(*  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 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 setup : theory -> theory

  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 -> int * int -> term Predicate.pred * (int * int)) ->

    Proof.context -> Proof.context

  val put_dseq_result : (unit -> term DSequence.dseq) -> Proof.context -> Proof.context

  val put_dseq_random_result : (unit -> int -> int -> int * int -> term DSequence.dseq * (int * int)) ->

    Proof.context -> Proof.context

  val put_new_dseq_result : (unit -> int -> term Lazy_Sequence.lazy_sequence) ->

    Proof.context -> Proof.context

  val put_lseq_random_result :

    (unit -> int -> int -> int * int -> int -> term Lazy_Sequence.lazy_sequence) ->

    Proof.context -> Proof.context

  val put_lseq_random_stats_result :

    (unit -> int -> int -> int * int -> int -> (term * int) 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 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

open Predicate_Compile_Aux;

open Core_Data;

open Mode_Inference;

open Predicate_Compile_Proof;

(** 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_scomp (t, u) =

  let

    val T = fastype_of t

    val U = fastype_of u

    val [A] = binder_types T

    val D = body_type U                   

  in 

    Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u

  end;

fun dest_randomT (Type ("fun", [@{typ Random.seed},

  Type (@{type_name Product_Type.prod}, [Type (@{type_name Product_Type.prod}, [T, @{typ "unit => Code_Evaluation.term"}]) ,@{typ Random.seed}])])) = T

  | dest_randomT T = raise TYPE ("dest_randomT", [T], [])

fun mk_tracing s t =

  Const(@{const_name Code_Evaluation.tracing},

    @{typ String.literal} --> (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 ((pol, 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 (PredData.get (Proof_Context.theory_of ctxt))

    fun print pred () = let

      val _ = writeln ("predicate: " ^ pred)

      val _ = writeln ("introrules: ")

      val _ = fold (fn thm => fn u => writeln (Display.string_of_thm ctxt thm))

        (rev (intros_of ctxt pred)) ()

    in

      if (has_elim ctxt pred) then

        writeln ("elimrule: " ^ Display.string_of_thm ctxt (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 (all_modes_of compilation ctxt) ()

  end

(* validity checks *)

fun check_expected_modes options preds 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 (m as Fun (m1, m2)) (Type("fun", [T1,T2])) = check m1 T1 andalso check m2 T2

      | check m (T as Type("fun", _)) = (m = Input orelse m = Output)

      | check (Pair (m1, m2)) (Type (@{type_name Product_Type.prod}, [T1, T2])) =

          check m1 T1 andalso check m2 T2 

      | check Input T = true

      | check Output T = true

      | check Bool @{typ bool} = true

      | check _ _ = false

    fun check_consistent_modes ms =

      if forall (fn Fun (m1', m2') => true | _ => false) ms then

        pairself 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 =

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 = PredicateCompFuns.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 code_numeral})] end,

  modify_funT = (fn T => let val (Ts, U) = strip_type T

  val Ts' = [@{typ code_numeral}] 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_predT compfuns (HOLogic.mk_tupleT Ts)

      val if_const = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')

    in

      if_const $ HOLogic.mk_eq (depth, @{term "0 :: code_numeral"})

        $ mk_bot compfuns (dest_predT compfuns T')

        $ compilation

    end,

  transform_additional_arguments =

    fn prem => fn additional_arguments =>

    let

      val [depth] = additional_arguments

      val depth' =

        Const (@{const_name Groups.minus}, @{typ "code_numeral => code_numeral => code_numeral"})

          $ depth $ Const (@{const_name Groups.one}, @{typ "Code_Numeral.code_numeral"})

    in [depth'] end

  }

val random_comp_modifiers = Comp_Mod.Comp_Modifiers

  {

  compilation = Random,

  function_name_prefix = "random_",

  compfuns = PredicateCompFuns.compfuns,

  mk_random = (fn T => fn additional_arguments =>

  list_comb (Const(@{const_name Quickcheck.iter},

  [@{typ code_numeral}, @{typ code_numeral}, @{typ Random.seed}] ---> 

    PredicateCompFuns.mk_predT T), additional_arguments)),

  modify_funT = (fn T =>

    let

      val (Ts, U) = strip_type T

      val Ts' = [@{typ code_numeral}, @{typ code_numeral}, @{typ "code_numeral * code_numeral"}]

    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 code_numeral}), Free (size, @{typ code_numeral}),

        Free (seed, @{typ "code_numeral * code_numeral"})]

    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 = PredicateCompFuns.compfuns,

  mk_random = (fn T => fn additional_arguments =>

  list_comb (Const(@{const_name Quickcheck.iter},

  [@{typ code_numeral}, @{typ code_numeral}, @{typ Random.seed}] ---> 

    PredicateCompFuns.mk_predT T), tl additional_arguments)),

  modify_funT = (fn T =>

    let

      val (Ts, U) = strip_type T

      val Ts' = [@{typ code_numeral}, @{typ code_numeral}, @{typ code_numeral},

        @{typ "code_numeral * code_numeral"}]

    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 code_numeral}), Free (nrandom, @{typ code_numeral}),

        Free (size, @{typ code_numeral}), Free (seed, @{typ "code_numeral * code_numeral"})]

    end),

  wrap_compilation =

  fn compfuns => fn s => 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_predT compfuns (HOLogic.mk_tupleT Ts)

      val if_const = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')

    in

      if_const $ HOLogic.mk_eq (depth, @{term "0 :: code_numeral"})

        $ mk_bot compfuns (dest_predT compfuns T')

        $ compilation

    end,

  transform_additional_arguments =

    fn prem => fn additional_arguments =>

    let

      val [depth, nrandom, size, seed] = additional_arguments

      val depth' =

        Const (@{const_name Groups.minus}, @{typ "code_numeral => code_numeral => code_numeral"})

          $ depth $ Const (@{const_name Groups.one}, @{typ "Code_Numeral.code_numeral"})

    in [depth', nrandom, size, seed] end

}

val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers

  {

  compilation = Pred,

  function_name_prefix = "",

  compfuns = PredicateCompFuns.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 annotated_comp_modifiers = Comp_Mod.Comp_Modifiers

  {

  compilation = Annotated,

  function_name_prefix = "annotated_",

  compfuns = PredicateCompFuns.compfuns,

  mk_random = (fn _ => error "no random generation"),

  modify_funT = I,

  additional_arguments = K [],

  wrap_compilation =

    fn compfuns => fn s => fn T => fn mode => fn additional_arguments => fn compilation =>

      mk_tracing ("calling predicate " ^ s ^

        " with mode " ^ string_of_mode mode) compilation,

  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 additional_arguments =>

  let

    val random = Const ("Quickcheck.random_class.random",

      @{typ code_numeral} --> @{typ Random.seed} -->

        HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed}))

  in

    Const ("Random_Sequence.Random", (@{typ code_numeral} --> @{typ Random.seed} -->

      HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->

      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 additional_arguments =>

  let

    val random = Const ("Quickcheck.random_class.random",

      @{typ code_numeral} --> @{typ Random.seed} -->

        HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed}))

  in

    Const ("New_Random_Sequence.Random", (@{typ code_numeral} --> @{typ Random.seed} -->

      HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->

      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 additional_arguments =>

      let

        val small_lazy =

         Const (@{const_name "Lazy_Sequence.small_lazy_class.small_lazy"},

         @{typ "Int.int"} --> Type (@{type_name "Lazy_Sequence.lazy_sequence"}, [T])) 

      in

        absdummy (@{typ code_numeral}, small_lazy $ HOLogic.mk_number @{typ int} 3)

      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_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)

  }

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

    | c => 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 (f, _)), T) mode =

let

  fun mk_bounds (Type (@{type_name Product_Type.prod}, [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 T 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 Product_Type.prod}, [T1, T2])) t = absdummy (T, HOLogic.split_const (T1, T2, @{typ bool}) $ (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 (inTs, outTs) = split_map_modeT (fn _ => fn T => (SOME T, NONE)) mode (binder_types T)

  val inner_term = PredicateCompFuns.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 additional_arguments ctxt 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_predT compfuns U;

    val v = Free (name, T);

    val v' = Free (name', T);

  in

    lambda v (Datatype.make_case ctxt Datatype_Case.Quiet [] v

      [(HOLogic.mk_tuple out_ts,

        if null eqs'' then success_t

        else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $

          foldr1 HOLogic.mk_conj eqs'' $ success_t $

            mk_bot compfuns U'),

       (v', mk_bot compfuns U')])

  end;

fun string_of_tderiv ctxt (t, deriv) = 

  (case (t, deriv) of

    (t1 $ t2, Mode_App (deriv1, deriv2)) =>

      string_of_tderiv ctxt (t1, deriv1) ^ " $ " ^ string_of_tderiv ctxt (t2, deriv2)

  | (Const (@{const_name Pair}, _) $ t1 $ t2, Mode_Pair (deriv1, deriv2)) =>

    "(" ^ string_of_tderiv ctxt (t1, deriv1) ^ ", " ^ string_of_tderiv ctxt (t2, deriv2) ^ ")"

  | (t, Term Input) => Syntax.string_of_term ctxt t ^ "[Input]"

  | (t, Term Output) => Syntax.string_of_term ctxt t ^ "[Output]"

  | (t, Context m) => Syntax.string_of_term ctxt t ^ "[" ^ string_of_mode m ^ "]")

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)

      | (t, Term Output) => NONE

      | (Const (name, T), Context mode) =>

        (case alternative_compilation_of ctxt name mode of

          SOME alt_comp => SOME (alt_comp compfuns T)

        | NONE =>

          SOME (Const (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 mode => 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 (list_abs (bs, mk_if compfuns (list_comb (t, bounds)))) end)

      | (t, Context m) =>

        let

          val bs = map (pair "x") (binder_types (fastype_of t))

          val bounds = map Bound (rev (0 upto (length bs) - 1))

        in SOME (list_abs (bs, mk_if compfuns (list_comb (t, bounds)))) end

      | (Const (@{const_name Pair}, _) $ 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''', (names'', 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 (m1, m2)) => map (pair i) (input_positions_pair m))

     (Predicate_Compile_Aux.strip_fun_mode mode))

fun argument_position_pair mode [] = []

  | 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 Pair}, _) $ t1 $ _) = nth_pair is t1

  | nth_pair (2 :: is) (Const (@{const_name Pair}, _) $ _ $ 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, prems) =

  let

    val t = nth_pair is (nth ts i)

    val T = fastype_of t

  in

    case T of

      TFree _ => NONE

    | Type (Tcon, _) =>

      (case Datatype_Data.get_constrs (Proof_Context.theory_of ctxt) Tcon of

        NONE => NONE

      | SOME cs =>

        (case strip_comb t of

          (Var _, []) => NONE

        | (Free _, []) => NONE

        | (Const (c, T), _) => if AList.defined (op =) cs 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 (pairself (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

    (f as 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_sup 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_bot compfuns (HOLogic.mk_tupleT outTs))

              (compile_switch_tree (argnames @ x :: all_vs) ctxt_eqs' switched)

        in

          (pattern, compilation)

        end

        val switch = Datatype.make_case ctxt Datatype_Case.Quiet [] inp_var

          ((map compile_single_case switched_clauses) @

            [(xt, mk_bot 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_sup 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_predT compfuns) T) orelse is_param_type T'

      | is_param_type T = is_some (try (dest_predT compfuns) T)

    val (inpTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode

      (binder_types T)

    val predT = mk_predT compfuns (HOLogic.mk_tupleT outTs)

    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_bot 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_bot compfuns (HOLogic.mk_tupleT outTs)

            else

              foldr1 (mk_sup compfuns) cl_ts)

        end

    val fun_const =

      Const (function_name_of (Comp_Mod.compilation compilation_modifiers)

      ctxt s mode, funT)

  in

    HOLogic.mk_Trueprop