fun compile_arg compilation_modifiers _ _ param_modes arg =
  let
    fun map_params (t as Free (f, T)) =
          (case (AList.lookup (op =) param_modes f) of
              SOME mode =>
                let
                  val T' = Comp_Mod.funT_of compilation_modifiers mode T
                in
                  mk_Eval_of (Free (f, T'), T) mode
                end
          | NONE => t)
      | map_params t = t
  in
    map_aterms map_params arg
  end

fun compile_match compilation_modifiers additional_arguments ctxt param_modes
      eqs eqs' out_ts success_t =
  let
    val compfuns = Comp_Mod.compfuns compilation_modifiers
    val eqs'' = maps mk_eq eqs @ eqs'
    val eqs'' =
      map (compile_arg compilation_modifiers additional_arguments ctxt param_modes) eqs''
    val names = fold Term.add_free_names (success_t :: eqs'' @ out_ts) [];
    val name = singleton (Name.variant_list names) "x";
    val name' = singleton (Name.variant_list (name :: names)) "y";
    val T = HOLogic.mk_tupleT (map fastype_of out_ts);
    val U = fastype_of success_t;
    val U' = dest_monadT compfuns U;
    val v = Free (name, T);
    val v' = Free (name', T);
  in
    lambda v (Case_Translation.make_case ctxt Case_Translation.Quiet Name.context v
      [(HOLogic.mk_tuple out_ts,
        if null eqs'' then success_t
        else Const (\<^const_name>\<open>HOL.If\<close>, HOLogic.boolT --> U --> U --> U) $
          foldr1 HOLogic.mk_conj eqs'' $ success_t $
            mk_empty compfuns U'),
       (v', mk_empty compfuns U')])
  end;

fun compile_expr compilation_modifiers ctxt (t, deriv) param_modes additional_arguments =
  let
    val compfuns = Comp_Mod.compfuns compilation_modifiers
    fun expr_of (t, deriv) =
      (case (t, deriv) of
        (t, Term Input) =>
          SOME (compile_arg compilation_modifiers additional_arguments ctxt param_modes t)
      | (_, Term Output) => NONE
      | (Const (name, T), Context mode) =>
          (case Core_Data.alternative_compilation_of ctxt name mode of
            SOME alt_comp => SOME (alt_comp compfuns T)
          | NONE =>
            SOME (Const (Core_Data.function_name_of (Comp_Mod.compilation compilation_modifiers)
              ctxt name mode,
              Comp_Mod.funT_of compilation_modifiers mode T)))
      | (Free (s, T), Context m) =>
          (case (AList.lookup (op =) param_modes s) of
            SOME _ => SOME (Free (s, Comp_Mod.funT_of compilation_modifiers m T))
          | NONE =>
              let
                val bs = map (pair "x") (binder_types (fastype_of t))
                val bounds = map Bound (rev (0 upto (length bs) - 1))
              in SOME (fold_rev Term.abs bs (mk_if compfuns (list_comb (t, bounds)))) end)
      | (t, Context _) =>
          let
            val bs = map (pair "x") (binder_types (fastype_of t))
            val bounds = map Bound (rev (0 upto (length bs) - 1))
          in SOME (fold_rev Term.abs bs (mk_if compfuns (list_comb (t, bounds)))) end
      | (Const (\<^const_name>\<open>Pair\<close>, _) $ t1 $ t2, Mode_Pair (d1, d2)) =>
          (case (expr_of (t1, d1), expr_of (t2, d2)) of
            (NONE, NONE) => NONE
          | (NONE, SOME t) => SOME t
          | (SOME t, NONE) => SOME t
          | (SOME t1, SOME t2) => SOME (HOLogic.mk_prod (t1, t2)))
      | (t1 $ t2, Mode_App (deriv1, deriv2)) =>
          (case (expr_of (t1, deriv1), expr_of (t2, deriv2)) of
            (SOME t, NONE) => SOME t
           | (SOME t, SOME u) => SOME (t $ u)
           | _ => error "something went wrong here!"))
  in
    list_comb (the (expr_of (t, deriv)), additional_arguments)
  end

fun compile_clause compilation_modifiers ctxt all_vs param_modes additional_arguments
  inp (in_ts, out_ts) moded_ps =
  let
    val compfuns = Comp_Mod.compfuns compilation_modifiers
    val compile_match = compile_match compilation_modifiers
      additional_arguments ctxt param_modes
    val (in_ts', (all_vs', eqs)) =
      fold_map (collect_non_invertible_subterms ctxt) in_ts (all_vs, []);
    fun compile_prems out_ts' vs names [] =
          let
            val (out_ts'', (names', eqs')) =
              fold_map (collect_non_invertible_subterms ctxt) out_ts' (names, []);
            val (out_ts''', (_, constr_vs)) = fold_map distinct_v
              out_ts'' (names', map (rpair []) vs);
            val processed_out_ts = map (compile_arg compilation_modifiers additional_arguments
              ctxt param_modes) out_ts
          in
            compile_match constr_vs (eqs @ eqs') out_ts'''
              (mk_single compfuns (HOLogic.mk_tuple processed_out_ts))
          end
      | compile_prems out_ts vs names ((p, deriv) :: ps) =
          let
            val vs' = distinct (op =) (flat (vs :: map term_vs out_ts));
            val (out_ts', (names', eqs)) =
              fold_map (collect_non_invertible_subterms ctxt) out_ts (names, [])
            val (out_ts'', (names'', constr_vs')) = fold_map distinct_v
              out_ts' ((names', map (rpair []) vs))
            val mode = head_mode_of deriv
            val additional_arguments' =
              Comp_Mod.transform_additional_arguments compilation_modifiers p additional_arguments
            val (compiled_clause, rest) =
              (case p of
                Prem t =>
                  let
                    val u =
                      compile_expr compilation_modifiers ctxt (t, deriv)
                       param_modes additional_arguments'
                    val (_, out_ts''') = split_mode mode (snd (strip_comb t))
                    val rest = compile_prems out_ts''' vs' names'' ps
                  in
                    (u, rest)
                  end
              | Negprem t =>
                  let
                    val neg_compilation_modifiers =
                      negative_comp_modifiers_of compilation_modifiers
                    val u =
                     mk_not compfuns
                       (compile_expr neg_compilation_modifiers ctxt (t, deriv)
                         param_modes additional_arguments')
                    val (_, out_ts''') = split_mode mode (snd (strip_comb t))
                    val rest = compile_prems out_ts''' vs' names'' ps
                  in
                    (u, rest)
                  end
              | Sidecond t =>
                  let
                    val t = compile_arg compilation_modifiers additional_arguments
                      ctxt param_modes t
                    val rest = compile_prems [] vs' names'' ps;
                  in
                    (mk_if compfuns t, rest)
                  end
              | Generator (v, T) =>
                  let
                    val u = Comp_Mod.mk_random compilation_modifiers T additional_arguments
                    val rest = compile_prems [Free (v, T)]  vs' names'' ps;
                  in
                    (u, rest)
                  end)
          in
            compile_match constr_vs' eqs out_ts''
              (mk_bind compfuns (compiled_clause, rest))
          end
    val prem_t = compile_prems in_ts' (map fst param_modes) all_vs' moded_ps
  in
    mk_bind compfuns (mk_single compfuns inp, prem_t)
  end

(* switch detection *)

(** argument position of an inductive predicates and the executable functions **)

type position = int * int list

fun input_positions_pair Input = [[]]
  | input_positions_pair Output = []
  | input_positions_pair (Fun _) = []
  | input_positions_pair (Pair (m1, m2)) =
      map (cons 1) (input_positions_pair m1) @ map (cons 2) (input_positions_pair m2)

fun input_positions_of_mode mode =
  flat
    (map_index
      (fn (i, Input) => [(i, [])]
        | (_, Output) => []
        | (_, Fun _) => []
        | (i, m as Pair _) => map (pair i) (input_positions_pair m))
      (Predicate_Compile_Aux.strip_fun_mode mode))

fun argument_position_pair _ [] = []
  | argument_position_pair (Pair (Fun _, m2)) (2 :: is) = argument_position_pair m2 is
  | argument_position_pair (Pair (m1, m2)) (i :: is) =
      (if eq_mode (m1, Output) andalso i = 2 then
        argument_position_pair m2 is
      else if eq_mode (m2, Output) andalso i = 1 then
        argument_position_pair m1 is
      else (i :: argument_position_pair (if i = 1 then m1 else m2) is))

fun argument_position_of mode (i, is) =
  (i - (length (filter (fn Output => true | Fun _ => true | _ => false)
    (List.take (strip_fun_mode mode, i)))),
  argument_position_pair (nth (strip_fun_mode mode) i) is)

fun nth_pair [] t = t
  | nth_pair (1 :: is) (Const (\<^const_name>\<open>Pair\<close>, _) $ t1 $ _) = nth_pair is t1
  | nth_pair (2 :: is) (Const (\<^const_name>\<open>Pair\<close>, _) $ _ $ t2) = nth_pair is t2
  | nth_pair _ _ = raise Fail "unexpected input for nth_tuple"

(** switch detection analysis **)

fun find_switch_test ctxt (i, is) (ts, _) =
  let
    val t = nth_pair is (nth ts i)
    val T = fastype_of t
  in
    (case T of
      TFree _ => NONE
    | Type (Tcon, _) =>
        (case Ctr_Sugar.ctr_sugar_of ctxt Tcon of
          NONE => NONE
        | SOME {ctrs, ...} =>
            (case strip_comb t of
              (Var _, []) => NONE
            | (Free _, []) => NONE
            | (Const (c, T), _) =>
                if AList.defined (op =) (map_filter (try dest_Const) ctrs) c
                then SOME (c, T) else NONE)))
  end

fun partition_clause ctxt pos moded_clauses =
  let
    fun insert_list eq (key, value) = AList.map_default eq (key, []) (cons value)
    fun find_switch_test' moded_clause (cases, left) =
      (case find_switch_test ctxt pos moded_clause of
        SOME (c, T) => (insert_list (op =) ((c, T), moded_clause) cases, left)
      | NONE => (cases, moded_clause :: left))
  in
    fold find_switch_test' moded_clauses ([], [])
  end

datatype switch_tree =
  Atom of moded_clause list | Node of (position * ((string * typ) * switch_tree) list) * switch_tree

fun mk_switch_tree ctxt mode moded_clauses =
  let
    fun select_best_switch moded_clauses input_position best_switch =
      let
        val ord = option_ord (rev_order o int_ord o (apply2 (length o snd o snd)))
        val partition = partition_clause ctxt input_position moded_clauses
        val switch = if (length (fst partition) > 1) then SOME (input_position, partition) else NONE
      in
        (case ord (switch, best_switch) of
          LESS => best_switch
        | EQUAL => best_switch
        | GREATER => switch)
      end
    fun detect_switches moded_clauses =
      (case fold (select_best_switch moded_clauses) (input_positions_of_mode mode) NONE of
        SOME (best_pos, (switched_on, left_clauses)) =>
          Node ((best_pos, map (apsnd detect_switches) switched_on),
            detect_switches left_clauses)
      | NONE => Atom moded_clauses)
  in
    detect_switches moded_clauses
  end

(** compilation of detected switches **)

fun destruct_constructor_pattern (pat, obj) =
  (case strip_comb pat of
      (Free _, []) => cons (pat, obj)
  | (Const (c, T), pat_args) =>
      (case strip_comb obj of
        (Const (c', T'), obj_args) =>
          (if c = c' andalso T = T' then
            fold destruct_constructor_pattern (pat_args ~~ obj_args)
          else raise Fail "pattern and object mismatch")
      | _ => raise Fail "unexpected object")
  | _ => raise Fail "unexpected pattern")

fun compile_switch compilation_modifiers ctxt all_vs param_modes additional_arguments mode
  in_ts' outTs switch_tree =
  let
    val compfuns = Comp_Mod.compfuns compilation_modifiers
    val thy = Proof_Context.theory_of ctxt
    fun compile_switch_tree _ _ (Atom []) = NONE
      | compile_switch_tree all_vs ctxt_eqs (Atom moded_clauses) =
        let
          val in_ts' = map (Pattern.rewrite_term thy ctxt_eqs []) in_ts'
          fun compile_clause' (ts, moded_ps) =
            let
              val (ts, out_ts) = split_mode mode ts
              val subst = fold destruct_constructor_pattern (in_ts' ~~ ts) []
              val (fsubst, pat') = List.partition (fn (_, Free _) => true | _ => false) subst
              val moded_ps' = (map o apfst o map_indprem)
                (Pattern.rewrite_term thy (map swap fsubst) []) moded_ps
              val inp = HOLogic.mk_tuple (map fst pat')
              val in_ts' = map (Pattern.rewrite_term thy (map swap fsubst) []) (map snd pat')
              val out_ts' = map (Pattern.rewrite_term thy (map swap fsubst) []) out_ts
            in
              compile_clause compilation_modifiers ctxt all_vs param_modes additional_arguments
                inp (in_ts', out_ts') moded_ps'
            end
        in SOME (foldr1 (mk_plus compfuns) (map compile_clause' moded_clauses)) end
    | compile_switch_tree all_vs ctxt_eqs (Node ((position, switched_clauses), left_clauses)) =
      let
        val (i, is) = argument_position_of mode position
        val inp_var = nth_pair is (nth in_ts' i)
        val x = singleton (Name.variant_list all_vs) "x"
        val xt = Free (x, fastype_of inp_var)
        fun compile_single_case ((c, T), switched) =
          let
            val Ts = binder_types T
            val argnames = Name.variant_list (x :: all_vs)
              (map (fn i => "c" ^ string_of_int i) (1 upto length Ts))
            val args = map2 (curry Free) argnames Ts
            val pattern = list_comb (Const (c, T), args)
            val ctxt_eqs' = (inp_var, pattern) :: ctxt_eqs
            val compilation = the_default (mk_empty compfuns (HOLogic.mk_tupleT outTs))
              (compile_switch_tree (argnames @ x :: all_vs) ctxt_eqs' switched)
        in
          (pattern, compilation)
        end
        val switch = Case_Translation.make_case ctxt Case_Translation.Quiet Name.context inp_var
          ((map compile_single_case switched_clauses) @
            [(xt, mk_empty compfuns (HOLogic.mk_tupleT outTs))])
      in
        (case compile_switch_tree all_vs ctxt_eqs left_clauses of
          NONE => SOME switch
        | SOME left_comp => SOME (mk_plus compfuns (switch, left_comp)))
      end
  in
    compile_switch_tree all_vs [] switch_tree
  end

(* compilation of predicates *)

fun compile_pred options compilation_modifiers ctxt all_vs param_vs s T (pol, mode) moded_cls =
  let
    val is_terminating = false (* FIXME: requires an termination analysis *)
    val compilation_modifiers =
      (if pol then compilation_modifiers else
        negative_comp_modifiers_of compilation_modifiers)
      |> (if is_depth_limited_compilation (Comp_Mod.compilation compilation_modifiers) then
           (if is_terminating then
              (Comp_Mod.set_compfuns
                (unlimited_compfuns_of pol (Comp_Mod.compilation compilation_modifiers)))
            else
              (Comp_Mod.set_compfuns
                (limited_compfuns_of pol (Comp_Mod.compilation compilation_modifiers))))
          else I)
    val additional_arguments =
      Comp_Mod.additional_arguments compilation_modifiers (all_vs @ param_vs)
    val compfuns = Comp_Mod.compfuns compilation_modifiers
    fun is_param_type (T as Type ("fun",[_ , T'])) =
          is_some (try (dest_monadT compfuns) T) orelse is_param_type T'
      | is_param_type T = is_some (try (dest_monadT compfuns) T)
    val (inpTs, outTs) =
      split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode
        (binder_types T)
    val funT = Comp_Mod.funT_of compilation_modifiers mode T
    val (in_ts, _) =
      fold_map (fold_map_aterms_prodT (curry HOLogic.mk_prod)
        (fn T => fn (param_vs, names) =>
          if is_param_type T then
            (Free (hd param_vs, T), (tl param_vs, names))
          else
            let
              val new = singleton (Name.variant_list names) "x"
            in (Free (new, T), (param_vs, new :: names)) end)) inpTs
        (param_vs, (all_vs @ param_vs))
    val in_ts' =
      map_filter (map_filter_prod
        (fn t as Free (x, _) =>
          if member (op =) param_vs x then NONE else SOME t | t => SOME t)) in_ts
    val param_modes = param_vs ~~ ho_arg_modes_of mode
    val compilation =
      if detect_switches options then
        the_default (mk_empty compfuns (HOLogic.mk_tupleT outTs))
          (compile_switch compilation_modifiers ctxt all_vs param_modes additional_arguments mode
            in_ts' outTs (mk_switch_tree ctxt mode moded_cls))
      else
        let
          val cl_ts =
            map (fn (ts, moded_prems) =>
              compile_clause compilation_modifiers ctxt all_vs param_modes additional_arguments
                (HOLogic.mk_tuple in_ts') (split_mode mode ts) moded_prems) moded_cls
        in
          Comp_Mod.wrap_compilation compilation_modifiers compfuns s T mode additional_arguments
            (if null cl_ts then
              mk_empty compfuns (HOLogic.mk_tupleT outTs)
            else
              foldr1 (mk_plus compfuns) cl_ts)
        end
    val fun_const =
      Const (Core_Data.function_name_of (Comp_Mod.compilation compilation_modifiers) ctxt s mode, funT)
  in
    HOLogic.mk_Trueprop
      (HOLogic.mk_eq (list_comb (fun_const, in_ts @ additional_arguments), compilation))
  end

(* Definition of executable functions and their intro and elim rules *)

fun strip_split_abs (Const (\<^const_name>\<open>case_prod\<close>, _) $ t) = strip_split_abs t
  | strip_split_abs (Abs (_, _, t)) = strip_split_abs t
  | strip_split_abs t = t

fun mk_args is_eval (m as Pair (m1, m2), T as Type (\<^type_name>\<open>Product_Type.prod\<close>, [T1, T2])) names =
      if eq_mode (m, Input) orelse eq_mode (m, Output) then
        let
          val x = singleton (Name.variant_list names) "x"
        in
          (Free (x, T), x :: names)
        end
      else
        let
          val (t1, names') = mk_args is_eval (m1, T1) names
          val (t2, names'') = mk_args is_eval (m2, T2) names'
        in
          (HOLogic.mk_prod (t1, t2), names'')
        end
  | mk_args is_eval ((m as Fun _), T) names =
      let
        val funT = funT_of Predicate_Comp_Funs.compfuns m T
        val x = singleton (Name.variant_list names) "x"
        val (args, _) = fold_map (mk_args is_eval) (strip_fun_mode m ~~ binder_types T) (x :: names)
        val (inargs, outargs) = split_map_mode (fn _ => fn t => (SOME t, NONE)) m args
        val t = fold_rev HOLogic.tupled_lambda args (Predicate_Comp_Funs.mk_Eval
          (list_comb (Free (x, funT), inargs), HOLogic.mk_tuple outargs))
      in
        (if is_eval then t else Free (x, funT), x :: names)
      end
  | mk_args _ (_, T) names =
      let
        val x = singleton (Name.variant_list names) "x"
      in
        (Free (x, T), x :: names)
      end

fun create_intro_elim_rule ctxt mode defthm mode_id funT pred =
  let
    val funtrm = Const (mode_id, funT)
    val Ts = binder_types (fastype_of pred)
    val (args, argnames) = fold_map (mk_args true) (strip_fun_mode mode ~~ Ts) []
    fun strip_eval _ t =
      let
        val t' = strip_split_abs t
        val (r, _) = Predicate_Comp_Funs.dest_Eval t'
      in (SOME (fst (strip_comb r)), NONE) end
    val (inargs, outargs) = split_map_mode strip_eval mode args
    val eval_hoargs = ho_args_of mode args
    val hoargTs = ho_argsT_of mode Ts
    val hoarg_names' =
      Name.variant_list argnames ((map (fn i => "x" ^ string_of_int i)) (1 upto (length hoargTs)))
    val hoargs' = map2 (curry Free) hoarg_names' hoargTs
    val args' = replace_ho_args mode hoargs' args
    val predpropI = HOLogic.mk_Trueprop (list_comb (pred, args'))
    val predpropE = HOLogic.mk_Trueprop (list_comb (pred, args))
    val param_eqs = map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) eval_hoargs hoargs'
    val funpropE = HOLogic.mk_Trueprop (Predicate_Comp_Funs.mk_Eval (list_comb (funtrm, inargs),
                    if null outargs then Free("y", HOLogic.unitT) else HOLogic.mk_tuple outargs))
    val funpropI = HOLogic.mk_Trueprop (Predicate_Comp_Funs.mk_Eval (list_comb (funtrm, inargs),
                     HOLogic.mk_tuple outargs))
    val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI)
    val simprules =
      [defthm, @{thm pred.sel},
        @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm prod.collapse}]
    val unfolddef_tac =
      Simplifier.asm_full_simp_tac (put_simpset HOL_basic_ss ctxt |> Simplifier.add_simps simprules) 1
    val introthm = Goal.prove ctxt
      (argnames @ hoarg_names' @ ["y"]) [] introtrm (fn _ => unfolddef_tac)
    val P = HOLogic.mk_Trueprop (Free ("P", HOLogic.boolT));
    val elimtrm = Logic.list_implies ([funpropE, Logic.mk_implies (predpropE, P)], P)
    val elimthm = Goal.prove ctxt
      (argnames @ ["y", "P"]) [] elimtrm (fn _ => unfolddef_tac)
    val opt_neg_introthm =
      if is_all_input mode then
        let
          val neg_predpropI = HOLogic.mk_Trueprop (HOLogic.mk_not (list_comb (pred, args')))
          val neg_funpropI =
            HOLogic.mk_Trueprop (Predicate_Comp_Funs.mk_Eval
              (Predicate_Comp_Funs.mk_not (list_comb (funtrm, inargs)), HOLogic.unit))
          val neg_introtrm = Logic.list_implies (neg_predpropI :: param_eqs, neg_funpropI)
          val tac =
            Simplifier.asm_full_simp_tac (put_simpset HOL_basic_ss ctxt
              |> Simplifier.add_simps (@{thm if_False} :: @{thm Predicate.not_pred_eq} :: simprules)) 1
            THEN resolve_tac ctxt @{thms Predicate.singleI} 1
        in SOME (Goal.prove ctxt (argnames @ hoarg_names') []
            neg_introtrm (fn _ => tac))
        end
      else NONE
  in
    ((introthm, elimthm), opt_neg_introthm)
  end

fun create_constname_of_mode options thy prefix name _ mode =
  let
    val system_proposal = prefix ^ (Long_Name.base_name name) ^ "_" ^ ascii_string_of_mode mode
    val name = the_default system_proposal (proposed_names options name mode)
  in
    Sign.full_bname thy name
  end

fun create_definitions options preds (name, modes) thy =
  let
    val compfuns = Predicate_Comp_Funs.compfuns
    val T = AList.lookup (op =) preds name |> the
    fun create_definition mode thy =
      let
        val mode_cname = create_constname_of_mode options thy "" name T mode
        val mode_cbasename = Long_Name.base_name mode_cname
        val funT = funT_of compfuns mode T
        val (args, _) = fold_map (mk_args true) (strip_fun_mode mode ~~ binder_types T) []
        fun strip_eval _ t =
          let
            val t' = strip_split_abs t
            val (r, _) = Predicate_Comp_Funs.dest_Eval t'
          in (SOME (fst (strip_comb r)), NONE) end
        val (inargs, outargs) = split_map_mode strip_eval mode args
        val predterm = fold_rev HOLogic.tupled_lambda inargs
          (Predicate_Comp_Funs.mk_Enum (HOLogic.tupled_lambda (HOLogic.mk_tuple outargs)
            (list_comb (Const (name, T), args))))
        val lhs = Const (mode_cname, funT)
        val def = Logic.mk_equals (lhs, predterm)
        val (definition, thy') = thy |>
          Sign.add_consts [(Binding.name mode_cbasename, funT, NoSyn)] |>
          Global_Theory.add_def (Binding.name (Thm.def_name mode_cbasename), def)
        val ctxt' = Proof_Context.init_global thy'
        val rules as ((intro, elim), _) =
          create_intro_elim_rule ctxt' mode definition mode_cname funT (Const (name, T))
        in
          thy'
          |> Core_Data.set_function_name Pred name mode mode_cname
          |> Core_Data.add_predfun_data name mode (definition, rules)
          |> Global_Theory.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd
          |> Global_Theory.store_thm (Binding.name (mode_cbasename ^ "E"), elim)  |> snd
        end;
  in
    thy |> Core_Data.defined_function_of Pred name |> fold create_definition modes
  end;

fun define_functions comp_modifiers _ options preds (name, modes) thy =
  let
    val T = AList.lookup (op =) preds name |> the
    fun create_definition mode thy =
      let
        val function_name_prefix = Comp_Mod.function_name_prefix comp_modifiers
        val mode_cname = create_constname_of_mode options thy function_name_prefix name T mode
        val funT = Comp_Mod.funT_of comp_modifiers mode T
      in
        thy |> Sign.add_consts [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]
        |> Core_Data.set_function_name (Comp_Mod.compilation comp_modifiers) name mode mode_cname
      end;
  in
    thy
    |> Core_Data.defined_function_of (Comp_Mod.compilation comp_modifiers) name
    |> fold create_definition modes
  end;

(* composition of mode inference, definition, compilation and proof *)

(** auxillary combinators for table of preds and modes **)

fun map_preds_modes f preds_modes_table =
  map (fn (pred, modes) =>
    (pred, map (fn (mode, value) => (mode, f pred mode value)) modes)) preds_modes_table

fun join_preds_modes table1 table2 =
  map_preds_modes (fn pred => fn mode => fn value =>
    (value, the (AList.lookup (op =) (the (AList.lookup (op =) table2 pred)) mode))) table1

fun maps_modes preds_modes_table =
  map (fn (pred, modes) =>
    (pred, map (fn (_, value) => value) modes)) preds_modes_table

fun compile_preds options comp_modifiers ctxt all_vs param_vs preds moded_clauses =
  map_preds_modes (fn pred => compile_pred options comp_modifiers ctxt all_vs param_vs pred
      (the (AList.lookup (op =) preds pred))) moded_clauses

fun prove options thy clauses preds moded_clauses compiled_terms =
  map_preds_modes (prove_pred options thy clauses preds)
    (join_preds_modes moded_clauses compiled_terms)

fun prove_by_skip _ thy _ _ _ compiled_terms =
  map_preds_modes
    (fn _ => fn _ => fn t => Drule.export_without_context (Skip_Proof.make_thm thy t))
    compiled_terms

(* preparation of introduction rules into special datastructures *)
fun dest_prem ctxt params t =
  (case strip_comb t of
    (v as Free _, _) => if member (op =) params v then Prem t else Sidecond t
  | (c as Const (\<^const_name>\<open>Not\<close>, _), [t]) =>
      (case dest_prem ctxt params t of
        Prem t => Negprem t
      | Negprem _ => error ("Double negation not allowed in premise: " ^
          Syntax.string_of_term ctxt (c $ t))
      | Sidecond t => Sidecond (c $ t))
  | (Const (s, _), _) =>
      if Core_Data.is_registered ctxt s then Prem t else Sidecond t
  | _ => Sidecond t)

fun prepare_intrs options ctxt prednames intros =
  let
    val thy = Proof_Context.theory_of ctxt
    val intrs = map Thm.prop_of intros
    val preds = map (fn c => Const (c, Sign.the_const_type thy c)) prednames
    val (preds, intrs) = unify_consts thy preds intrs
    val ([preds, intrs], _) = fold_burrow (Variable.import_terms false) [preds, intrs] ctxt
    val preds = map dest_Const preds
    val all_vs = terms_vs intrs
    fun generate_modes s T =
      if member (op =) (no_higher_order_predicate options) s then
        all_smodes_of_typ T
      else
        all_modes_of_typ T
    val all_modes =
      map (fn (s, T) =>
        (s,
          (case proposed_modes options s of
            SOME ms => check_matches_type ctxt s T ms
          | NONE => generate_modes s T))) preds
    val params =
      (case intrs of
        [] =>
          let
            val T = snd (hd preds)
            val one_mode = hd (the (AList.lookup (op =) all_modes (fst (hd preds))))
            val paramTs =
              ho_argsT_of one_mode (binder_types T)
            val param_names = Name.variant_list [] (map (fn i => "p" ^ string_of_int i)
              (1 upto length paramTs))
          in
            map2 (curry Free) param_names paramTs
          end
      | (intr :: _) =>
          let
            val (p, args) = strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))
            val one_mode = hd (the (AList.lookup (op =) all_modes (dest_Const_name p)))
          in
            ho_args_of one_mode args
          end)
    val param_vs = map (fst o dest_Free) params
    fun add_clause intr clauses =
      let
        val (Const (name, _), ts) =
          strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))
        val prems =
          map (dest_prem ctxt params o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr)
      in
        AList.update op =
          (name, these (AList.lookup op = clauses name) @ [(ts, prems)])
          clauses
      end;
    val clauses = fold add_clause intrs []
  in
    (preds, all_vs, param_vs, all_modes, clauses)
  end

(* sanity check of introduction rules *)
(* TODO: rethink check with new modes *)
(*
fun check_format_of_intro_rule thy intro =
  let
    val concl = Logic.strip_imp_concl (prop_of intro)
    val (p, args) = strip_comb (HOLogic.dest_Trueprop concl)
    val params = fst (chop (nparams_of thy (dest_Const_name p)) args)
    fun check_arg arg = case HOLogic.strip_tupleT (fastype_of arg) of
      (Ts as _ :: _ :: _) =>
        if length (HOLogic.strip_tuple arg) = length Ts then
          true
        else
          error ("Format of introduction rule is invalid: tuples must be expanded:"
          ^ (Syntax.string_of_term_global thy arg) ^ " in " ^
          (Thm.string_of_thm_global thy intro))
      | _ => true
    val prems = Logic.strip_imp_prems (prop_of intro)
    fun check_prem (Prem t) = forall check_arg args
      | check_prem (Negprem t) = forall check_arg args
      | check_prem _ = true
  in
    forall check_arg args andalso
    forall (check_prem o dest_prem thy params o HOLogic.dest_Trueprop) prems
  end
*)
(*
fun check_intros_elim_match thy prednames =
  let
    fun check predname =
      let
        val intros = intros_of thy predname
        val elim = the_elim_of thy predname
        val nparams = nparams_of thy predname
        val elim' =
          (Drule.export_without_context o Skip_Proof.make_thm thy)
          (mk_casesrule (Proof_Context.init_global thy) nparams intros)
      in
        if not (Thm.equiv_thm (elim, elim')) then
          error "Introduction and elimination rules do not match!"
        else true
      end
  in forall check prednames end
*)

(* create code equation *)

fun add_code_equations ctxt preds result_thmss =
  let
    fun add_code_equation (predname, T) (pred, result_thms) =
      let
        val full_mode = fold_rev (curry Fun) (map (K Input) (binder_types T)) Bool
      in
        if member eq_mode (Core_Data.modes_of Pred ctxt predname) full_mode then
          let
            val Ts = binder_types T
            val arg_names = Name.variant_list []
              (map (fn i => "x" ^ string_of_int i) (1 upto length Ts))
            val args = map2 (curry Free) arg_names Ts
            val predfun = Const (Core_Data.function_name_of Pred ctxt predname full_mode,
              Ts ---> Predicate_Comp_Funs.mk_monadT \<^typ>\<open>unit\<close>)
            val rhs = \<^term>\<open>Predicate.holds\<close> $ (list_comb (predfun, args))
            val eq_term = HOLogic.mk_Trueprop
              (HOLogic.mk_eq (list_comb (Const (predname, T), args), rhs))
            val def = Core_Data.predfun_definition_of ctxt predname full_mode
            val tac = fn _ =>
              Simplifier.simp_tac
                (put_simpset HOL_basic_ss ctxt
                  |> Simplifier.add_simps [def, @{thm holds_eq}, @{thm pred.sel}]) 1
            val eq = Goal.prove ctxt arg_names [] eq_term tac
          in
            (pred, result_thms @ [eq])
          end
        else
          (pred, result_thms)
      end
  in
    map2 add_code_equation preds result_thmss
  end

(** main function of predicate compiler **)

datatype steps = Steps of
  {
  define_functions : options -> (string * typ) list -> string * (bool * mode) list -> theory -> theory,
  prove : options -> theory -> (string * (term list * indprem list) list) list -> (string * typ) list
    -> moded_clause list pred_mode_table -> term pred_mode_table -> thm pred_mode_table,
  add_code_equations : Proof.context -> (string * typ) list
    -> (string * thm list) list -> (string * thm list) list,
  comp_modifiers : Comp_Mod.comp_modifiers,
  use_generators : bool,
  qname : bstring
  }

fun add_equations_of steps mode_analysis_options options prednames thy =
  let
    fun dest_steps (Steps s) = s
    val compilation = Comp_Mod.compilation (#comp_modifiers (dest_steps steps))
    val ctxt = Proof_Context.init_global thy
    val _ =
      print_step options
        ("Starting predicate compiler (compilation: " ^ string_of_compilation compilation ^
          ") for predicates " ^ commas prednames ^ "...")
    (*val _ = check_intros_elim_match thy prednames*)
    (*val _ = map (check_format_of_intro_rule thy) (maps (intros_of thy) prednames)*)
    val _ =
      if show_intermediate_results options then
        tracing (commas (map (Thm.string_of_thm ctxt) (maps (Core_Data.intros_of ctxt) prednames)))
      else ()
    val (preds, all_vs, param_vs, all_modes, clauses) =
      prepare_intrs options ctxt prednames (maps (Core_Data.intros_of ctxt) prednames)
    val _ = print_step options "Infering modes..."
    val (lookup_mode, lookup_neg_mode, needs_random) = (Core_Data.modes_of compilation ctxt,
      Core_Data.modes_of (negative_compilation_of compilation) ctxt, Core_Data.needs_random ctxt)
    val ((moded_clauses, needs_random), errors) =
      cond_timeit (Config.get ctxt Quickcheck.timing) "Infering modes"
      (fn _ => infer_modes mode_analysis_options
        options (lookup_mode, lookup_neg_mode, needs_random) ctxt preds all_modes param_vs clauses)
    val thy' = fold (fn (s, ms) => Core_Data.set_needs_random s ms) needs_random thy
    val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses
    val _ = check_expected_modes options preds modes
    val _ = check_proposed_modes options preds modes errors
    val _ = print_modes options modes
    val _ = print_step options "Defining executable functions..."
    val thy'' =
      cond_timeit (Config.get ctxt Quickcheck.timing) "Defining executable functions..."
      (fn _ => fold (#define_functions (dest_steps steps) options preds) modes thy')
    val ctxt'' = Proof_Context.init_global thy''
    val _ = print_step options "Compiling equations..."
    val compiled_terms =
      cond_timeit (Config.get ctxt Quickcheck.timing) "Compiling equations...." (fn _ =>
        compile_preds options
          (#comp_modifiers (dest_steps steps)) ctxt'' all_vs param_vs preds moded_clauses)
    val _ = print_compiled_terms options ctxt'' compiled_terms
    val _ = print_step options "Proving equations..."
    val result_thms =
      cond_timeit (Config.get ctxt Quickcheck.timing) "Proving equations...." (fn _ =>
      #prove (dest_steps steps) options thy'' clauses preds moded_clauses compiled_terms)
    val result_thms' = #add_code_equations (dest_steps steps) ctxt'' preds
      (maps_modes result_thms)
    val qname = #qname (dest_steps steps)
    val thy''' = cond_timeit (Config.get ctxt Quickcheck.timing) "Setting code equations...."
      (fn _ =>
        thy''
        |> fold_map (fn (name, result_thms) => (Global_Theory.add_thmss
            [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms), [])]))
            result_thms'
        |-> (fn notes => Code.declare_default_eqns_global (map (rpair true) ((flat o flat) notes))))
  in
    thy'''
  end

fun gen_add_equations steps options names thy =
  let
    fun dest_steps (Steps s) = s
    val defined = Core_Data.defined_functions (Comp_Mod.compilation (#comp_modifiers (dest_steps steps)))
    val thy' = Core_Data.extend_intro_graph names thy;
    fun strong_conn_of gr keys =
      Graph.strong_conn (Graph.restrict (member (op =) (Graph.all_succs gr keys)) gr)
    val scc = strong_conn_of (Core_Data.PredData.get thy') names
    val thy'' = fold Core_Data.preprocess_intros (flat scc) thy'
    val thy''' = fold_rev
      (fn preds => fn thy =>
        if not (forall (defined (Proof_Context.init_global thy)) preds) then
          let
            val mode_analysis_options = {use_generators = #use_generators (dest_steps steps),
              reorder_premises =
                not (no_topmost_reordering options andalso not (null (inter (op =) preds names))),
              infer_pos_and_neg_modes = #use_generators (dest_steps steps)}
          in
            add_equations_of steps mode_analysis_options options preds thy
          end
        else thy)
      scc thy''
  in thy''' end

val add_equations = gen_add_equations
  (Steps {
  define_functions =
    fn options => fn preds => fn (s, modes) =>
      create_definitions
      options preds (s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
  prove = prove,
  add_code_equations = add_code_equations,
  comp_modifiers = predicate_comp_modifiers,
  use_generators = false,
  qname = "equation"})

val add_depth_limited_equations = gen_add_equations
  (Steps {
  define_functions =
    fn options => fn preds => fn (s, modes) =>
    define_functions depth_limited_comp_modifiers Predicate_Comp_Funs.compfuns
    options preds (s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
  prove = prove_by_skip,
  add_code_equations = K (K I),
  comp_modifiers = depth_limited_comp_modifiers,
  use_generators = false,
  qname = "depth_limited_equation"})

val add_random_equations = gen_add_equations
  (Steps {
  define_functions =
    fn options => fn preds => fn (s, modes) =>
      define_functions random_comp_modifiers Predicate_Comp_Funs.compfuns options preds
      (s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
  comp_modifiers = random_comp_modifiers,
  prove = prove_by_skip,
  add_code_equations = K (K I),
  use_generators = true,
  qname = "random_equation"})

val add_depth_limited_random_equations = gen_add_equations
  (Steps {
  define_functions =
    fn options => fn preds => fn (s, modes) =>
      define_functions depth_limited_random_comp_modifiers Predicate_Comp_Funs.compfuns options preds
      (s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
  comp_modifiers = depth_limited_random_comp_modifiers,
  prove = prove_by_skip,
  add_code_equations = K (K I),
  use_generators = true,
  qname = "depth_limited_random_equation"})

val add_dseq_equations = gen_add_equations
  (Steps {
  define_functions =
  fn options => fn preds => fn (s, modes) =>
    define_functions dseq_comp_modifiers DSequence_CompFuns.compfuns
    options preds (s, map_filter (fn (true, m) => SOME m | _ => NONE) modes),
  prove = prove_by_skip,
  add_code_equations = K (K I),
  comp_modifiers = dseq_comp_modifiers,
  use_generators = false,
  qname = "dseq_equation"})

val add_random_dseq_equations = gen_add_equations
  (Steps {
  define_functions =
    fn options => fn preds => fn (s, modes) =>
    let
      val pos_modes = map_filter (fn (true, m) => SOME m | _ => NONE) modes
      val neg_modes = map_filter (fn (false, m) => SOME m | _ => NONE) modes
    in define_functions pos_random_dseq_comp_modifiers Random_Sequence_CompFuns.compfuns
      options preds (s, pos_modes)
      #> define_functions neg_random_dseq_comp_modifiers Random_Sequence_CompFuns.compfuns
      options preds (s, neg_modes)
    end,
  prove = prove_by_skip,
  add_code_equations = K (K I),
  comp_modifiers = pos_random_dseq_comp_modifiers,
  use_generators = true,
  qname = "random_dseq_equation"})

val add_new_random_dseq_equations = gen_add_equations
  (Steps {
  define_functions =
    fn options => fn preds => fn (s, modes) =>
      let
        val pos_modes = map_filter (fn (true, m) => SOME m | _ => NONE) modes
        val neg_modes = map_filter (fn (false, m) => SOME m | _ => NONE) modes
      in
        define_functions new_pos_random_dseq_comp_modifiers
          New_Pos_Random_Sequence_CompFuns.depth_limited_compfuns
          options preds (s, pos_modes) #>
        define_functions new_neg_random_dseq_comp_modifiers
--> --------------------

--> maximum size reached

--> --------------------

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