(*  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

       (HOLogic.mk_eq (list_comb (fun_const, in_ts @ additional_arguments), compilation))

   end;

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

 fun print_arities arities = tracing ("Arities:\n" ^

   cat_lines (map (fn (s, (ks, k)) => s ^ ": " ^

     space_implode " -> " (map

       (fn NONE => "X" | SOME k' => string_of_int k')

         (ks @ [SOME k]))) arities));

 fun strip_split_abs (Const (@{const_name prod_case}, _) $ 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 Product_Type.prod}, [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 PredicateCompFuns.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 (PredicateCompFuns.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 is_eval (_, 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, _) = PredicateCompFuns.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 (PredicateCompFuns.mk_Eval (list_comb (funtrm, inargs),

                     if null outargs then Free("y", HOLogic.unitT) else HOLogic.mk_tuple outargs))

     val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, inargs),

                      HOLogic.mk_tuple outargs))

     val introtrm = Logic.list_implies (predpropI :: param_eqs, funpropI)

     val simprules = [defthm, @{thm eval_pred},

       @{thm "split_beta"}, @{thm "fst_conv"}, @{thm "snd_conv"}, @{thm pair_collapse}]

     val unfolddef_tac = Simplifier.asm_full_simp_tac (HOL_basic_ss addsimps 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 (PredicateCompFuns.mk_Eval

               (PredicateCompFuns.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 (HOL_basic_ss addsimps

               (@{thm if_False} :: @{thm Predicate.not_pred_eq} :: simprules)) 1

             THEN rtac @{thm 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 T 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 = PredicateCompFuns.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 m t =

           let

             val t' = strip_split_abs t

             val (r, _) = PredicateCompFuns.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

           (PredicateCompFuns.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_i [(Binding.name mode_cbasename, funT, NoSyn)] |>

           Global_Theory.add_defs false [((Binding.name (mode_cbasename ^ "_def"), 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'

           |> set_function_name Pred name mode mode_cname

           |> 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

           |> Theory.checkpoint

         end;

   in

     thy |> defined_function_of Pred name |> fold create_definition modes

   end;

 fun define_functions comp_modifiers compfuns 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_i [(Binding.name (Long_Name.base_name mode_cname), funT, NoSyn)]

         |> set_function_name (Comp_Mod.compilation comp_modifiers) name mode mode_cname

       end;

   in

     thy

     |> 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 (mode, 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 options thy _ _ _ compiled_terms =

   map_preds_modes

     (fn pred => fn mode => 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 _, ts) => if member (op =) params v then Prem t else Sidecond t

   | (c as Const (@{const_name Not}, _), [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))

   | (c as Const (s, _), ts) =>

     if 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 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 (fst (dest_Const 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, T), 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 (fst (dest_Const 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 " ^

           (Display.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 (op =) (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 (function_name_of Pred ctxt predname full_mode,

               Ts ---> PredicateCompFuns.mk_predT @{typ unit})

             val rhs = @{term Predicate.holds} $ (list_comb (predfun, args))

             val eq_term = HOLogic.mk_Trueprop

               (HOLogic.mk_eq (list_comb (Const (predname, T), args), rhs))

             val def = predfun_definition_of ctxt predname full_mode

             val tac = fn _ => Simplifier.simp_tac

               (HOL_basic_ss addsimps [def, @{thm holds_eq}, @{thm eval_pred}]) 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 (Display.string_of_thm ctxt) (maps (intros_of ctxt) prednames)))

       else ()

     val (preds, all_vs, param_vs, all_modes, clauses) =

       prepare_intrs options ctxt prednames (maps (intros_of ctxt) prednames)

     val _ = print_step options "Infering modes..."

     val (lookup_mode, lookup_neg_mode, needs_random) = (modes_of compilation ctxt,

       modes_of (negative_compilation_of compilation) ctxt, 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) => 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'

       |> Theory.checkpoint)

     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 attrib = fn thy => Attrib.attribute_i thy (Attrib.internal (K (Thm.declaration_attribute

       (fn thm => Context.mapping (Code.add_eqn thm) I))))

     val thy''' =

       cond_timeit (Config.get ctxt Quickcheck.timing) "Setting code equations...." (fn _ =>

       fold (fn (name, result_thms) => fn thy => snd (Global_Theory.add_thmss

       [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms),

         [attrib thy ])] thy))

       result_thms' thy'' |> Theory.checkpoint)

   in

     thy'''

   end

 fun gen_add_equations steps options names thy =

   let

     fun dest_steps (Steps s) = s

     val defined = defined_functions (Comp_Mod.compilation (#comp_modifiers (dest_steps steps)))

     val thy' = extend_intro_graph names thy |> Theory.checkpoint;

     fun strong_conn_of gr keys =

       Graph.strong_conn (Graph.subgraph (member (op =) (Graph.all_succs gr keys)) gr)

     val scc = strong_conn_of (PredData.get thy') names

     val thy'' = fold 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'' |> Theory.checkpoint

   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 PredicateCompFuns.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_annotated_equations = gen_add_equations

   (Steps {

   define_functions =

     fn options => fn preds => fn (s, modes) =>

       define_functions annotated_comp_modifiers PredicateCompFuns.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 = annotated_comp_modifiers,

   use_generators = false,

   qname = "annotated_equation"})

 val add_random_equations = gen_add_equations

   (Steps {

   define_functions =

     fn options => fn preds => fn (s, modes) =>

       define_functions random_comp_modifiers PredicateCompFuns.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 PredicateCompFuns.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 New_Neg_Random_Sequence_CompFuns.depth_limited_compfuns

       options preds (s, neg_modes)

     end,

   prove = prove_by_skip,

   add_code_equations = K (K I),

   comp_modifiers = new_pos_random_dseq_comp_modifiers,

   use_generators = true,

   qname = "new_random_dseq_equation"})

 val add_generator_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_generator_dseq_comp_modifiers New_Pos_DSequence_CompFuns.depth_limited_compfuns

         options preds (s, pos_modes)

       #> define_functions neg_generator_dseq_comp_modifiers New_Neg_DSequence_CompFuns.depth_limited_compfuns

         options preds (s, neg_modes)

     end,

   prove = prove_by_skip,

   add_code_equations = K (K I),

   comp_modifiers = pos_generator_dseq_comp_modifiers,

   use_generators = true,

   qname = "generator_dseq_equation"})

 (** user interface **)

 (* code_pred_intro attribute *)

 fun attrib' f opt_case_name =

   Thm.declaration_attribute (fn thm => Context.mapping (f (opt_case_name, thm)) I);

 val code_pred_intro_attrib = attrib' add_intro NONE;

 (*FIXME

 - Naming of auxiliary rules necessary?

 *)

 (* values_timeout configuration *)

 val default_values_timeout =

   if String.isPrefix "smlnj" (getenv "ML_SYSTEM") then 600.0 else 20.0

 val values_timeout = Attrib.setup_config_real @{binding values_timeout} (K default_values_timeout)

 val setup = PredData.put (Graph.empty) #>

   Attrib.setup @{binding code_pred_intro} (Scan.lift (Scan.option Args.name) >> attrib' add_intro)

     "adding alternative introduction rules for code generation of inductive predicates"

 (* TODO: make Theory_Data to Generic_Data & remove duplication of local theory and theory *)

 (* FIXME ... this is important to avoid changing the background theory below *)

 fun generic_code_pred prep_const options raw_const lthy =

   let

     val thy = Proof_Context.theory_of lthy

     val const = prep_const thy raw_const

     val lthy' = Local_Theory.background_theory (extend_intro_graph [const]) lthy

     val thy' = Proof_Context.theory_of lthy'

     val ctxt' = Proof_Context.init_global thy'

     val preds = Graph.all_succs (PredData.get thy') [const] |> filter_out (has_elim ctxt')

     fun mk_cases const =

       let

         val T = Sign.the_const_type thy' const

         val pred = Const (const, T)

         val intros = intros_of ctxt' const

       in mk_casesrule lthy' pred intros end  

     val cases_rules = map mk_cases preds

     val cases =

       map2 (fn pred_name => fn case_rule => Rule_Cases.Case {fixes = [],

         assumes = ("that", tl (Logic.strip_imp_prems case_rule))

           :: (map_filter (fn (fact_name, fact) => Option.map (rpair [fact]) fact_name)

             ((SOME (Long_Name.base_name pred_name ^ ".prems") :: names_of ctxt' pred_name) ~~ Logic.strip_imp_prems case_rule)),

         binds = [], cases = []}) preds cases_rules

     val case_env = map2 (fn p => fn c => (Long_Name.base_name p, SOME c)) preds cases

     val lthy'' = lthy'

       |> fold Variable.auto_fixes cases_rules

       |> Proof_Context.add_cases true case_env

     fun after_qed thms goal_ctxt =

       let

         val global_thms = Proof_Context.export goal_ctxt

           (Proof_Context.init_global (Proof_Context.theory_of goal_ctxt)) (map the_single thms)

       in

         goal_ctxt |> Local_Theory.background_theory (fold set_elim global_thms #>

           ((case compilation options of

              Pred => add_equations

            | DSeq => add_dseq_equations

            | Pos_Random_DSeq => add_random_dseq_equations

            | Depth_Limited => add_depth_limited_equations

            | Random => add_random_equations

            | Depth_Limited_Random => add_depth_limited_random_equations

            | New_Pos_Random_DSeq => add_new_random_dseq_equations

            | Pos_Generator_DSeq => add_generator_dseq_equations

            | compilation => error ("Compilation not supported")

            ) options [const]))

       end

   in

     Proof.theorem NONE after_qed (map (single o (rpair [])) cases_rules) lthy''

   end;

 val code_pred = generic_code_pred (K I);

 val code_pred_cmd = generic_code_pred Code.read_const

 (* transformation for code generation *)

 (* FIXME just one data slot (record) per program unit *)

 structure Pred_Result = Proof_Data

 (

   type T = unit -> term Predicate.pred

   (* FIXME avoid user error with non-user text *)

   fun init _ () = error "Pred_Result"

 );

 val put_pred_result = Pred_Result.put;

 structure Pred_Random_Result = Proof_Data

 (

   type T = unit -> int * int -> term Predicate.pred * (int * int)

   (* FIXME avoid user error with non-user text *)

   fun init _ () = error "Pred_Random_Result"

 );

 val put_pred_random_result = Pred_Random_Result.put;

 structure Dseq_Result = Proof_Data

 (

   type T = unit -> term DSequence.dseq

   (* FIXME avoid user error with non-user text *)

   fun init _ () = error "Dseq_Result"

 );

 val put_dseq_result = Dseq_Result.put;

 structure Dseq_Random_Result = Proof_Data

 (

   type T = unit -> int -> int -> int * int -> term DSequence.dseq * (int * int)

   (* FIXME avoid user error with non-user text *)

   fun init _ () = error "Dseq_Random_Result"

 );

 val put_dseq_random_result = Dseq_Random_Result.put;

 structure New_Dseq_Result = Proof_Data

 (

   type T = unit -> int -> term Lazy_Sequence.lazy_sequence

   (* FIXME avoid user error with non-user text *)

   fun init _ () = error "New_Dseq_Random_Result"

 );

 val put_new_dseq_result = New_Dseq_Result.put;

 structure Lseq_Random_Result = Proof_Data

 (

   type T = unit -> int -> int -> int * int -> int -> term Lazy_Sequence.lazy_sequence

   (* FIXME avoid user error with non-user text *)

   fun init _ () = error "Lseq_Random_Result"

 );

 val put_lseq_random_result = Lseq_Random_Result.put;

 structure Lseq_Random_Stats_Result = Proof_Data

 (

   type T = unit -> int -> int -> int * int -> int -> (term * int) Lazy_Sequence.lazy_sequence

   (* FIXME avoid user error with non-user text *)

   fun init _ () = error "Lseq_Random_Stats_Result"

 );

 val put_lseq_random_stats_result = Lseq_Random_Stats_Result.put;

 fun dest_special_compr t =

   let

     val (inner_t, T_compr) = case t of (Const (@{const_name Collect}, _) $ Abs (x, T, t)) => (t, T)

       | _ => raise TERM ("dest_special_compr", [t])

     val (Ts, conj) = apfst (map snd) (Predicate_Compile_Aux.strip_ex inner_t)

     val [eq, body] = HOLogic.dest_conj conj

     val rhs = case HOLogic.dest_eq eq of

         (Bound i, rhs) => if i = length Ts then rhs else raise TERM ("dest_special_compr", [t])

       | _ => raise TERM ("dest_special_compr", [t])

     val output_names = Name.variant_list (fold Term.add_free_names [rhs, body] [])

       (map (fn i => "x" ^ string_of_int i) (1 upto length Ts))

     val output_frees = map2 (curry Free) output_names (rev Ts)

     val body = subst_bounds (output_frees, body)

     val output = subst_bounds (output_frees, rhs)

   in

     (((body, output), T_compr), output_names)

   end

 fun dest_general_compr ctxt t_compr =

   let      

     val inner_t = case t_compr of (Const (@{const_name Collect}, _) $ t) => t

       | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term ctxt t_compr);    

     val (body, Ts, fp) = HOLogic.strip_psplits inner_t;

     val output_names = Name.variant_list (Term.add_free_names body [])

       (map (fn i => "x" ^ string_of_int i) (1 upto length Ts))

     val output_frees = map2 (curry Free) output_names (rev Ts)

     val body = subst_bounds (output_frees, body)

     val T_compr = HOLogic.mk_ptupleT fp Ts

     val output = HOLogic.mk_ptuple fp T_compr (rev output_frees)

   in

     (((body, output), T_compr), output_names)

   end

 (*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)

 fun analyze_compr ctxt (comp_modifiers, additional_arguments) param_user_modes

   (compilation, arguments) t_compr =

   let

     val compfuns = Comp_Mod.compfuns comp_modifiers

     val all_modes_of = all_modes_of compilation

     val (((body, output), T_compr), output_names) =

       case try dest_special_compr t_compr of SOME r => r | NONE => dest_general_compr ctxt t_compr

     val (pred as Const (name, T), all_args) =

       case strip_comb body of

         (Const (name, T), all_args) => (Const (name, T), all_args)

       | (head, _) => error ("Not a constant: " ^ Syntax.string_of_term ctxt head)

   in

     if defined_functions compilation ctxt name then

       let

         fun extract_mode (Const (@{const_name Pair}, _) $ t1 $ t2) = Pair (extract_mode t1, extract_mode t2)

           | extract_mode (Free (x, _)) = if member (op =) output_names x then Output else Input

           | extract_mode _ = Input

         val user_mode = fold_rev (curry Fun) (map extract_mode all_args) Bool

         fun valid modes1 modes2 =

           case int_ord (length modes1, length modes2) of

             GREATER => error "Not enough mode annotations"

           | LESS => error "Too many mode annotations"

           | EQUAL => forall (fn (m, NONE) => true | (m, SOME m2) => eq_mode (m, m2))

             (modes1 ~~ modes2)

         fun mode_instance_of (m1, m2) =

           let

             fun instance_of (Fun _, Input) = true

               | instance_of (Input, Input) = true

               | instance_of (Output, Output) = true

               | instance_of (Pair (m1, m2), Pair (m1', m2')) =

                   instance_of  (m1, m1') andalso instance_of (m2, m2')

               | instance_of (Pair (m1, m2), Input) =

                   instance_of (m1, Input) andalso instance_of (m2, Input)

               | instance_of (Pair (m1, m2), Output) =

                   instance_of (m1, Output) andalso instance_of (m2, Output)

               | instance_of (Input, Pair (m1, m2)) =

                   instance_of (Input, m1) andalso instance_of (Input, m2)

               | instance_of (Output, Pair (m1, m2)) =

                   instance_of (Output, m1) andalso instance_of (Output, m2)

               | instance_of _ = false

           in forall instance_of (strip_fun_mode m1 ~~ strip_fun_mode m2) end

         val derivs = all_derivations_of ctxt (all_modes_of ctxt) [] body

           |> filter (fn (d, missing_vars) =>

             let

               val (p_mode :: modes) = collect_context_modes d

             in

               null missing_vars andalso

               mode_instance_of (p_mode, user_mode) andalso

               the_default true (Option.map (valid modes) param_user_modes)

             end)

           |> map fst

         val deriv = case derivs of

             [] => error ("No mode possible for comprehension "

                     ^ Syntax.string_of_term ctxt t_compr)

           | [d] => d

           | d :: _ :: _ => (warning ("Multiple modes possible for comprehension "

                     ^ Syntax.string_of_term ctxt t_compr); d);

         val (_, outargs) = split_mode (head_mode_of deriv) all_args

         val t_pred = compile_expr comp_modifiers ctxt

           (body, deriv) [] additional_arguments;

         val T_pred = dest_predT compfuns (fastype_of t_pred)

         val arrange = HOLogic.tupled_lambda (HOLogic.mk_tuple outargs) output

       in

         if null outargs then t_pred else mk_map compfuns T_pred T_compr arrange t_pred

       end

     else

       error "Evaluation with values is not possible because compilation with code_pred was not invoked"

   end

 fun eval ctxt stats param_user_modes (options as (compilation, arguments)) k t_compr =

   let

     fun count xs x =

       let

         fun count' i [] = i

           | count' i (x' :: xs) = if x = x' then count' (i + 1) xs else count' i xs

       in count' 0 xs end

     fun accumulate xs = map (fn x => (x, count xs x)) (sort int_ord (distinct (op =) xs))

     val comp_modifiers =

       case compilation of

           Pred => predicate_comp_modifiers

         | Random => random_comp_modifiers

         | Depth_Limited => depth_limited_comp_modifiers

         | Depth_Limited_Random => depth_limited_random_comp_modifiers

         (*| Annotated => annotated_comp_modifiers*)

         | DSeq => dseq_comp_modifiers

         | Pos_Random_DSeq => pos_random_dseq_comp_modifiers

         | New_Pos_Random_DSeq => new_pos_random_dseq_comp_modifiers

         | Pos_Generator_DSeq => pos_generator_dseq_comp_modifiers

     val compfuns = Comp_Mod.compfuns comp_modifiers

     val additional_arguments =

       case compilation of

         Pred => []

       | Random => map (HOLogic.mk_number @{typ "code_numeral"}) arguments @

         [@{term "(1, 1) :: code_numeral * code_numeral"}]

       | Annotated => []

       | Depth_Limited => [HOLogic.mk_number @{typ "code_numeral"} (hd arguments)]

       | Depth_Limited_Random => map (HOLogic.mk_number @{typ "code_numeral"}) arguments @

         [@{term "(1, 1) :: code_numeral * code_numeral"}]

       | DSeq => []

       | Pos_Random_DSeq => []

       | New_Pos_Random_DSeq => []

       | Pos_Generator_DSeq => []

     val t = analyze_compr ctxt (comp_modifiers, additional_arguments) param_user_modes options t_compr;

     val T = dest_predT compfuns (fastype_of t);

     val t' =

       if stats andalso compilation = New_Pos_Random_DSeq then

         mk_map compfuns T (HOLogic.mk_prodT (HOLogic.termT, @{typ code_numeral}))

           (absdummy (T, HOLogic.mk_prod (HOLogic.term_of_const T $ Bound 0,

             @{term Code_Numeral.of_nat} $ (HOLogic.size_const T $ Bound 0)))) t

       else

         mk_map compfuns T HOLogic.termT (HOLogic.term_of_const T) t

     val thy = Proof_Context.theory_of ctxt

     val time_limit = seconds (Config.get ctxt values_timeout)

     val (ts, statistics) =

       (case compilation of

        (* Random =>

           fst (Predicate.yieldn k

           (Code_Eval.eval NONE ("Predicate_Compile_Core.random_eval_ref", random_eval_ref)

             (fn proc => fn g => fn s => g s |>> Predicate.map proc) thy t' []

             |> Random_Engine.run))*)

         Pos_Random_DSeq =>

           let

             val [nrandom, size, depth] = arguments

           in

             rpair NONE (TimeLimit.timeLimit time_limit (fn () => fst (DSequence.yieldn k

               (Code_Runtime.dynamic_value_strict (Dseq_Random_Result.get, put_dseq_random_result, "Predicate_Compile_Core.put_dseq_random_result")

                 thy NONE (fn proc => fn g => fn nrandom => fn size => fn s => g nrandom size s |>> DSequence.map proc)

                   t' [] nrandom size

                 |> Random_Engine.run)

               depth true)) ())

           end

       | DSeq =>

           rpair NONE (TimeLimit.timeLimit time_limit (fn () => fst (DSequence.yieldn k

             (Code_Runtime.dynamic_value_strict (Dseq_Result.get, put_dseq_result, "Predicate_Compile_Core.put_dseq_result")

               thy NONE DSequence.map t' []) (the_single arguments) true)) ())

       | Pos_Generator_DSeq =>

           let

             val depth = (the_single arguments)

           in

             rpair NONE (TimeLimit.timeLimit time_limit (fn () => fst (Lazy_Sequence.yieldn k

               (Code_Runtime.dynamic_value_strict (New_Dseq_Result.get, put_new_dseq_result, "Predicate_Compile_Core.put_new_dseq_result")

               thy NONE (fn proc => fn g => fn depth => g depth |> Lazy_Sequence.mapa proc)

               t' [] depth))) ())

           end

       | New_Pos_Random_DSeq =>

           let

             val [nrandom, size, depth] = arguments

             val seed = Random_Engine.next_seed ()

           in

             if stats then

               apsnd (SOME o accumulate) (split_list (TimeLimit.timeLimit time_limit

               (fn () => fst (Lazy_Sequence.yieldn k

                 (Code_Runtime.dynamic_value_strict

                   (Lseq_Random_Stats_Result.get, put_lseq_random_stats_result, "Predicate_Compile_Core.put_lseq_random_stats_result")

                   thy NONE

                   (fn proc => fn g => fn nrandom => fn size => fn s => fn depth => g nrandom size s depth

                     |> Lazy_Sequence.mapa (apfst proc))

                     t' [] nrandom size seed depth))) ()))

             else rpair NONE

               (TimeLimit.timeLimit time_limit (fn () => fst (Lazy_Sequence.yieldn k

                 (Code_Runtime.dynamic_value_strict

                   (Lseq_Random_Result.get, put_lseq_random_result, "Predicate_Compile_Core.put_lseq_random_result")

                   thy NONE 

                   (fn proc => fn g => fn nrandom => fn size => fn s => fn depth => g nrandom size s depth

                     |> Lazy_Sequence.mapa proc)

                     t' [] nrandom size seed depth))) ())

           end

       | _ =>

           rpair NONE (TimeLimit.timeLimit time_limit (fn () => fst (Predicate.yieldn k

             (Code_Runtime.dynamic_value_strict (Pred_Result.get, put_pred_result, "Predicate_Compile_Core.put_pred_result")

               thy NONE Predicate.map t' []))) ()))

      handle TimeLimit.TimeOut => error "Reached timeout during execution of values"

   in ((T, ts), statistics) end;

 fun values param_user_modes ((raw_expected, stats), comp_options) k t_compr ctxt =

   let

     val ((T, ts), statistics) = eval ctxt stats param_user_modes comp_options k t_compr

     val setT = HOLogic.mk_setT T

     val elems = HOLogic.mk_set T ts

     val ([dots], ctxt') =

       Proof_Context.add_fixes [(@{binding dots}, SOME setT, Mixfix ("...", [], 1000))] ctxt 

     (* check expected values *)

     val union = Const (@{const_abbrev Set.union}, setT --> setT --> setT)

     val () =

       case raw_expected of

         NONE => ()

       | SOME s =>

         if eq_set (op =) (HOLogic.dest_set (Syntax.read_term ctxt s), ts) then ()

         else

           error ("expected and computed values do not match:\n" ^

             "expected values: " ^ Syntax.string_of_term ctxt (Syntax.read_term ctxt s) ^ "\n" ^

             "computed values: " ^ Syntax.string_of_term ctxt elems ^ "\n")

   in

     ((if k = ~1 orelse length ts < k then elems else union $ elems $ Free (dots, setT), statistics), ctxt')

   end;

 fun values_cmd print_modes param_user_modes options k raw_t state =

   let

     val ctxt = Toplevel.context_of state

     val t = Syntax.read_term ctxt raw_t

     val ((t', stats), ctxt') = values param_user_modes options k t ctxt

     val ty' = Term.type_of t'

     val ctxt'' = Variable.auto_fixes t' ctxt'

     val pretty_stat =

       case stats of

           NONE => []

         | SOME xs =>

           let

             val total = fold (curry (op +)) (map snd xs) 0

             fun pretty_entry (s, n) =

               [Pretty.str "size", Pretty.brk 1,

                Pretty.str (string_of_int s), Pretty.str ":", Pretty.brk 1,

                Pretty.str (string_of_int n), Pretty.fbrk]

           in

             [Pretty.fbrk, Pretty.str "Statistics:", Pretty.fbrk,

              Pretty.str "total:", Pretty.brk 1, Pretty.str (string_of_int total), Pretty.fbrk]

              @ maps pretty_entry xs

           end

     val p = Print_Mode.with_modes print_modes (fn () =>

       Pretty.block ([Pretty.quote (Syntax.pretty_term ctxt'' t'), Pretty.fbrk,

         Pretty.str "::", Pretty.brk 1, Pretty.quote (Syntax.pretty_typ ctxt'' ty')]

         @ pretty_stat)) ();

   in Pretty.writeln p end;

 end;