merged

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/DSequence.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -0,0 +1,112 @@
+
+(* Author: Lukas Bulwahn, TU Muenchen *)
+
+header {* Depth-Limited Sequences with failure element *}
+
+theory DSequence
+imports Lazy_Sequence Code_Numeral
+begin
+
+types 'a dseq = "code_numeral => bool => 'a Lazy_Sequence.lazy_sequence option"
+
+definition empty :: "'a dseq"
+where
+  "empty = (%i pol. Some Lazy_Sequence.empty)"
+
+definition single :: "'a => 'a dseq"
+where
+  "single x = (%i pol. Some (Lazy_Sequence.single x))"
+
+fun eval :: "'a dseq => code_numeral => bool => 'a Lazy_Sequence.lazy_sequence option"
+where
+  "eval f i pol = f i pol"
+
+definition yield :: "'a dseq => code_numeral => bool => ('a * 'a dseq) option" 
+where
+  "yield dseq i pol = (case eval dseq i pol of
+    None => None
+  | Some s => Option.map (apsnd (%r i pol. Some r)) (Lazy_Sequence.yield s))"
+
+definition yieldn :: "code_numeral => 'a dseq => code_numeral => bool => 'a list * 'a dseq"
+where
+  "yieldn n dseq i pol = (case eval dseq i pol of
+    None => ([], %i pol. None)
+  | Some s => let (xs, s') = Lazy_Sequence.yieldn n s in (xs, %i pol. Some s))"
+
+fun map_seq :: "('a => 'b dseq) => 'a Lazy_Sequence.lazy_sequence => 'b dseq"
+where
+  "map_seq f xq i pol = (case Lazy_Sequence.yield xq of
+    None => Some Lazy_Sequence.empty
+  | Some (x, xq') => (case eval (f x) i pol of
+      None => None
+    | Some yq => (case map_seq f xq' i pol of
+        None => None
+      | Some zq => Some (Lazy_Sequence.append yq zq))))"
+
+fun bind :: "'a dseq => ('a => 'b dseq) => 'b dseq"
+where
+  "bind x f = (%i pol. 
+     if i = 0 then
+       (if pol then Some Lazy_Sequence.empty else None)
+     else
+       (case x (i - 1) pol of
+         None => None
+       | Some xq => map_seq f xq i pol))"
+
+fun union :: "'a dseq => 'a dseq => 'a dseq"
+where
+  "union x y = (%i pol. case (x i pol, y i pol) of
+      (Some xq, Some yq) => Some (Lazy_Sequence.append xq yq)
+    | _ => None)"
+
+definition if_seq :: "bool => unit dseq"
+where
+  "if_seq b = (if b then single () else empty)"
+
+fun not_seq :: "unit dseq => unit dseq"
+where
+  "not_seq x = (%i pol. case x i (\<not>pol) of
+    None => Some Lazy_Sequence.empty
+  | Some xq => (case Lazy_Sequence.yield xq of
+      None => Some (Lazy_Sequence.single ())
+    | Some _ => Some (Lazy_Sequence.empty)))"
+
+fun map :: "('a => 'b) => 'a dseq => 'b dseq"
+where
+  "map f g = (%i pol. case g i pol of
+     None => None
+   | Some xq => Some (Lazy_Sequence.map f xq))"
+
+ML {*
+signature DSEQUENCE =
+sig
+  type 'a dseq = int -> bool -> 'a Lazy_Sequence.lazy_sequence option
+  val yield : 'a dseq -> int -> bool -> ('a * 'a dseq) option
+  val yieldn : int -> 'a dseq -> int -> bool -> 'a list * 'a dseq
+  val map : ('a -> 'b) -> 'a dseq -> 'b dseq
+end;
+
+structure DSequence : DSEQUENCE =
+struct
+
+type 'a dseq = int -> bool -> 'a Lazy_Sequence.lazy_sequence option
+
+val yieldn = @{code yieldn}
+val yield = @{code yield}
+val map = @{code map}
+
+end;
+*}
+
+code_reserved Eval DSequence
+(*
+hide type Sequence.seq
+
+hide const Sequence.Seq Sequence.yield Sequence.yieldn Sequence.empty Sequence.single
+  Sequence.append Sequence.flat Sequence.map Sequence.bind Sequence.ifpred Sequence.not_seq
+*)
+hide (open) const empty single eval map_seq bind union if_seq not_seq map
+hide (open) fact empty_def single_def eval.simps map_seq.simps bind.simps union.simps
+  if_seq_def not_seq.simps map.simps
+
+end

--- a/src/HOL/IsaMakefile	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/IsaMakefile	Wed Jan 20 14:05:17 2010 +0100
@@ -246,10 +246,12 @@
   Code_Evaluation.thy \
   Code_Numeral.thy \
   Divides.thy \
+  DSequence.thy \
   Equiv_Relations.thy \
   Groebner_Basis.thy \
   Hilbert_Choice.thy \
   Int.thy \
+  Lazy_Sequence.thy \
   List.thy \
   Main.thy \
   Map.thy \
@@ -260,6 +262,7 @@
   Predicate_Compile.thy \
   Quickcheck.thy \
   Random.thy \
+  Random_Sequence.thy \
   Recdef.thy \
   SetInterval.thy \
   String.thy \

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Lazy_Sequence.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -0,0 +1,158 @@
+
+(* Author: Lukas Bulwahn, TU Muenchen *)
+
+header {* Lazy sequences *}
+
+theory Lazy_Sequence
+imports List Code_Numeral
+begin
+
+datatype 'a lazy_sequence = Empty | Insert 'a "'a lazy_sequence"
+
+definition Lazy_Sequence :: "(unit => ('a * 'a lazy_sequence) option) => 'a lazy_sequence"
+where
+  "Lazy_Sequence f = (case f () of None => Empty | Some (x, xq) => Insert x xq)"
+
+code_datatype Lazy_Sequence 
+
+primrec yield :: "'a lazy_sequence => ('a * 'a lazy_sequence) option"
+where
+  "yield Empty = None"
+| "yield (Insert x xq) = Some (x, xq)"
+
+fun yieldn :: "code_numeral => 'a lazy_sequence => 'a list * 'a lazy_sequence"
+where
+  "yieldn i S = (if i = 0 then ([], S) else
+    case yield S of
+      None => ([], S)
+    | Some (x, S') => let
+       (xs, S'') = yieldn (i - 1) S'
+      in (x # xs, S''))"
+
+lemma [simp]: "yield xq = Some (x, xq') ==> size xq' < size xq"
+by (cases xq) auto
+
+lemma yield_Seq [code]:
+  "yield (Lazy_Sequence f) = f ()"
+unfolding Lazy_Sequence_def by (cases "f ()") auto
+
+lemma Seq_yield:
+  "Lazy_Sequence (%u. yield f) = f"
+unfolding Lazy_Sequence_def by (cases f) auto
+
+lemma lazy_sequence_size_code [code]:
+  "lazy_sequence_size s xq = (case yield xq of None => 0 | Some (x, xq') => s x + lazy_sequence_size s xq' + 1)"
+by (cases xq) auto
+
+lemma size_code [code]:
+  "size xq = (case yield xq of None => 0 | Some (x, xq') => size xq' + 1)"
+by (cases xq) auto
+
+lemma [code]: "eq_class.eq xq yq = (case (yield xq, yield yq) of
+  (None, None) => True | (Some (x, xq'), Some (y, yq')) => (HOL.eq x y) \<and> (eq_class.eq xq yq) | _ => False)"
+apply (cases xq) apply (cases yq) apply (auto simp add: eq_class.eq_equals) 
+apply (cases yq) apply (auto simp add: eq_class.eq_equals) done
+
+lemma seq_case [code]:
+  "lazy_sequence_case f g xq = (case (yield xq) of None => f | Some (x, xq') => g x xq')"
+by (cases xq) auto
+
+lemma [code]: "lazy_sequence_rec f g xq = (case (yield xq) of None => f | Some (x, xq') => g x xq' (lazy_sequence_rec f g xq'))"
+by (cases xq) auto
+
+definition empty :: "'a lazy_sequence"
+where
+  [code]: "empty = Lazy_Sequence (%u. None)"
+
+definition single :: "'a => 'a lazy_sequence"
+where
+  [code]: "single x = Lazy_Sequence (%u. Some (x, empty))"
+
+primrec append :: "'a lazy_sequence => 'a lazy_sequence => 'a lazy_sequence"
+where
+  "append Empty yq = yq"
+| "append (Insert x xq) yq = Insert x (append xq yq)"
+
+lemma [code]:
+  "append xq yq = Lazy_Sequence (%u. case yield xq of
+     None => yield yq
+  | Some (x, xq') => Some (x, append xq' yq))"
+unfolding Lazy_Sequence_def
+apply (cases "xq")
+apply auto
+apply (cases "yq")
+apply auto
+done
+
+primrec flat :: "'a lazy_sequence lazy_sequence => 'a lazy_sequence"
+where
+  "flat Empty = Empty"
+| "flat (Insert xq xqq) = append xq (flat xqq)"
+ 
+lemma [code]:
+  "flat xqq = Lazy_Sequence (%u. case yield xqq of
+    None => None
+  | Some (xq, xqq') => yield (append xq (flat xqq')))"
+apply (cases "xqq")
+apply (auto simp add: Seq_yield)
+unfolding Lazy_Sequence_def
+by auto
+
+primrec map :: "('a => 'b) => 'a lazy_sequence => 'b lazy_sequence"
+where
+  "map f Empty = Empty"
+| "map f (Insert x xq) = Insert (f x) (map f xq)"
+
+lemma [code]:
+  "map f xq = Lazy_Sequence (%u. Option.map (%(x, xq'). (f x, map f xq')) (yield xq))"
+apply (cases xq)
+apply (auto simp add: Seq_yield)
+unfolding Lazy_Sequence_def
+apply auto
+done
+
+definition bind :: "'a lazy_sequence => ('a => 'b lazy_sequence) => 'b lazy_sequence"
+where
+  [code]: "bind xq f = flat (map f xq)"
+
+definition if_seq :: "bool => unit lazy_sequence"
+where
+  "if_seq b = (if b then single () else empty)"
+
+definition not_seq :: "unit lazy_sequence => unit lazy_sequence"
+where
+  "not_seq xq = (case yield xq of None => single () | Some ((), xq) => empty)"
+
+subsection {* Code setup *}
+
+ML {*
+signature LAZY_SEQUENCE =
+sig
+  datatype 'a lazy_sequence = Lazy_Sequence of unit -> ('a * 'a lazy_sequence) option
+  val yield : 'a lazy_sequence -> ('a * 'a lazy_sequence) option
+  val yieldn : int -> 'a lazy_sequence -> ('a list * 'a lazy_sequence)
+end;
+
+structure Lazy_Sequence : LAZY_SEQUENCE =
+struct
+
+@{code_datatype lazy_sequence = Lazy_Sequence}
+
+val yield = @{code yield}
+
+val yieldn = @{code yieldn}
+
+end;
+*}
+
+code_reserved Eval Lazy_Sequence
+
+code_type lazy_sequence (Eval "_/ Lazy'_Sequence.lazy'_sequence")
+
+code_const Lazy_Sequence (Eval "Lazy'_Sequence.Lazy'_Sequence")
+
+hide (open) type lazy_sequence
+hide (open) const Empty Insert Lazy_Sequence yield yieldn empty single append flat map bind if_seq not_seq
+hide (open) fact yield.simps yieldn.simps empty_def single_def append.simps flat.simps map.simps bind_def if_seq_def not_seq_def
+
+end

--- a/src/HOL/Predicate_Compile.thy	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Predicate_Compile.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -5,7 +5,7 @@
 header {* A compiler for predicates defined by introduction rules *}
 
 theory Predicate_Compile
-imports Quickcheck
+imports Random_Sequence Quickcheck
 uses
   "Tools/Predicate_Compile/predicate_compile_aux.ML"
   "Tools/Predicate_Compile/predicate_compile_core.ML"
@@ -18,4 +18,4 @@
 
 setup Predicate_Compile.setup
 
-end
\ No newline at end of file
+end

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Random_Sequence.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -0,0 +1,61 @@
+
+(* Author: Lukas Bulwahn, TU Muenchen *)
+
+theory Random_Sequence
+imports Quickcheck DSequence
+begin
+
+types 'a random_dseq = "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a DSequence.dseq \<times> Random.seed)"
+
+definition empty :: "'a random_dseq"
+where
+  "empty = (%nrandom size. Pair (DSequence.empty))"
+
+definition single :: "'a => 'a random_dseq"
+where
+  "single x = (%nrandom size. Pair (DSequence.single x))"
+
+definition bind :: "'a random_dseq => ('a \<Rightarrow> 'b random_dseq) \<Rightarrow> 'b random_dseq"
+where
+  "bind R f = (\<lambda>nrandom size s. let
+     (P, s') = R nrandom size s;
+     (s1, s2) = Random.split_seed s'
+  in (DSequence.bind P (%a. fst (f a nrandom size s1)), s2))"
+
+definition union :: "'a random_dseq => 'a random_dseq => 'a random_dseq"
+where
+  "union R1 R2 = (\<lambda>nrandom size s. let
+     (S1, s') = R1 nrandom size s; (S2, s'') = R2 nrandom size s'
+  in (DSequence.union S1 S2, s''))"
+
+definition if_random_dseq :: "bool => unit random_dseq"
+where
+  "if_random_dseq b = (if b then single () else empty)"
+
+definition not_random_dseq :: "unit random_dseq => unit random_dseq"
+where
+  "not_random_dseq R = (\<lambda>nrandom size s. let
+     (S, s') = R nrandom size s
+   in (DSequence.not_seq S, s'))"
+
+fun Random :: "(code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed)) \<Rightarrow> 'a random_dseq"
+where
+  "Random g nrandom = (%size. if nrandom <= 0 then (Pair DSequence.empty) else
+     (scomp (g size) (%r. scomp (Random g (nrandom - 1) size) (%rs. Pair (DSequence.union (DSequence.single (fst r)) rs)))))"
+
+definition map :: "('a => 'b) => 'a random_dseq => 'b random_dseq"
+where
+  "map f P = bind P (single o f)"
+
+(*
+hide const DSequence.empty DSequence.single DSequence.eval
+  DSequence.map_seq DSequence.bind DSequence.union DSequence.if_seq DSequence.not_seq
+  DSequence.map
+*)
+
+hide (open) const empty single bind union if_random_dseq not_random_dseq Random map
+
+hide type DSequence.dseq random_dseq
+hide (open) fact empty_def single_def bind_def union_def if_random_dseq_def not_random_dseq_def Random_def map_def
+
+end
\ No newline at end of file

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -69,14 +69,19 @@
     (intross3 @ new_intross, thy'''')
   end
 
-fun preprocess_strong_conn_constnames options gr constnames thy =
+fun preprocess_strong_conn_constnames options gr ts thy =
   let
-    val get_specs = map (fn k => (k, Graph.get_node gr k))
-    val _ = print_step options ("Preprocessing scc of " ^ commas constnames)
-    val (prednames, funnames) = List.partition (is_pred thy) constnames
+    fun get_specs ts = map_filter (fn t =>
+      TermGraph.get_node gr t |>
+      (fn ths => if null ths then NONE else SOME (fst (dest_Const t), ths)))
+      ts
+    val _ = print_step options ("Preprocessing scc of " ^
+      commas (map (Syntax.string_of_term_global thy) ts))
+    val (prednames, funnames) = List.partition (fn t => body_type (fastype_of t) = @{typ bool}) ts
     (* untangle recursion by defining predicates for all functions *)
     val _ = print_step options
-      ("Compiling functions (" ^ commas funnames ^ ") to predicates...")
+      ("Compiling functions (" ^ commas (map (Syntax.string_of_term_global thy) funnames) ^
+        ") to predicates...")
     val (fun_pred_specs, thy') =
       if not (null funnames) then Predicate_Compile_Fun.define_predicates
       (get_specs funnames) thy else ([], thy)
@@ -95,17 +100,19 @@
     thy''''
   end;
 
-fun preprocess options const thy =
+fun preprocess options t thy =
   let
     val _ = print_step options "Fetching definitions from theory..."
-    val table = Predicate_Compile_Data.make_const_spec_table options thy
-    val gr = Predicate_Compile_Data.obtain_specification_graph options thy table const
-    val gr = Graph.subgraph (member (op =) (Graph.all_succs gr [const])) gr
-  in fold_rev (preprocess_strong_conn_constnames options gr)
-    (Graph.strong_conn gr) thy
+    val gr = Output.cond_timeit (!Quickcheck.timing) "preprocess-obtain graph"
+          (fn () => Predicate_Compile_Data.obtain_specification_graph options thy t
+          |> (fn gr => TermGraph.subgraph (member (op =) (TermGraph.all_succs gr [t])) gr))
+  in
+    Output.cond_timeit (!Quickcheck.timing) "preprocess-process"
+      (fn () => (fold_rev (preprocess_strong_conn_constnames options gr)
+        (TermGraph.strong_conn gr) thy))
   end
 
-fun extract_options (((expected_modes, proposed_modes), raw_options), const) =
+fun extract_options (((expected_modes, proposed_modes), (compilation, raw_options)), const) =
   let
     fun chk s = member (op =) raw_options s
   in
@@ -123,9 +130,7 @@
       show_compilation = chk "show_compilation",
       skip_proof = chk "skip_proof",
       inductify = chk "inductify",
-      random = chk "random",
-      depth_limited = chk "depth_limited",
-      annotated = chk "annotated"
+      compilation = compilation
     }
   end
 
@@ -133,11 +138,13 @@
   let
      val thy = ProofContext.theory_of lthy
      val const = Code.read_const thy raw_const
+     val T = Sign.the_const_type thy const
+     val t = Const (const, T)
      val options = extract_options (((expected_modes, proposed_modes), raw_options), const)
   in
     if (is_inductify options) then
       let
-        val lthy' = Local_Theory.theory (preprocess options const) lthy
+        val lthy' = Local_Theory.theory (preprocess options t) lthy
           |> Local_Theory.checkpoint
         val const =
           case Predicate_Compile_Fun.pred_of_function (ProofContext.theory_of lthy') const of
@@ -153,10 +160,6 @@
 
 val setup = Predicate_Compile_Core.setup
 
-val bool_options = ["show_steps", "show_intermediate_results", "show_proof_trace", "show_modes",
-  "show_mode_inference", "show_compilation", "skip_proof", "inductify", "random", "depth_limited",
-  "annotated"]
-
 local structure P = OuterParse
 in
 
@@ -187,8 +190,11 @@
 val scan_options =
   let
     val scan_bool_option = foldl1 (op ||) (map Args.$$$ bool_options)
+    val scan_compilation = foldl1 (op ||) (map (fn (s, c) => Args.$$$ s >> K c) compilation_names)
   in
-    Scan.optional (P.$$$ "[" |-- P.enum1 "," scan_bool_option --| P.$$$ "]") []
+    Scan.optional (P.$$$ "[" |-- Scan.optional scan_compilation Pred
+      -- P.enum "," scan_bool_option --| P.$$$ "]")
+      (Pred, [])
   end
 
 val opt_print_modes = Scan.optional (P.$$$ "(" |-- P.!!! (Scan.repeat1 P.xname --| P.$$$ ")")) [];
@@ -200,12 +206,15 @@
 
 val value_options =
   let
-    val depth_limit = Scan.optional (Args.$$$ "depth_limit" |-- P.$$$ "=" |-- P.nat >> SOME) NONE
-    val random = Scan.optional (Args.$$$ "random" >> K true) false
-    val annotated = Scan.optional (Args.$$$ "annotated" >> K true) false
+    val expected_values = Scan.optional (Args.$$$ "expected" |-- P.term >> SOME) NONE
+    val scan_compilation =
+      Scan.optional
+        (foldl1 (op ||)
+          (map (fn (s, c) => Args.$$$ s -- P.enum "," P.int >> (fn (_, ps) => (c, ps)))
+            compilation_names))
+        (Pred, [])
   in
-    Scan.optional (P.$$$ "[" |-- depth_limit -- (random -- annotated) --| P.$$$ "]")
-      (NONE, (false, false))
+    Scan.optional (P.$$$ "[" |-- expected_values -- scan_compilation --| P.$$$ "]") (NONE, (Pred, []))
   end
 
 (* code_pred command and values command *)
@@ -217,7 +226,7 @@
 
 val _ = OuterSyntax.improper_command "values" "enumerate and print comprehensions" OuterKeyword.diag
   (opt_print_modes -- opt_param_modes -- value_options -- Scan.optional P.nat ~1 -- P.term
-    >> (fn ((((print_modes, param_modes), options), k), t) => Toplevel.no_timing o Toplevel.keep
+    >> (fn ((((print_modes, param_modes), options), k), t) => Toplevel.keep
         (Predicate_Compile_Core.values_cmd print_modes param_modes options k t)));
 
 end

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -6,49 +6,45 @@
 
 (* FIXME proper signature *)
 
+structure TermGraph = Graph(type key = term val ord = TermOrd.fast_term_ord);
+
 structure Predicate_Compile_Aux =
 struct
 
+(* general functions *)
+
+fun apfst3 f (x, y, z) = (f x, y, z)
+fun apsnd3 f (x, y, z) = (x, f y, z)
+fun aptrd3 f (x, y, z) = (x, y, f z)
+
+fun comb_option f (SOME x1, SOME x2) = SOME (f (x1, x2))
+  | comb_option f (NONE, SOME x2) = SOME x2
+  | comb_option f (SOME x1, NONE) = SOME x1
+  | comb_option f (NONE, NONE) = NONE
+
+fun map2_optional f (x :: xs) (y :: ys) = (f x (SOME y)) :: (map2_optional f xs ys)
+  | map2_optional f (x :: xs) [] = (f x NONE) :: (map2_optional f xs [])
+  | map2_optional f [] [] = []
+
+fun find_indices f xs =
+  map_filter (fn (i, true) => SOME i | (i, false) => NONE) (map_index (apsnd f) xs)
 
 (* mode *)
 
-type smode = (int * int list option) list
-type mode = smode option list * smode
-datatype tmode = Mode of mode * smode * tmode option list;
-
-fun string_of_smode js =
-    commas (map
-      (fn (i, is) =>
-        string_of_int i ^ (case is of NONE => ""
-    | SOME is => "p" ^ enclose "[" "]" (commas (map string_of_int is)))) js)
-(* FIXME: remove! *)
-
-fun string_of_mode (iss, is) = space_implode " -> " (map
-  (fn NONE => "X"
-    | SOME js => enclose "[" "]" (string_of_smode js))
-       (iss @ [SOME is]));
-
-fun string_of_tmode (Mode (predmode, termmode, param_modes)) =
-  "predmode: " ^ (string_of_mode predmode) ^
-  (if null param_modes then "" else
-    "; " ^ "params: " ^ commas (map (the_default "NONE" o Option.map string_of_tmode) param_modes))
-
-(* new datatype for mode *)
-
-datatype mode' = Bool | Input | Output | Pair of mode' * mode' | Fun of mode' * mode'
+datatype mode = Bool | Input | Output | Pair of mode * mode | Fun of mode * mode
 
 (* equality of instantiatedness with respect to equivalences:
   Pair Input Input == Input and Pair Output Output == Output *)
-fun eq_mode' (Fun (m1, m2), Fun (m3, m4)) = eq_mode' (m1, m3) andalso eq_mode' (m2, m4)
-  | eq_mode' (Pair (m1, m2), Pair (m3, m4)) = eq_mode' (m1, m3) andalso eq_mode' (m2, m4)
-  | eq_mode' (Pair (m1, m2), Input) = eq_mode' (m1, Input) andalso eq_mode' (m2, Input)
-  | eq_mode' (Pair (m1, m2), Output) = eq_mode' (m1, Output) andalso eq_mode' (m2, Output)
-  | eq_mode' (Input, Pair (m1, m2)) = eq_mode' (Input, m1) andalso eq_mode' (Input, m2)
-  | eq_mode' (Output, Pair (m1, m2)) = eq_mode' (Output, m1) andalso eq_mode' (Output, m2)
-  | eq_mode' (Input, Input) = true
-  | eq_mode' (Output, Output) = true
-  | eq_mode' (Bool, Bool) = true
-  | eq_mode' _ = false
+fun eq_mode (Fun (m1, m2), Fun (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
+  | eq_mode (Pair (m1, m2), Pair (m3, m4)) = eq_mode (m1, m3) andalso eq_mode (m2, m4)
+  | eq_mode (Pair (m1, m2), Input) = eq_mode (m1, Input) andalso eq_mode (m2, Input)
+  | eq_mode (Pair (m1, m2), Output) = eq_mode (m1, Output) andalso eq_mode (m2, Output)
+  | eq_mode (Input, Pair (m1, m2)) = eq_mode (Input, m1) andalso eq_mode (Input, m2)
+  | eq_mode (Output, Pair (m1, m2)) = eq_mode (Output, m1) andalso eq_mode (Output, m2)
+  | eq_mode (Input, Input) = true
+  | eq_mode (Output, Output) = true
+  | eq_mode (Bool, Bool) = true
+  | eq_mode _ = false
 
 (* name: binder_modes? *)
 fun strip_fun_mode (Fun (mode, mode')) = mode :: strip_fun_mode mode'
@@ -61,7 +57,153 @@
 fun dest_tuple_mode (Pair (mode, mode')) = mode :: dest_tuple_mode mode'
   | dest_tuple_mode _ = []
 
-fun string_of_mode' mode' =
+fun all_modes_of_typ (T as Type ("fun", _)) = 
+  let
+    val (S, U) = strip_type T
+  in
+    if U = HOLogic.boolT then
+      fold_rev (fn m1 => fn m2 => map_product (curry Fun) m1 m2)
+        (map all_modes_of_typ S) [Bool]
+    else
+      [Input, Output]
+  end
+  | all_modes_of_typ (Type ("*", [T1, T2])) = 
+    map_product (curry Pair) (all_modes_of_typ T1) (all_modes_of_typ T2)
+  | all_modes_of_typ (Type ("bool", [])) = [Bool]
+  | all_modes_of_typ _ = [Input, Output]
+
+fun extract_params arg =
+  case fastype_of arg of
+    (T as Type ("fun", _)) =>
+      (if (body_type T = HOLogic.boolT) then
+        (case arg of
+          Free _ => [arg] | _ => error "extract_params: Unexpected term")
+      else [])
+  | (Type ("*", [T1, T2])) =>
+      let
+        val (t1, t2) = HOLogic.dest_prod arg
+      in
+        extract_params t1 @ extract_params t2
+      end
+  | _ => []
+
+fun ho_arg_modes_of mode =
+  let
+    fun ho_arg_mode (m as Fun _) =  [m]
+      | ho_arg_mode (Pair (m1, m2)) = ho_arg_mode m1 @ ho_arg_mode m2
+      | ho_arg_mode _ = []
+  in
+    maps ho_arg_mode (strip_fun_mode mode)
+  end
+
+fun ho_args_of mode ts =
+  let
+    fun ho_arg (Fun _) (SOME t) = [t]
+      | ho_arg (Fun _) NONE = error "ho_arg_of"
+      | ho_arg (Pair (m1, m2)) (SOME (Const ("Pair", _) $ t1 $ t2)) =
+          ho_arg m1 (SOME t1) @ ho_arg m2 (SOME t2)
+      | ho_arg (Pair (m1, m2)) NONE = ho_arg m1 NONE @ ho_arg m2 NONE
+      | ho_arg _ _ = []
+  in
+    flat (map2_optional ho_arg (strip_fun_mode mode) ts)
+  end
+
+(* temporary function should be replaced by unsplit_input or so? *)
+fun replace_ho_args mode hoargs ts =
+  let
+    fun replace (Fun _, _) (arg' :: hoargs') = (arg', hoargs')
+      | replace (Pair (m1, m2), Const ("Pair", T) $ t1 $ t2) hoargs =
+        let
+          val (t1', hoargs') = replace (m1, t1) hoargs
+          val (t2', hoargs'') = replace (m2, t2) hoargs'
+        in
+          (Const ("Pair", T) $ t1' $ t2', hoargs'')
+        end
+      | replace (_, t) hoargs = (t, hoargs)
+  in
+    fst (fold_map replace ((strip_fun_mode mode) ~~ ts) hoargs)
+  end
+
+fun ho_argsT_of mode Ts =
+  let
+    fun ho_arg (Fun _) T = [T]
+      | ho_arg (Pair (m1, m2)) (Type ("*", [T1, T2])) = ho_arg m1 T1 @ ho_arg m2 T2
+      | ho_arg _ _ = []
+  in
+    flat (map2 ho_arg (strip_fun_mode mode) Ts)
+  end
+
+(* splits mode and maps function to higher-order argument types *)
+fun split_map_mode f mode ts =
+  let
+    fun split_arg_mode' (m as Fun _) t = f m t
+      | split_arg_mode' (Pair (m1, m2)) (Const ("Pair", _) $ t1 $ t2) =
+        let
+          val (i1, o1) = split_arg_mode' m1 t1
+          val (i2, o2) = split_arg_mode' m2 t2
+        in
+          (comb_option HOLogic.mk_prod (i1, i2), comb_option HOLogic.mk_prod (o1, o2))
+        end
+      | split_arg_mode' Input t = (SOME t, NONE)
+      | split_arg_mode' Output t = (NONE,  SOME t)
+      | split_arg_mode' _ _ = error "split_map_mode: mode and term do not match"
+  in
+    (pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) ts)
+  end
+
+(* splits mode and maps function to higher-order argument types *)
+fun split_map_modeT f mode Ts =
+  let
+    fun split_arg_mode' (m as Fun _) T = f m T
+      | split_arg_mode' (Pair (m1, m2)) (Type ("*", [T1, T2])) =
+        let
+          val (i1, o1) = split_arg_mode' m1 T1
+          val (i2, o2) = split_arg_mode' m2 T2
+        in
+          (comb_option HOLogic.mk_prodT (i1, i2), comb_option HOLogic.mk_prodT (o1, o2))
+        end
+      | split_arg_mode' Input T = (SOME T, NONE)
+      | split_arg_mode' Output T = (NONE,  SOME T)
+      | split_arg_mode' _ _ = error "split_modeT': mode and type do not match"
+  in
+    (pairself (map_filter I) o split_list) (map2 split_arg_mode' (strip_fun_mode mode) Ts)
+  end
+
+fun split_mode mode ts = split_map_mode (fn _ => fn _ => (NONE, NONE)) mode ts
+
+fun fold_map_aterms_prodT comb f (Type ("*", [T1, T2])) s =
+  let
+    val (x1, s') = fold_map_aterms_prodT comb f T1 s
+    val (x2, s'') = fold_map_aterms_prodT comb f T2 s'
+  in
+    (comb x1 x2, s'')
+  end
+  | fold_map_aterms_prodT comb f T s = f T s
+
+fun map_filter_prod f (Const ("Pair", _) $ t1 $ t2) =
+  comb_option HOLogic.mk_prod (map_filter_prod f t1, map_filter_prod f t2)
+  | map_filter_prod f t = f t
+
+(* obviously, split_mode' and split_modeT' do not match? where does that cause problems? *)
+  
+fun split_modeT' mode Ts =
+  let
+    fun split_arg_mode' (Fun _) T = ([], [])
+      | split_arg_mode' (Pair (m1, m2)) (Type ("*", [T1, T2])) =
+        let
+          val (i1, o1) = split_arg_mode' m1 T1
+          val (i2, o2) = split_arg_mode' m2 T2
+        in
+          (i1 @ i2, o1 @ o2)
+        end
+      | split_arg_mode' Input T = ([T], [])
+      | split_arg_mode' Output T = ([], [T])
+      | split_arg_mode' _ _ = error "split_modeT': mode and type do not match"
+  in
+    (pairself flat o split_list) (map2 split_arg_mode' (strip_fun_mode mode) Ts)
+  end
+
+fun string_of_mode mode =
   let
     fun string_of_mode1 Input = "i"
       | string_of_mode1 Output = "o"
@@ -71,9 +213,9 @@
       | string_of_mode2 mode = string_of_mode1 mode
     and string_of_mode3 (Fun (m1, m2)) = string_of_mode2 m1 ^ " => " ^ string_of_mode3 m2
       | string_of_mode3 mode = string_of_mode2 mode
-  in string_of_mode3 mode' end
+  in string_of_mode3 mode end
 
-fun ascii_string_of_mode' mode' =
+fun ascii_string_of_mode mode' =
   let
     fun ascii_string_of_mode' Input = "i"
       | ascii_string_of_mode' Output = "o"
@@ -91,55 +233,10 @@
       | ascii_string_of_mode'_Pair m = ascii_string_of_mode' m
   in ascii_string_of_mode'_Fun mode' end
 
-fun translate_mode T (iss, is) =
-  let
-    val Ts = binder_types T
-    val (Ts1, Ts2) = chop (length iss) Ts
-    fun translate_smode Ts is =
-      let
-        fun translate_arg (i, T) =
-          case AList.lookup (op =) is (i + 1) of
-            SOME NONE => Input
-          | SOME (SOME its) =>
-            let
-              fun translate_tuple (i, T) = if member (op =) its (i + 1) then Input else Output
-            in 
-              foldr1 Pair (map_index translate_tuple (HOLogic.strip_tupleT T))
-            end
-          | NONE => Output
-      in map_index translate_arg Ts end
-    fun mk_mode arg_modes = foldr1 Fun (arg_modes @ [Bool])
-    val param_modes =
-      map (fn (T, NONE) => Input | (T, SOME is) => mk_mode (translate_smode (binder_types T) is))
-        (Ts1 ~~ iss)
-  in
-    mk_mode (param_modes @ translate_smode Ts2 is)
-  end;
+(* premises *)
 
-fun translate_mode' nparams mode' =
-  let
-    fun err () = error "translate_mode': given mode cannot be translated"
-    val (m1, m2) = chop nparams (strip_fun_mode mode')
-    val translate_to_tupled_mode =
-      (map_filter I) o (map_index (fn (i, m) =>
-        if eq_mode' (m, Input) then SOME (i + 1)
-        else if eq_mode' (m, Output) then NONE
-        else err ()))
-    val translate_to_smode =
-      (map_filter I) o (map_index (fn (i, m) =>
-        if eq_mode' (m, Input) then SOME (i + 1, NONE)
-        else if eq_mode' (m, Output) then NONE
-        else SOME (i + 1, SOME (translate_to_tupled_mode (dest_tuple_mode m)))))
-    fun translate_to_param_mode m =
-      case rev (dest_fun_mode m) of
-        Bool :: _ :: _ => SOME (translate_to_smode (strip_fun_mode m))
-      | _ => if eq_mode' (m, Input) then NONE else err ()
-  in
-    (map translate_to_param_mode m1, translate_to_smode m2)
-  end
-
-fun string_of_mode thy constname mode =
-  string_of_mode' (translate_mode (Sign.the_const_type thy constname) mode)
+datatype indprem = Prem of term | Negprem of term | Sidecond of term
+  | Generator of (string * typ);
 
 (* general syntactic functions *)
 
@@ -162,9 +259,9 @@
 val is_pred_equation = is_pred_equation_term o prop_of 
 
 fun is_intro_term constname t =
-  case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
+  the_default false (try (fn t => case fst (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl t))) of
     Const (c, _) => c = constname
-  | _ => false
+  | _ => false) t)
   
 fun is_intro constname t = is_intro_term constname (prop_of t)
 
@@ -177,21 +274,8 @@
 fun is_predT (T as Type("fun", [_, _])) = (snd (strip_type T) = HOLogic.boolT)
   | is_predT _ = false
 
-(* guessing number of parameters *)
-fun find_indexes pred xs =
-  let
-    fun find is n [] = is
-      | find is n (x :: xs) = find (if pred x then (n :: is) else is) (n + 1) xs;
-  in rev (find [] 0 xs) end;
-
-fun guess_nparams T =
-  let
-    val argTs = binder_types T
-    val nparams = fold Integer.max
-      (map (fn x => x + 1) (find_indexes is_predT argTs)) 0
-  in nparams end;
-
 (*** check if a term contains only constructor functions ***)
+(* TODO: another copy in the core! *)
 (* FIXME: constructor terms are supposed to be seen in the way the code generator
   sees constructors.*)
 fun is_constrt thy =
@@ -206,7 +290,34 @@
           | _ => false)
       | _ => false)
   in check end;  
-  
+
+fun is_funtype (Type ("fun", [_, _])) = true
+  | is_funtype _ = false;
+
+fun is_Type (Type _) = true
+  | is_Type _ = false
+
+(* returns true if t is an application of an datatype constructor *)
+(* which then consequently would be splitted *)
+(* else false *)
+(*
+fun is_constructor thy t =
+  if (is_Type (fastype_of t)) then
+    (case DatatypePackage.get_datatype thy ((fst o dest_Type o fastype_of) t) of
+      NONE => false
+    | SOME info => (let
+      val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
+      val (c, _) = strip_comb t
+      in (case c of
+        Const (name, _) => name mem_string constr_consts
+        | _ => false) end))
+  else false
+*)
+
+(* must be exported in code.ML *)
+(* TODO: is there copy in the core? *)
+fun is_constr thy = is_some o Code.get_datatype_of_constr thy;
+
 fun strip_ex (Const ("Ex", _) $ Abs (x, T, t)) =
   let
     val (xTs, t') = strip_ex t
@@ -224,7 +335,6 @@
     val t'' = Term.subst_bounds (rev vs, t');
   in ((ps', t''), nctxt') end;
 
-
 (* introduction rule combinators *)
 
 (* combinators to apply a function to all literals of an introduction rules *)
@@ -280,10 +390,23 @@
 
 (* Different options for compiler *)
 
+datatype compilation = Pred | Random | Depth_Limited | DSeq | Annotated | Random_DSeq
+
+fun string_of_compilation c = case c of
+    Pred => ""
+  | Random => "random"
+  | Depth_Limited => "depth limited"
+  | DSeq => "dseq"
+  | Annotated => "annotated"
+  | Random_DSeq => "random dseq"
+
+(*datatype compilation_options =
+  Pred | Random of int | Depth_Limited of int | DSeq of int | Annotated*)
+
 datatype options = Options of {  
-  expected_modes : (string * mode' list) option,
-  proposed_modes : (string * mode' list) option,
-  proposed_names : ((string * mode') * string) list,
+  expected_modes : (string * mode list) option,
+  proposed_modes : (string * mode list) option,
+  proposed_names : ((string * mode) * string) list,
   show_steps : bool,
   show_proof_trace : bool,
   show_intermediate_results : bool,
@@ -293,14 +416,12 @@
   skip_proof : bool,
 
   inductify : bool,
-  random : bool,
-  depth_limited : bool,
-  annotated : bool
+  compilation : compilation
 };
 
 fun expected_modes (Options opt) = #expected_modes opt
 fun proposed_modes (Options opt) = #proposed_modes opt
-fun proposed_names (Options opt) name mode = AList.lookup (eq_pair (op =) eq_mode')
+fun proposed_names (Options opt) name mode = AList.lookup (eq_pair (op =) eq_mode)
   (#proposed_names opt) (name, mode)
 
 fun show_steps (Options opt) = #show_steps opt
@@ -312,9 +433,8 @@
 fun skip_proof (Options opt) = #skip_proof opt
 
 fun is_inductify (Options opt) = #inductify opt
-fun is_random (Options opt) = #random opt
-fun is_depth_limited (Options opt) = #depth_limited opt
-fun is_annotated (Options opt) = #annotated opt
+
+fun compilation (Options opt) = #compilation opt
 
 val default_options = Options {
   expected_modes = NONE,
@@ -326,14 +446,18 @@
   show_modes = false,
   show_mode_inference = false,
   show_compilation = false,
-  skip_proof = false,
+  skip_proof = true,
   
   inductify = false,
-  random = false,
-  depth_limited = false,
-  annotated = false
+  compilation = Pred
 }
 
+val bool_options = ["show_steps", "show_intermediate_results", "show_proof_trace", "show_modes",
+  "show_mode_inference", "show_compilation", "skip_proof", "inductify"]
+
+val compilation_names = [("pred", Pred),
+  (*("random", Random), ("depth_limited", Depth_Limited), ("annotated", Annotated),*)
+  ("dseq", DSeq), ("random_dseq", Random_DSeq)]
 
 fun print_step options s =
   if show_steps options then tracing s else ()

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -9,36 +9,41 @@
   val setup : theory -> theory
   val code_pred : Predicate_Compile_Aux.options -> string -> Proof.context -> Proof.state
   val code_pred_cmd : Predicate_Compile_Aux.options -> string -> Proof.context -> Proof.state
-  val values_cmd : string list -> Predicate_Compile_Aux.mode' option list option
-    -> int option * (bool * bool) -> int -> string -> Toplevel.state -> unit
-  val register_predicate : (string * thm list * thm * int) -> theory -> theory
+  val values_cmd : string list -> Predicate_Compile_Aux.mode option list option
+    -> (string option * (Predicate_Compile_Aux.compilation * int list))
+    -> int -> string -> Toplevel.state -> unit
+  val register_predicate : (string * thm list * thm) -> theory -> theory
   val register_intros : string * thm list -> theory -> theory
   val is_registered : theory -> string -> bool
+  val function_name_of : Predicate_Compile_Aux.compilation -> theory
+    -> string -> Predicate_Compile_Aux.mode -> string
   val predfun_intro_of: theory -> string -> Predicate_Compile_Aux.mode -> thm
   val predfun_elim_of: theory -> string -> Predicate_Compile_Aux.mode -> thm
-  val predfun_name_of: theory -> string -> Predicate_Compile_Aux.mode -> string
   val all_preds_of : theory -> string list
-  val modes_of: theory -> string -> Predicate_Compile_Aux.mode list
-  val depth_limited_modes_of: theory -> string -> Predicate_Compile_Aux.mode list
-  val depth_limited_function_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string
-  val random_modes_of: theory -> string -> Predicate_Compile_Aux.mode list
-  val random_function_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string
-  val all_modes_of : theory -> (string * Predicate_Compile_Aux.mode list) list
+  val modes_of: Predicate_Compile_Aux.compilation
+    -> theory -> string -> Predicate_Compile_Aux.mode list
+  val all_modes_of : Predicate_Compile_Aux.compilation
+    -> theory -> (string * Predicate_Compile_Aux.mode list) list
   val all_random_modes_of : theory -> (string * Predicate_Compile_Aux.mode list) list
   val intros_of : theory -> string -> thm list
-  val nparams_of : theory -> string -> int
   val add_intro : thm -> theory -> theory
   val set_elim : thm -> theory -> theory
-  val set_nparams : string -> int -> theory -> theory
+  val preprocess_intro : theory -> thm -> thm
   val print_stored_rules : theory -> unit
-  val print_all_modes : theory -> unit
-  val mk_casesrule : Proof.context -> term -> int -> thm list -> term
+  val print_all_modes : Predicate_Compile_Aux.compilation -> theory -> unit
+  val mk_casesrule : Proof.context -> term -> thm list -> term
+  
   val eval_ref : (unit -> term Predicate.pred) option Unsynchronized.ref
   val random_eval_ref : (unit -> int * int -> term Predicate.pred * (int * int))
     option Unsynchronized.ref
+  val dseq_eval_ref : (unit -> term DSequence.dseq) option Unsynchronized.ref
+  val random_dseq_eval_ref : (unit -> int -> int -> int * int -> term DSequence.dseq * (int * int))
+    option Unsynchronized.ref
   val code_pred_intro_attrib : attribute
+  
   (* used by Quickcheck_Generator *) 
   (* temporary for testing of the compilation *)
+  
   datatype compilation_funs = CompilationFuns of {
     mk_predT : typ -> typ,
     dest_predT : typ -> typ,
@@ -50,12 +55,11 @@
     mk_not : term -> term,
     mk_map : typ -> typ -> term -> term -> term
   };
+  
   val pred_compfuns : compilation_funs
   val randompred_compfuns : compilation_funs
   val add_equations : Predicate_Compile_Aux.options -> string list -> theory -> theory
-  val add_quickcheck_equations : Predicate_Compile_Aux.options -> string list -> theory -> theory
-  val add_depth_limited_equations : Predicate_Compile_Aux.options
-    -> string list -> theory -> theory
+  val add_random_dseq_equations : Predicate_Compile_Aux.options -> string list -> theory -> theory
   val mk_tracing : string -> term -> term
 end;
 
@@ -75,6 +79,8 @@
 
 fun debug_tac msg = Seq.single; (* (fn st => (Output.tracing msg; Seq.single st)); *)
 
+fun assert b = if not b then error "Assertion failed" else warning "Assertion holds"
+
 datatype assertion = Max_number_of_subgoals of int
 fun assert_tac (Max_number_of_subgoals i) st =
   if (nprems_of st <= i) then Seq.single st
@@ -97,7 +103,7 @@
     val T = fastype_of t
     val U = fastype_of u
     val [A] = binder_types T
-    val D = body_type U 
+    val D = body_type U                   
   in 
     Const (@{const_name "scomp"}, T --> U --> A --> D) $ t $ u
   end;
@@ -121,96 +127,92 @@
   Const(@{const_name Code_Evaluation.tracing},
     @{typ String.literal} --> (fastype_of t) --> (fastype_of t)) $ (HOLogic.mk_literal s) $ t
 
-(* destruction of intro rules *)
+val strip_intro_concl = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of)
+
+(* derivation trees for modes of premises *)
+
+datatype mode_derivation = Mode_App of mode_derivation * mode_derivation | Context of mode
+  | Mode_Pair of mode_derivation * mode_derivation | Term of mode
 
-(* FIXME: look for other place where this functionality was used before *)
-fun strip_intro_concl nparams intro =
-  let
-    val _ $ u = Logic.strip_imp_concl intro
-    val (pred, all_args) = strip_comb u
-    val (params, args) = chop nparams all_args
-  in (pred, (params, args)) end
+fun string_of_derivation (Mode_App (m1, m2)) =
+  "App (" ^ string_of_derivation m1 ^ ", " ^ string_of_derivation m2 ^ ")"
+  | string_of_derivation (Mode_Pair (m1, m2)) =
+  "Pair (" ^ string_of_derivation m1 ^ ", " ^ string_of_derivation m2 ^ ")"
+  | string_of_derivation (Term m) = "Term (" ^ string_of_mode m ^ ")"
+  | string_of_derivation (Context m) = "Context (" ^ string_of_mode m ^ ")"
 
-(** data structures **)
-
-fun gen_split_smode (mk_tuple, strip_tuple) smode ts =
+fun strip_mode_derivation deriv =
   let
-    fun split_tuple' _ _ [] = ([], [])
-    | split_tuple' is i (t::ts) =
-      (if member (op =) is i then apfst else apsnd) (cons t)
-        (split_tuple' is (i+1) ts)
-    fun split_tuple is t = split_tuple' is 1 (strip_tuple t)
-    fun split_smode' _ _ [] = ([], [])
-      | split_smode' smode i (t::ts) =
-        (if member (op =) (map fst smode) i then
-          case (the (AList.lookup (op =) smode i)) of
-            NONE => apfst (cons t)
-            | SOME is =>
-              let
-                val (ts1, ts2) = split_tuple is t
-                fun cons_tuple ts = if null ts then I else cons (mk_tuple ts)
-                in (apfst (cons_tuple ts1)) o (apsnd (cons_tuple ts2)) end
-          else apsnd (cons t))
-        (split_smode' smode (i+1) ts)
-  in split_smode' smode 1 ts end
+    fun strip (Mode_App (deriv1, deriv2)) ds = strip deriv1 (deriv2 :: ds)
+      | strip deriv ds = (deriv, ds)
+  in
+    strip deriv []
+  end
+
+fun mode_of (Context m) = m
+  | mode_of (Term m) = m
+  | mode_of (Mode_App (d1, d2)) =
+    (case mode_of d1 of Fun (m, m') =>
+        (if m = mode_of d2 then m' else error "mode_of")
+      | _ => error "mode_of2")
+  | mode_of (Mode_Pair (d1, d2)) =
+    Pair (mode_of d1, mode_of d2)
+
+fun head_mode_of deriv = mode_of (fst (strip_mode_derivation deriv))
 
-fun split_smode smode ts = gen_split_smode (HOLogic.mk_tuple, HOLogic.strip_tuple) smode ts
-fun split_smodeT smode ts = gen_split_smode (HOLogic.mk_tupleT, HOLogic.strip_tupleT) smode ts
-
-fun gen_split_mode split_smode (iss, is) ts =
+fun param_derivations_of deriv =
   let
-    val (t1, t2) = chop (length iss) ts 
-  in (t1, split_smode is t2) end
+    val (_, argument_derivs) = strip_mode_derivation deriv
+    fun param_derivation (Mode_Pair (m1, m2)) =
+        param_derivation m1 @ param_derivation m2
+      | param_derivation (Term _) = []
+      | param_derivation m = [m]
+  in
+    maps param_derivation argument_derivs
+  end
 
-fun split_mode (iss, is) ts = gen_split_mode split_smode (iss, is) ts
-fun split_modeT (iss, is) ts = gen_split_mode split_smodeT (iss, is) ts
+fun collect_context_modes (Mode_App (m1, m2)) =
+      collect_context_modes m1 @ collect_context_modes m2
+  | collect_context_modes (Mode_Pair (m1, m2)) =
+      collect_context_modes m1 @ collect_context_modes m2
+  | collect_context_modes (Context m) = [m]
+  | collect_context_modes (Term _) = []
 
-datatype indprem = Prem of term list * term | Negprem of term list * term | Sidecond of term
-  | Generator of (string * typ);
+(* representation of inferred clauses with modes *)
 
-type moded_clause = term list * (indprem * tmode) list
+type moded_clause = term list * (indprem * mode_derivation) list
+
 type 'a pred_mode_table = (string * (mode * 'a) list) list
 
+(* book-keeping *)
+
 datatype predfun_data = PredfunData of {
-  name : string,
   definition : thm,
   intro : thm,
   elim : thm
 };
 
 fun rep_predfun_data (PredfunData data) = data;
-fun mk_predfun_data (name, definition, intro, elim) =
-  PredfunData {name = name, definition = definition, intro = intro, elim = elim}
 
-datatype function_data = FunctionData of {
-  name : string,
-  equation : thm option (* is not used at all? *)
-};
-
-fun rep_function_data (FunctionData data) = data;
-fun mk_function_data (name, equation) =
-  FunctionData {name = name, equation = equation}
+fun mk_predfun_data (definition, intro, elim) =
+  PredfunData {definition = definition, intro = intro, elim = elim}
 
 datatype pred_data = PredData of {
   intros : thm list,
   elim : thm option,
-  nparams : int,
-  functions : bool * (mode * predfun_data) list,
-  random_functions : bool * (mode * function_data) list,
-  depth_limited_functions : bool * (mode * function_data) list,
-  annotated_functions : bool * (mode * function_data) list
+  function_names : (compilation * (mode * string) list) list,
+  predfun_data : (mode * predfun_data) list,
+  needs_random : mode list
 };
 
 fun rep_pred_data (PredData data) = data;
-fun mk_pred_data ((intros, elim, nparams),
-  (functions, random_functions, depth_limited_functions, annotated_functions)) =
-  PredData {intros = intros, elim = elim, nparams = nparams,
-    functions = functions, random_functions = random_functions,
-    depth_limited_functions = depth_limited_functions, annotated_functions = annotated_functions}
-fun map_pred_data f (PredData {intros, elim, nparams,
-  functions, random_functions, depth_limited_functions, annotated_functions}) =
-  mk_pred_data (f ((intros, elim, nparams), (functions, random_functions,
-    depth_limited_functions, annotated_functions)))
+
+fun mk_pred_data ((intros, elim), (function_names, predfun_data, needs_random)) =
+  PredData {intros = intros, elim = elim,
+    function_names = function_names, predfun_data = predfun_data, needs_random = needs_random}
+
+fun map_pred_data f (PredData {intros, elim, function_names, predfun_data, needs_random}) =
+  mk_pred_data (f ((intros, elim), (function_names, predfun_data, needs_random)))
 
 fun eq_option eq (NONE, NONE) = true
   | eq_option eq (SOME x, SOME y) = eq (x, y)
@@ -218,8 +220,7 @@
 
 fun eq_pred_data (PredData d1, PredData d2) = 
   eq_list (Thm.eq_thm) (#intros d1, #intros d2) andalso
-  eq_option (Thm.eq_thm) (#elim d1, #elim d2) andalso
-  #nparams d1 = #nparams d2
+  eq_option (Thm.eq_thm) (#elim d1, #elim d2)
 
 structure PredData = Theory_Data
 (
@@ -238,7 +239,7 @@
  of NONE => error ("No such predicate " ^ quote name)  
   | SOME data => data;
 
-val is_registered = is_some oo lookup_pred_data 
+val is_registered = is_some oo lookup_pred_data
 
 val all_preds_of = Graph.keys o PredData.get
 
@@ -250,24 +251,38 @@
   
 val has_elim = is_some o #elim oo the_pred_data;
 
-val nparams_of = #nparams oo the_pred_data
-
-val modes_of = (map fst) o snd o #functions oo the_pred_data
+fun function_names_of compilation thy name =
+  case AList.lookup (op =) (#function_names (the_pred_data thy name)) compilation of
+    NONE => error ("No " ^ string_of_compilation compilation
+      ^ "functions defined for predicate " ^ quote name)
+  | SOME fun_names => fun_names
 
-fun all_modes_of thy = map (fn name => (name, modes_of thy name)) (all_preds_of thy) 
+fun function_name_of compilation thy name mode =
+  case AList.lookup (op =) (function_names_of compilation thy name) mode of
+    NONE => error ("No " ^ string_of_compilation compilation
+      ^ "function defined for mode " ^ string_of_mode mode ^ " of predicate " ^ quote name)
+  | SOME function_name => function_name
+
+fun modes_of compilation thy name = map fst (function_names_of compilation thy name)
 
-val defined_functions = fst o #functions oo the_pred_data
+fun all_modes_of compilation thy =
+  map_filter (fn name => Option.map (pair name) (try (modes_of compilation thy) name))
+    (all_preds_of thy)
+
+val all_random_modes_of = all_modes_of Random
+
+fun defined_functions compilation thy name =
+  AList.defined (op =) (#function_names (the_pred_data thy name)) compilation
 
 fun lookup_predfun_data thy name mode =
   Option.map rep_predfun_data
-    (AList.lookup (op =) (snd (#functions (the_pred_data thy name))) mode)
+    (AList.lookup (op =) (#predfun_data (the_pred_data thy name)) mode)
 
-fun the_predfun_data thy name mode = case lookup_predfun_data thy name mode
-  of NONE => error ("No function defined for mode " ^ string_of_mode thy name mode ^
-    " of predicate " ^ name)
-   | SOME data => data;
-
-val predfun_name_of = #name ooo the_predfun_data
+fun the_predfun_data thy name mode =
+  case lookup_predfun_data thy name mode of
+    NONE => error ("No function defined for mode " ^ string_of_mode mode ^
+      " of predicate " ^ name)
+  | SOME data => data;
 
 val predfun_definition_of = #definition ooo the_predfun_data
 
@@ -275,102 +290,32 @@
 
 val predfun_elim_of = #elim ooo the_predfun_data
 
-fun lookup_random_function_data thy name mode =
-  Option.map rep_function_data
-  (AList.lookup (op =) (snd (#random_functions (the_pred_data thy name))) mode)
-
-fun the_random_function_data thy name mode = case lookup_random_function_data thy name mode of
-     NONE => error ("No random function defined for mode " ^ string_of_mode thy name mode ^
-       " of predicate " ^ name)
-   | SOME data => data
-
-val random_function_name_of = #name ooo the_random_function_data
-
-val random_modes_of = (map fst) o snd o #random_functions oo the_pred_data
-
-val defined_random_functions = fst o #random_functions oo the_pred_data
-
-fun all_random_modes_of thy =
-  map (fn name => (name, random_modes_of thy name)) (all_preds_of thy) 
-
-fun lookup_depth_limited_function_data thy name mode =
-  Option.map rep_function_data
-    (AList.lookup (op =) (snd (#depth_limited_functions (the_pred_data thy name))) mode)
-
-fun the_depth_limited_function_data thy name mode =
-  case lookup_depth_limited_function_data thy name mode of
-    NONE => error ("No depth-limited function defined for mode " ^ string_of_mode thy name mode
-      ^ " of predicate " ^ name)
-   | SOME data => data
-
-val depth_limited_function_name_of = #name ooo the_depth_limited_function_data
-
-val depth_limited_modes_of = (map fst) o snd o #depth_limited_functions oo the_pred_data
-
-val defined_depth_limited_functions = fst o #depth_limited_functions oo the_pred_data
-
-fun lookup_annotated_function_data thy name mode =
-  Option.map rep_function_data
-    (AList.lookup (op =) (snd (#annotated_functions (the_pred_data thy name))) mode)
-
-fun the_annotated_function_data thy name mode = case lookup_annotated_function_data thy name mode
-  of NONE => error ("No annotated function defined for mode " ^ string_of_mode thy name mode
-    ^ " of predicate " ^ name)
-   | SOME data => data
-
-val annotated_function_name_of = #name ooo the_annotated_function_data
-
-val annotated_modes_of = (map fst) o snd o #annotated_functions oo the_pred_data
-
-val defined_annotated_functions = fst o #annotated_functions oo the_pred_data
-
 (* diagnostic display functions *)
 
 fun print_modes options thy modes =
   if show_modes options then
     tracing ("Inferred modes:\n" ^
       cat_lines (map (fn (s, ms) => s ^ ": " ^ commas (map
-        (string_of_mode thy s) ms)) modes))
+        string_of_mode ms)) modes))
   else ()
 
 fun print_pred_mode_table string_of_entry thy pred_mode_table =
   let
-    fun print_mode pred (mode, entry) =  "mode : " ^ string_of_mode thy pred mode
+    fun print_mode pred (mode, entry) =  "mode : " ^ string_of_mode mode
       ^ string_of_entry pred mode entry
     fun print_pred (pred, modes) =
       "predicate " ^ pred ^ ": " ^ cat_lines (map (print_mode pred) modes)
     val _ = tracing (cat_lines (map print_pred pred_mode_table))
   in () end;
 
-fun string_of_prem thy (Prem (ts, p)) =
-    (Syntax.string_of_term_global thy (list_comb (p, ts))) ^ "(premise)"
-  | string_of_prem thy (Negprem (ts, p)) =
-    (Syntax.string_of_term_global thy (HOLogic.mk_not (list_comb (p, ts)))) ^ "(negative premise)"
+fun string_of_prem thy (Prem t) =
+    (Syntax.string_of_term_global thy t) ^ "(premise)"
+  | string_of_prem thy (Negprem t) =
+    (Syntax.string_of_term_global thy (HOLogic.mk_not t)) ^ "(negative premise)"
   | string_of_prem thy (Sidecond t) =
     (Syntax.string_of_term_global thy t) ^ "(sidecondition)"
   | string_of_prem thy _ = error "string_of_prem: unexpected input"
 
-fun string_of_moded_prem thy (Prem (ts, p), tmode) =
-    (Syntax.string_of_term_global thy (list_comb (p, ts))) ^
-    "(" ^ (string_of_tmode tmode) ^ ")"
-  | string_of_moded_prem thy (Generator (v, T), _) =
-    "Generator for " ^ v ^ " of Type " ^ (Syntax.string_of_typ_global thy T)
-  | string_of_moded_prem thy (Negprem (ts, p), Mode (_, is, _)) =
-    (Syntax.string_of_term_global thy (list_comb (p, ts))) ^
-    "(negative mode: " ^ string_of_smode is ^ ")"
-  | string_of_moded_prem thy (Sidecond t, Mode (_, is, _)) =
-    (Syntax.string_of_term_global thy t) ^
-    "(sidecond mode: " ^ string_of_smode is ^ ")"    
-  | string_of_moded_prem _ _ = error "string_of_moded_prem: unimplemented"
-
-fun print_moded_clauses thy =
-  let
-    fun string_of_clause pred mode clauses =
-      cat_lines (map (fn (ts, prems) => (space_implode " --> "
-        (map (string_of_moded_prem thy) prems)) ^ " --> " ^ pred ^ " "
-        ^ (space_implode " " (map (Syntax.string_of_term_global thy) ts))) clauses)
-  in print_pred_mode_table string_of_clause thy end;
-
 fun string_of_clause thy pred (ts, prems) =
   (space_implode " --> "
   (map (string_of_prem thy) prems)) ^ " --> " ^ pred ^ " "
@@ -386,7 +331,6 @@
     val preds = (Graph.keys o PredData.get) thy
     fun print pred () = let
       val _ = writeln ("predicate: " ^ pred)
-      val _ = writeln ("number of parameters: " ^ string_of_int (nparams_of thy pred))
       val _ = writeln ("introrules: ")
       val _ = fold (fn thm => fn u => writeln (Display.string_of_thm_global thy thm))
         (rev (intros_of thy pred)) ()
@@ -400,16 +344,16 @@
     fold print preds ()
   end;
 
-fun print_all_modes thy =
+fun print_all_modes compilation thy =
   let
     val _ = writeln ("Inferred modes:")
     fun print (pred, modes) u =
       let
         val _ = writeln ("predicate: " ^ pred)
-        val _ = writeln ("modes: " ^ (commas (map (string_of_mode thy pred) modes)))
+        val _ = writeln ("modes: " ^ (commas (map string_of_mode modes)))
       in u end
   in
-    fold print (all_modes_of thy) ()
+    fold print (all_modes_of compilation thy) ()
   end
 
 (* validity checks *)
@@ -420,12 +364,12 @@
     SOME (s, ms) => (case AList.lookup (op =) modes s of
       SOME modes =>
         let
-          val modes' = map (translate_mode (the (AList.lookup (op =) preds s))) modes
+          val modes' = modes
         in
-          if not (eq_set eq_mode' (ms, modes')) then
+          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))
+            ^ "  inferred modes for " ^ s ^ ": " ^ commas (map string_of_mode modes')  ^ "\n"
+            ^ "  expected modes for " ^ s ^ ": " ^ commas (map string_of_mode ms))
           else ()
         end
       | NONE => ())
@@ -437,12 +381,12 @@
       SOME inferred_ms =>
         let
           val preds_without_modes = map fst (filter (null o snd) (modes @ extra_modes))
-          val modes' = map (translate_mode (the (AList.lookup (op =) preds s))) inferred_ms
+          val modes' = inferred_ms
         in
-          if not (eq_set eq_mode' (ms, modes')) then
+          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"
+            ^ "  inferred modes for " ^ s ^ ": " ^ commas (map string_of_mode modes')  ^ "\n"
+            ^ "  expected modes for " ^ s ^ ": " ^ commas (map string_of_mode ms) ^ "\n"
             ^ "For the following clauses, the following modes could not be inferred: " ^ "\n"
             ^ cat_lines errors ^
             (if not (null preds_without_modes) then
@@ -474,58 +418,88 @@
    end) handle Type.TUNIFY =>
      (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
 
-fun import_intros inp_pred nparams [] ctxt =
+fun import_intros inp_pred [] ctxt =
   let
-    val ([outp_pred], ctxt') = Variable.import_terms false [inp_pred] ctxt
-    val (paramTs, _) = chop nparams (binder_types (fastype_of outp_pred))
-    val (param_names, ctxt'') = Variable.variant_fixes (map (fn i => "p" ^ (string_of_int i))
-      (1 upto nparams)) ctxt'
+    val ([outp_pred], ctxt') = Variable.import_terms true [inp_pred] ctxt
+    val T = fastype_of outp_pred
+    (* TODO: put in a function for this next line! *)
+    val paramTs = ho_argsT_of (hd (all_modes_of_typ T)) (binder_types T)
+    val (param_names, ctxt'') = Variable.variant_fixes
+      (map (fn i => "p" ^ (string_of_int i)) (1 upto (length paramTs))) ctxt'
     val params = map2 (curry Free) param_names paramTs
-    in (((outp_pred, params), []), ctxt') end
-  | import_intros inp_pred nparams (th :: ths) ctxt =
+  in
+    (((outp_pred, params), []), ctxt')
+  end
+  | import_intros inp_pred (th :: ths) ctxt =
     let
-      val ((_, [th']), ctxt') = Variable.import false [th] ctxt
+      val ((_, [th']), ctxt') = Variable.import true [th] ctxt
       val thy = ProofContext.theory_of ctxt'
-      val (pred, (params, args)) = strip_intro_concl nparams (prop_of th')
-      val ho_args = filter (is_predT o fastype_of) args
+      val (pred, args) = strip_intro_concl th'
+      val T = fastype_of pred
+      val ho_args = ho_args_of (hd (all_modes_of_typ T)) args
       fun subst_of (pred', pred) =
         let
           val subst = Sign.typ_match thy (fastype_of pred', fastype_of pred) Vartab.empty
         in map (fn (indexname, (s, T)) => ((indexname, s), T)) (Vartab.dest subst) end
       fun instantiate_typ th =
         let
-          val (pred', _) = strip_intro_concl 0 (prop_of th)
+          val (pred', _) = strip_intro_concl th
           val _ = if not (fst (dest_Const pred) = fst (dest_Const pred')) then
             error "Trying to instantiate another predicate" else ()
         in Thm.certify_instantiate (subst_of (pred', pred), []) th end;
       fun instantiate_ho_args th =
         let
-          val (_, (params', args')) = strip_intro_concl nparams (prop_of th)
-          val ho_args' = map dest_Var (filter (is_predT o fastype_of) args')
-        in Thm.certify_instantiate ([], map dest_Var params' ~~ params) th end
+          val (_, args') = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl o prop_of) th
+          val ho_args' = map dest_Var (ho_args_of (hd (all_modes_of_typ T)) args')
+        in Thm.certify_instantiate ([], ho_args' ~~ ho_args) th end
       val outp_pred =
         Term_Subst.instantiate (subst_of (inp_pred, pred), []) inp_pred
       val ((_, ths'), ctxt1) =
         Variable.import false (map (instantiate_typ #> instantiate_ho_args) ths) ctxt'
     in
-      (((outp_pred, params), th' :: ths'), ctxt1)
+      (((outp_pred, ho_args), th' :: ths'), ctxt1)
     end
 
 (* generation of case rules from user-given introduction rules *)
 
-fun mk_casesrule ctxt pred nparams introrules =
+fun mk_args2 (Type ("*", [T1, T2])) st =
+    let
+      val (t1, st') = mk_args2 T1 st
+      val (t2, st'') = mk_args2 T2 st'
+    in
+      (HOLogic.mk_prod (t1, t2), st'')
+    end
+  | mk_args2 (T as Type ("fun", _)) (params, ctxt) = 
+    let
+      val (S, U) = strip_type T
+    in
+      if U = HOLogic.boolT then
+        (hd params, (tl params, ctxt))
+      else
+        let
+          val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
+        in
+          (Free (x, T), (params, ctxt'))
+        end
+    end
+  | mk_args2 T (params, ctxt) =
+    let
+      val ([x], ctxt') = Variable.variant_fixes ["x"] ctxt
+    in
+      (Free (x, T), (params, ctxt'))
+    end
+  
+fun mk_casesrule ctxt pred introrules =
   let
-    val (((pred, params), intros_th), ctxt1) = import_intros pred nparams introrules ctxt
+    val (((pred, params), intros_th), ctxt1) = import_intros pred introrules ctxt
     val intros = map prop_of intros_th
     val ([propname], ctxt2) = Variable.variant_fixes ["thesis"] ctxt1
     val prop = HOLogic.mk_Trueprop (Free (propname, HOLogic.boolT))
-    val (_, argsT) = chop nparams (binder_types (fastype_of pred))
-    val (argnames, ctxt3) = Variable.variant_fixes
-      (map (fn i => "a" ^ string_of_int i) (1 upto length argsT)) ctxt2
-    val argvs = map2 (curry Free) argnames argsT
+    val argsT = binder_types (fastype_of pred)
+    val (argvs, _) = fold_map mk_args2 argsT (params, ctxt2)
     fun mk_case intro =
       let
-        val (_, (_, args)) = strip_intro_concl nparams intro
+        val (_, args) = (strip_comb o HOLogic.dest_Trueprop o Logic.strip_imp_concl) intro
         val prems = Logic.strip_imp_prems intro
         val eqprems = map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) argvs args
         val frees = (fold o fold_aterms)
@@ -533,11 +507,11 @@
               if member (op aconv) params t then I else insert (op aconv) t
            | _ => I) (args @ prems) []
       in fold Logic.all frees (Logic.list_implies (eqprems @ prems, prop)) end
-    val assm = HOLogic.mk_Trueprop (list_comb (pred, params @ argvs))
+    val assm = HOLogic.mk_Trueprop (list_comb (pred, argvs))
     val cases = map mk_case intros
   in Logic.list_implies (assm :: cases, prop) end;
 
-(** preprocessing rules **)  
+(** preprocessing rules **)
 
 fun imp_prems_conv cv ct =
   case Thm.term_of ct of
@@ -555,7 +529,7 @@
       (Trueprop_conv (Conv.try_conv (Conv.rewr_conv (Thm.symmetric @{thm Predicate.eq_is_eq})))))
     (Thm.transfer thy rule)
 
-fun preprocess_elim thy nparams elimrule =
+fun preprocess_elim thy elimrule =
   let
     fun replace_eqs (Const ("Trueprop", _) $ (Const ("op =", T) $ lhs $ rhs)) =
        HOLogic.mk_Trueprop (Const (@{const_name Predicate.eq}, T) $ lhs $ rhs)
@@ -563,7 +537,7 @@
     val ctxt = ProofContext.init thy
     val ((_, [elimrule]), ctxt') = Variable.import false [elimrule] ctxt
     val prems = Thm.prems_of elimrule
-    val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems)))) - nparams
+    val nargs = length (snd (strip_comb (HOLogic.dest_Trueprop (hd prems))))
     fun preprocess_case t =
       let
        val params = Logic.strip_params t
@@ -585,15 +559,7 @@
 
 fun expand_tuples_elim th = th
 
-(* updaters *)
-
-fun apfst4 f (x1, x2, x3, x4) = (f x1, x2, x3, x4)
-fun apsnd4 f (x1, x2, x3, x4) = (x1, f x2, x3, x4)
-fun aptrd4 f (x1, x2, x3, x4) = (x1, x2, f x3, x4)
-fun apfourth4 f (x1, x2, x3, x4) = (x1, x2, x3, f x4)
-fun appair f g (x, y) = (f x, g x)
-
-val no_compilation = ((false, []), (false, []), (false, []), (false, []))
+val no_compilation = ([], [], [])
 
 fun fetch_pred_data thy name =
   case try (Inductive.the_inductive (ProofContext.init thy)) name of
@@ -608,20 +574,19 @@
         val index = find_index (fn s => s = name) (#names (fst info))
         val pre_elim = nth (#elims result) index
         val pred = nth (#preds result) index
-        val nparams = length (Inductive.params_of (#raw_induct result))
         (*val elim = singleton (Inductive_Set.codegen_preproc thy) (preprocess_elim thy nparams 
           (expand_tuples_elim pre_elim))*)
         val elim =
           (Drule.standard o Skip_Proof.make_thm thy)
-          (mk_casesrule (ProofContext.init thy) pred nparams intros)
+          (mk_casesrule (ProofContext.init thy) pred intros)
       in
-        mk_pred_data ((intros, SOME elim, nparams), no_compilation)
+        mk_pred_data ((intros, SOME elim), no_compilation)
       end
   | NONE => error ("No such predicate: " ^ quote name)
 
-fun add_predfun name mode data =
+fun add_predfun_data name mode data =
   let
-    val add = (apsnd o apfst4) (fn (x, y) => (true, cons (mode, mk_predfun_data data) y))
+    val add = (apsnd o apsnd3) (cons (mode, mk_predfun_data data))
   in PredData.map (Graph.map_node name (map_pred_data add)) end
 
 fun is_inductive_predicate thy name =
@@ -636,96 +601,74 @@
         (is_inductive_predicate thy c orelse is_registered thy c))
   end;
 
-
-(* code dependency graph *)
-(*
-fun dependencies_of thy name =
-  let
-    val (intros, elim, nparams) = fetch_pred_data thy name 
-    val data = mk_pred_data ((intros, SOME elim, nparams), ([], [], []))
-    val keys = depending_preds_of thy intros
-  in
-    (data, keys)
-  end;
-*)
-
 fun add_intro thm thy =
   let
-    val (name, T) = dest_Const (fst (strip_intro_concl 0 (prop_of thm)))
+    val (name, T) = dest_Const (fst (strip_intro_concl thm))
     fun cons_intro gr =
      case try (Graph.get_node gr) name of
        SOME pred_data => Graph.map_node name (map_pred_data
-         (apfst (fn (intros, elim, nparams) => (intros @ [thm], elim, nparams)))) gr
-     | NONE =>
-       let
-         val nparams = the_default (guess_nparams T)
-           (try (#nparams o rep_pred_data o (fetch_pred_data thy)) name)
-       in Graph.new_node (name, mk_pred_data (([thm], NONE, nparams), no_compilation)) gr end;
+         (apfst (fn (intros, elim) => (intros @ [thm], elim)))) gr
+     | NONE => Graph.new_node (name, mk_pred_data (([thm], NONE), no_compilation)) gr
   in PredData.map cons_intro thy end
 
 fun set_elim thm =
   let
     val (name, _) = dest_Const (fst 
       (strip_comb (HOLogic.dest_Trueprop (hd (prems_of thm)))))
-    fun set (intros, _, nparams) = (intros, SOME thm, nparams)  
+    fun set (intros, _) = (intros, SOME thm)
   in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
 
-fun set_nparams name nparams =
+fun register_predicate (constname, pre_intros, pre_elim) thy =
   let
-    fun set (intros, elim, _ ) = (intros, elim, nparams) 
-  in PredData.map (Graph.map_node name (map_pred_data (apfst set))) end
-
-fun register_predicate (constname, pre_intros, pre_elim, nparams) thy =
-  let
-    (* preprocessing *)
     val intros = map (preprocess_intro thy) pre_intros
-    val elim = preprocess_elim thy nparams pre_elim
+    val elim = preprocess_elim thy pre_elim
   in
     if not (member (op =) (Graph.keys (PredData.get thy)) constname) then
       PredData.map
         (Graph.new_node (constname,
-          mk_pred_data ((intros, SOME elim, nparams), no_compilation))) thy
+          mk_pred_data ((intros, SOME elim), no_compilation))) thy
     else thy
   end
 
 fun register_intros (constname, pre_intros) thy =
   let
     val T = Sign.the_const_type thy constname
-    fun constname_of_intro intr = fst (dest_Const (fst (strip_intro_concl 0 (prop_of intr))))
+    fun constname_of_intro intr = fst (dest_Const (fst (strip_intro_concl intr)))
     val _ = if not (forall (fn intr => constname_of_intro intr = constname) pre_intros) then
       error ("register_intros: Introduction rules of different constants are used\n" ^
         "expected rules for " ^ constname ^ ", but received rules for " ^
           commas (map constname_of_intro pre_intros))
       else ()
     val pred = Const (constname, T)
-    val nparams = guess_nparams T
     val pre_elim = 
       (Drule.standard o Skip_Proof.make_thm thy)
-      (mk_casesrule (ProofContext.init thy) pred nparams pre_intros)
-  in register_predicate (constname, pre_intros, pre_elim, nparams) thy end
+      (mk_casesrule (ProofContext.init thy) pred pre_intros)
+  in register_predicate (constname, pre_intros, pre_elim) thy end
 
-fun set_random_function_name pred mode name = 
+fun defined_function_of compilation pred =
   let
-    val set = (apsnd o apsnd4) (fn (x, y) => (true, cons (mode, mk_function_data (name, NONE)) y))
+    val set = (apsnd o apfst3) (cons (compilation, []))
   in
     PredData.map (Graph.map_node pred (map_pred_data set))
   end
 
-fun set_depth_limited_function_name pred mode name = 
+fun set_function_name compilation pred mode name =
   let
-    val set = (apsnd o aptrd4) (fn (x, y) => (true, cons (mode, mk_function_data (name, NONE)) y))
+    val set = (apsnd o apfst3)
+      (AList.map_default (op =) (compilation, [(mode, name)]) (cons (mode, name)))
   in
     PredData.map (Graph.map_node pred (map_pred_data set))
   end
 
-fun set_annotated_function_name pred mode name =
+fun set_needs_random name modes =
   let
-    val set = (apsnd o apfourth4)
-      (fn (x, y) => (true, cons (mode, mk_function_data (name, NONE)) y))
+    val set = (apsnd o aptrd3) (K modes)
   in
-    PredData.map (Graph.map_node pred (map_pred_data set))
+    PredData.map (Graph.map_node name (map_pred_data set))
   end
 
+(* datastructures and setup for generic compilation *)
+
 datatype compilation_funs = CompilationFuns of {
   mk_predT : typ -> typ,
   dest_predT : typ -> typ,
@@ -789,6 +732,8 @@
     Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x
   end;
 
+fun dest_Eval (Const (@{const_name Predicate.eval}, _) $ f $ x) = (f, x)
+
 fun mk_map T1 T2 tf tp = Const (@{const_name Predicate.map},
   (T1 --> T2) --> mk_predT T1 --> mk_predT T2) $ tf $ tp;
 
@@ -811,7 +756,7 @@
 fun mk_bot T = Const(@{const_name Quickcheck.empty}, mk_randompredT T)
 
 fun mk_single t =
-  let
+  let               
     val T = fastype_of t
   in
     Const (@{const_name Quickcheck.single}, T --> mk_randompredT T) $ t
@@ -840,54 +785,119 @@
     mk_not = mk_not, mk_map = mk_map};
 
 end;
+
+structure DSequence_CompFuns =
+struct
+
+fun mk_dseqT T = Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ bool},
+  Type (@{type_name Option.option}, [Type  ("Lazy_Sequence.lazy_sequence", [T])])])])
+
+fun dest_dseqT (Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ bool},
+  Type (@{type_name Option.option}, [Type ("Lazy_Sequence.lazy_sequence", [T])])])])) = T
+  | dest_dseqT T = raise TYPE ("dest_dseqT", [T], []);
+
+fun mk_bot T = Const ("DSequence.empty", mk_dseqT T);
+
+fun mk_single t =
+  let val T = fastype_of t
+  in Const("DSequence.single", T --> mk_dseqT T) $ t end;
+
+fun mk_bind (x, f) =
+  let val T as Type ("fun", [_, U]) = fastype_of f
+  in
+    Const ("DSequence.bind", fastype_of x --> T --> U) $ x $ f
+  end;
+
+val mk_sup = HOLogic.mk_binop "DSequence.union";
+
+fun mk_if cond = Const ("DSequence.if_seq",
+  HOLogic.boolT --> mk_dseqT HOLogic.unitT) $ cond;
+
+fun mk_not t = let val T = mk_dseqT HOLogic.unitT
+  in Const ("DSequence.not_seq", T --> T) $ t end
+
+fun mk_map T1 T2 tf tp = Const ("DSequence.map",
+  (T1 --> T2) --> mk_dseqT T1 --> mk_dseqT T2) $ tf $ tp
+
+val compfuns = CompilationFuns {mk_predT = mk_dseqT, dest_predT = dest_dseqT,
+    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    mk_not = mk_not, mk_map = mk_map}
+
+end;
+
+structure Random_Sequence_CompFuns =
+struct
+
+fun mk_random_dseqT T =
+  @{typ code_numeral} --> @{typ code_numeral} --> @{typ Random.seed} -->
+    HOLogic.mk_prodT (DSequence_CompFuns.mk_dseqT T, @{typ Random.seed})
+
+fun dest_random_dseqT (Type ("fun", [@{typ code_numeral}, Type ("fun", [@{typ code_numeral},
+  Type ("fun", [@{typ Random.seed},
+  Type (@{type_name "*"}, [T, @{typ Random.seed}])])])])) = DSequence_CompFuns.dest_dseqT T
+  | dest_random_dseqT T = raise TYPE ("dest_random_dseqT", [T], []);
+
+fun mk_bot T = Const ("Random_Sequence.empty", mk_random_dseqT T);
+
+fun mk_single t =
+  let val T = fastype_of t
+  in Const("Random_Sequence.single", T --> mk_random_dseqT T) $ t end;
+
+fun mk_bind (x, f) =
+  let
+    val T as Type ("fun", [_, U]) = fastype_of f
+  in
+    Const ("Random_Sequence.bind", fastype_of x --> T --> U) $ x $ f
+  end;
+
+val mk_sup = HOLogic.mk_binop "Random_Sequence.union";
+
+fun mk_if cond = Const ("Random_Sequence.if_random_dseq",
+  HOLogic.boolT --> mk_random_dseqT HOLogic.unitT) $ cond;
+
+fun mk_not t = let val T = mk_random_dseqT HOLogic.unitT
+  in Const ("Random_Sequence.not_random_dseq", T --> T) $ t end
+
+fun mk_map T1 T2 tf tp = Const ("Random_Sequence.map",
+  (T1 --> T2) --> mk_random_dseqT T1 --> mk_random_dseqT T2) $ tf $ tp
+
+val compfuns = CompilationFuns {mk_predT = mk_random_dseqT, dest_predT = dest_random_dseqT,
+    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    mk_not = mk_not, mk_map = mk_map}
+
+end;
+
+
+
+fun mk_random T =
+  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;
+
+
+
 (* for external use with interactive mode *)
 val pred_compfuns = PredicateCompFuns.compfuns
-val randompred_compfuns = RandomPredCompFuns.compfuns;
-
-fun lift_random random =
-  let
-    val T = dest_randomT (fastype_of random)
-  in
-    Const (@{const_name Quickcheck.Random}, (@{typ Random.seed} -->
-      HOLogic.mk_prodT (HOLogic.mk_prodT (T, @{typ "unit => term"}), @{typ Random.seed})) -->
-      RandomPredCompFuns.mk_randompredT T) $ random
-  end;
+val randompred_compfuns = Random_Sequence_CompFuns.compfuns;
 
 (* function types and names of different compilations *)
 
-fun funT_of compfuns (iss, is) T =
-  let
-    val Ts = binder_types T
-    val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
-    val paramTs' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss paramTs
-  in
-    (paramTs' @ inargTs) ---> (mk_predT compfuns (HOLogic.mk_tupleT outargTs))
-  end;
-
-fun depth_limited_funT_of compfuns (iss, is) T =
+fun funT_of compfuns mode T =
   let
     val Ts = binder_types T
-    val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
-    val paramTs' =
-      map2 (fn SOME is => depth_limited_funT_of compfuns ([], is) | NONE => I) iss paramTs
+    val (inTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts
   in
-    (paramTs' @ inargTs @ [@{typ bool}, @{typ "code_numeral"}])
-      ---> (mk_predT compfuns (HOLogic.mk_tupleT outargTs))
+    inTs ---> (mk_predT compfuns (HOLogic.mk_tupleT outTs))
   end;
 
-fun random_function_funT_of (iss, is) T =
-  let
-    val Ts = binder_types T
-    val (paramTs, (inargTs, outargTs)) = split_modeT (iss, is) Ts
-    val paramTs' = map2 (fn SOME is => random_function_funT_of ([], is) | NONE => I) iss paramTs
-  in
-    (paramTs' @ inargTs @ [@{typ code_numeral}]) --->
-      (mk_predT RandomPredCompFuns.compfuns (HOLogic.mk_tupleT outargTs))
-  end
+(** mode analysis **)
 
-(* Mode analysis *)
-
-(*** check if a term contains only constructor functions ***)
 fun is_constrt thy =
   let
     val cnstrs = flat (maps
@@ -924,235 +934,347 @@
       val is = subsets (i+1) j
     in merge (map (fn ks => i::ks) is) is end
   else [[]];
-     
-(* FIXME: should be in library - cprod = map_prod I *)
-fun cprod ([], ys) = []
-  | cprod (x :: xs, ys) = map (pair x) ys @ cprod (xs, ys);
-
-fun cprods xss = List.foldr (map op :: o cprod) [[]] xss;
-
-fun cprods_subset [] = [[]]
-  | cprods_subset (xs :: xss) =
-  let
-    val yss = (cprods_subset xss)
-  in maps (fn ys => map (fn x => cons x ys) xs) yss @ yss end
-  
-fun modes_of_term modes t =
-  let
-    val ks = map_index (fn (i, T) => (i + 1, NONE)) (binder_types (fastype_of t));
-    val default = [Mode (([], ks), ks, [])];
-    fun mk_modes name args = Option.map (maps (fn (m as (iss, is)) =>
-        let
-          val (args1, args2) =
-            if length args < length iss then
-              error ("Too few arguments for inductive predicate " ^ name)
-            else chop (length iss) args;
-          val k = length args2;
-          val prfx = map (rpair NONE) (1 upto k)
-        in
-          if not (is_prefix op = prfx is) then [] else
-          let val is' = map (fn (i, t) => (i - k, t)) (List.drop (is, k))
-          in map (fn x => Mode (m, is', x)) (cprods (map
-            (fn (NONE, _) => [NONE]
-              | (SOME js, arg) => map SOME (filter
-                  (fn Mode (_, js', _) => js=js') (modes_of_term modes arg)))
-                    (iss ~~ args1)))
-          end
-        end)) (AList.lookup op = modes name)
-  in
-    case strip_comb (Envir.eta_contract t) of
-      (Const (name, _), args) => the_default default (mk_modes name args)
-    | (Var ((name, _), _), args) => the (mk_modes name args)
-    | (Free (name, _), args) => the (mk_modes name args)
-    | (Abs _, []) => error "Abs at param position" (* modes_of_param default modes t *)
-    | _ => default
-  end
-  
-fun select_mode_prem thy modes vs ps =
-  find_first (is_some o snd) (ps ~~ map
-    (fn Prem (us, t) => find_first (fn Mode (_, is, _) =>
-          let
-            val (in_ts, out_ts) = split_smode is us;
-            val (out_ts', in_ts') = List.partition (is_constrt thy) out_ts;
-            val vTs = maps term_vTs out_ts';
-            val dupTs = map snd (duplicates (op =) vTs) @
-              map_filter (AList.lookup (op =) vTs) vs;
-          in
-            subset (op =) (terms_vs (in_ts @ in_ts'), vs) andalso
-            forall (is_eqT o fastype_of) in_ts' andalso
-            subset (op =) (term_vs t, vs) andalso
-            forall is_eqT dupTs
-          end)
-            (modes_of_term modes t handle Option =>
-               error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
-      | Negprem (us, t) => find_first (fn Mode (_, is, _) =>
-            is = map (rpair NONE) (1 upto length us) andalso
-            subset (op =) (terms_vs us, vs) andalso
-            subset (op =) (term_vs t, vs))
-            (modes_of_term modes t handle Option =>
-               error ("Bad predicate: " ^ Syntax.string_of_term_global thy t))
-      | Sidecond t => if subset (op =) (term_vs t, vs) then SOME (Mode (([], []), [], []))
-          else NONE
-      ) ps);
-
-fun fold_prem f (Prem (args, _)) = fold f args
-  | fold_prem f (Negprem (args, _)) = fold f args
-  | fold_prem f (Sidecond t) = f t
-
-fun all_subsets [] = [[]]
-  | all_subsets (x::xs) = let val xss' = all_subsets xs in xss' @ (map (cons x) xss') end
-
-fun generator vTs v = 
-  let
-    val T = the (AList.lookup (op =) vTs v)
-  in
-    (Generator (v, T), Mode (([], []), [], []))
-  end;
-
-fun check_mode_clause with_generator thy param_vs modes gen_modes (iss, is) (ts, ps) =
-  let
-    val modes' = modes @ map_filter
-      (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
-        (param_vs ~~ iss);
-    val gen_modes' = gen_modes @ map_filter
-      (fn (_, NONE) => NONE | (v, SOME js) => SOME (v, [([], js)]))
-        (param_vs ~~ iss);  
-    val vTs = distinct (op =) ((fold o fold_prem) Term.add_frees ps (fold Term.add_frees ts []))
-    val prem_vs = distinct (op =) ((fold o fold_prem) Term.add_free_names ps [])
-    fun check_mode_prems acc_ps vs [] = SOME (acc_ps, vs)
-      | check_mode_prems acc_ps vs ps = (case select_mode_prem thy modes' vs ps of
-          NONE =>
-            (if with_generator then
-              (case select_mode_prem thy gen_modes' vs ps of
-                SOME (p as Prem _, SOME mode) => check_mode_prems ((p, mode) :: acc_ps) 
-                  (case p of Prem (us, _) => union (op =) vs (terms_vs us) | _ => vs)
-                  (filter_out (equal p) ps)
-              | _ =>
-                  let 
-                    val all_generator_vs = all_subsets (subtract (op =) vs prem_vs)
-                      |> sort (int_ord o (pairself length))
-                  in
-                    case (find_first (fn generator_vs => is_some
-                      (select_mode_prem thy modes' (union (op =) vs generator_vs) ps))
-                        all_generator_vs) of
-                      SOME generator_vs => check_mode_prems
-                        ((map (generator vTs) generator_vs) @ acc_ps)
-                        (union (op =) vs generator_vs) ps
-                    | NONE => NONE
-                  end)
-            else
-              NONE)
-        | SOME (p, SOME mode) => check_mode_prems ((p, mode) :: acc_ps) 
-            (case p of Prem (us, _) => union (op =) vs (terms_vs us) | _ => vs)
-            (filter_out (equal p) ps))
-    val (in_ts, in_ts') = List.partition (is_constrt thy) (fst (split_smode is ts));
-    val in_vs = terms_vs in_ts;
-    val concl_vs = terms_vs ts
-  in
-    if forall is_eqT (map snd (duplicates (op =) (maps term_vTs in_ts))) andalso
-    forall (is_eqT o fastype_of) in_ts' then
-      case check_mode_prems [] (union (op =) param_vs in_vs) ps of
-         NONE => NONE
-       | SOME (acc_ps, vs) =>
-         if with_generator then
-           SOME (ts, (rev acc_ps) @ (map (generator vTs) (subtract (op =) vs concl_vs)))
-         else
-           if subset (op =) (concl_vs, vs) then SOME (ts, rev acc_ps) else NONE
-    else NONE
-  end;
 
 fun print_failed_mode options thy modes p m rs is =
   if show_mode_inference options then
     let
       val _ = tracing ("Clauses " ^ commas (map (fn i => string_of_int (i + 1)) is) ^ " of " ^
-        p ^ " violates mode " ^ string_of_mode thy p m)
+        p ^ " violates mode " ^ string_of_mode m)
     in () end
   else ()
 
-fun error_of thy p m is =
+fun error_of p m is =
   ("  Clauses " ^ commas (map (fn i => string_of_int (i + 1)) is) ^ " of " ^
-        p ^ " violates mode " ^ string_of_mode thy p m)
+        p ^ " violates mode " ^ string_of_mode m)
+
+fun is_all_input mode =
+  let
+    fun is_all_input' (Fun _) = true
+      | is_all_input' (Pair (m1, m2)) = is_all_input' m1 andalso is_all_input' m2
+      | is_all_input' Input = true
+      | is_all_input' Output = false
+  in
+    forall is_all_input' (strip_fun_mode mode)
+  end
+
+fun all_input_of T =
+  let
+    val (Ts, U) = strip_type T
+    fun input_of (Type ("*", [T1, T2])) = Pair (input_of T1, input_of T2)
+      | input_of _ = Input
+  in
+    if U = HOLogic.boolT then
+      fold_rev (curry Fun) (map input_of Ts) Bool
+    else
+      error "all_input_of: not a predicate"
+  end
+
+fun partial_hd [] = NONE
+  | partial_hd (x :: xs) = SOME x
+
+fun term_vs tm = fold_aterms (fn Free (x, T) => cons x | _ => I) tm [];
+val terms_vs = distinct (op =) o maps term_vs;
+
+fun input_mode T =
+  let
+    val (Ts, U) = strip_type T
+  in
+    fold_rev (curry Fun) (map (K Input) Ts) Input
+  end
+
+fun output_mode T =
+  let
+    val (Ts, U) = strip_type T
+  in
+    fold_rev (curry Fun) (map (K Output) Ts) Output
+  end
+
+fun is_invertible_function thy (Const (f, _)) = is_constr thy f
+  | is_invertible_function thy _ = false
+
+fun non_invertible_subterms thy (Free _) = []
+  | non_invertible_subterms thy t = 
+  case (strip_comb t) of (f, args) =>
+    if is_invertible_function thy f then
+      maps (non_invertible_subterms thy) args
+    else
+      [t]
 
-fun find_indices f xs =
-  map_filter (fn (i, true) => SOME i | (i, false) => NONE) (map_index (apsnd f) xs)
+fun collect_non_invertible_subterms thy (f as Free _) (names, eqs) = (f, (names, eqs))
+  | collect_non_invertible_subterms thy t (names, eqs) =
+    case (strip_comb t) of (f, args) =>
+      if is_invertible_function thy f then
+          let
+            val (args', (names', eqs')) =
+              fold_map (collect_non_invertible_subterms thy) args (names, eqs)
+          in
+            (list_comb (f, args'), (names', eqs'))
+          end
+        else
+          let
+            val s = Name.variant names "x"
+            val v = Free (s, fastype_of t)
+          in
+            (v, (s :: names, HOLogic.mk_eq (v, t) :: eqs))
+          end
+(*
+  if is_constrt thy t then (t, (names, eqs)) else
+    let
+      val s = Name.variant names "x"
+      val v = Free (s, fastype_of t)
+    in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end;
+*)
+
+fun is_possible_output thy vs t =
+  forall
+    (fn t => is_eqT (fastype_of t) andalso forall (member (op =) vs) (term_vs t))
+      (non_invertible_subterms thy t)
 
-fun check_modes_pred options with_generator thy param_vs clauses modes gen_modes (p, ms) =
+fun vars_of_destructable_term thy (Free (x, _)) = [x]
+  | vars_of_destructable_term thy t =
+  case (strip_comb t) of (f, args) =>
+    if is_invertible_function thy f then
+      maps (vars_of_destructable_term thy) args
+    else
+      []
+
+fun is_constructable thy vs t = forall (member (op =) vs) (term_vs t)
+
+fun missing_vars vs t = subtract (op =) vs (term_vs t)
+
+fun derivations_of thy modes vs t Input = 
+    [(Term Input, missing_vars vs t)]
+  | derivations_of thy modes vs t Output =
+    if is_possible_output thy vs t then [(Term Output, [])] else []
+  | derivations_of thy modes vs (Const ("Pair", _) $ t1 $ t2) (Pair (m1, m2)) =
+    map_product
+      (fn (m1, mvars1) => fn (m2, mvars2) => (Mode_Pair (m1, m2), union (op =) mvars1 mvars2))
+        (derivations_of thy modes vs t1 m1) (derivations_of thy modes vs t2 m2)
+  | derivations_of thy modes vs t m =
+    (case try (all_derivations_of thy modes vs) t of
+      SOME derivs => filter (fn (d, mvars) => mode_of d = m) derivs
+    | NONE => (if is_all_input m then [(Context m, [])] else []))
+and all_derivations_of thy modes vs (Const ("Pair", _) $ t1 $ t2) =
+  let
+    val derivs1 = all_derivations_of thy modes vs t1
+    val derivs2 = all_derivations_of thy modes vs t2
+  in
+    map_product
+      (fn (m1, mvars1) => fn (m2, mvars2) => (Mode_Pair (m1, m2), union (op =) mvars1 mvars2))
+        derivs1 derivs2
+  end
+  | all_derivations_of thy modes vs (t1 $ t2) =
   let
-    val rs = case AList.lookup (op =) clauses p of SOME rs => rs | NONE => []
-    fun invalid_mode m =
-      case find_indices
-        (is_none o check_mode_clause with_generator thy param_vs modes gen_modes m) rs of
-        [] => NONE
-      | is => SOME (error_of thy p m is)
-    val res = map (fn m => (m, invalid_mode m)) ms
-    val ms' = map_filter (fn (m, NONE) => SOME m | _ => NONE) res
-    val errors = map_filter snd res
+    val derivs1 = all_derivations_of thy modes vs t1
+  in
+    maps (fn (d1, mvars1) =>
+      case mode_of d1 of
+        Fun (m', _) => map (fn (d2, mvars2) =>
+          (Mode_App (d1, d2), union (op =) mvars1 mvars2)) (derivations_of thy modes vs t2 m')
+        | _ => error "Something went wrong") derivs1
+  end
+  | all_derivations_of thy modes vs (Const (s, T)) =
+    (case (AList.lookup (op =) modes s) of
+      SOME ms => map (fn m => (Context m, [])) ms
+    | NONE => error ("No mode for constant " ^ s))
+  | all_derivations_of _ modes vs (Free (x, _)) =
+    (case (AList.lookup (op =) modes x) of
+      SOME ms => map (fn m => (Context m , [])) ms
+    | NONE => error ("No mode for parameter variable " ^ x))
+  | all_derivations_of _ modes vs _ = error "all_derivations_of"
+
+fun rev_option_ord ord (NONE, NONE) = EQUAL
+  | rev_option_ord ord (NONE, SOME _) = GREATER
+  | rev_option_ord ord (SOME _, NONE) = LESS
+  | rev_option_ord ord (SOME x, SOME y) = ord (x, y)
+
+fun term_of_prem (Prem t) = t
+  | term_of_prem (Negprem t) = t
+  | term_of_prem (Sidecond t) = t
+
+fun random_mode_in_deriv modes t deriv =
+  case try dest_Const (fst (strip_comb t)) of
+    SOME (s, _) =>
+      (case AList.lookup (op =) modes s of
+        SOME ms =>
+          (case AList.lookup (op =) ms (head_mode_of deriv) of
+            SOME r => r
+          | NONE => false)
+      | NONE => false)
+  | NONE => false
+
+fun number_of_output_positions mode =
+  let
+    val args = strip_fun_mode mode
+    fun contains_output (Fun _) = false
+      | contains_output Input = false
+      | contains_output Output = true
+      | contains_output (Pair (m1, m2)) = contains_output m1 orelse contains_output m2
+  in
+    length (filter contains_output args)
+  end
+
+fun lex_ord ord1 ord2 (x, x') =
+  case ord1 (x, x') of
+    EQUAL => ord2 (x, x')
+  | ord => ord
+
+fun deriv_ord2' thy modes t1 t2 ((deriv1, mvars1), (deriv2, mvars2)) =
+  let
+    fun mvars_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
+      int_ord (length mvars1, length mvars2)
+    fun random_mode_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
+      int_ord (if random_mode_in_deriv modes t1 deriv1 then 1 else 0,
+        if random_mode_in_deriv modes t1 deriv1 then 1 else 0)
+    fun output_mode_ord ((t1, deriv1, mvars1), (t2, deriv2, mvars2)) =
+      int_ord (number_of_output_positions (head_mode_of deriv1),
+        number_of_output_positions (head_mode_of deriv2))
+  in
+    lex_ord mvars_ord (lex_ord random_mode_ord output_mode_ord)
+      ((t1, deriv1, mvars1), (t2, deriv2, mvars2))
+  end
+
+fun deriv_ord2 thy modes t = deriv_ord2' thy modes t t
+
+fun deriv_ord ((deriv1, mvars1), (deriv2, mvars2)) =
+  int_ord (length mvars1, length mvars2)
+
+fun premise_ord thy modes ((prem1, a1), (prem2, a2)) =
+  rev_option_ord (deriv_ord2' thy modes (term_of_prem prem1) (term_of_prem prem2)) (a1, a2)
+
+fun print_mode_list modes =
+  tracing ("modes: " ^ (commas (map (fn (s, ms) => s ^ ": " ^
+    commas (map (fn (m, r) => string_of_mode m ^ (if r then " random " else " not ")) ms)) modes)))
+
+fun select_mode_prem' thy modes vs ps =
+  let
+    val modes' = map (fn (s, ms) => (s, map fst ms)) modes
+  in
+    partial_hd (sort (premise_ord thy modes) (ps ~~ map
+    (fn Prem t =>
+      partial_hd
+        (sort (deriv_ord2 thy modes t) (all_derivations_of thy modes' vs t))
+     | Sidecond t => SOME (Context Bool, missing_vars vs t)
+     | Negprem t =>
+         partial_hd
+          (sort (deriv_ord2 thy modes t) (filter (fn (d, missing_vars) => is_all_input (head_mode_of d))
+             (all_derivations_of thy modes' vs t)))
+     | p => error (string_of_prem thy p))
+    ps))
+  end
+
+fun check_mode_clause' use_random thy param_vs modes mode (ts, ps) =
+  let
+    val vTs = distinct (op =) (fold Term.add_frees (map term_of_prem ps) (fold Term.add_frees ts []))
+    val modes' = modes @ (param_vs ~~ map (fn x => [(x, false)]) (ho_arg_modes_of mode))
+    val (in_ts, out_ts) = split_mode mode ts    
+    val in_vs = maps (vars_of_destructable_term thy) in_ts
+    val out_vs = terms_vs out_ts
+    fun check_mode_prems acc_ps rnd vs [] = SOME (acc_ps, vs, rnd)
+      | check_mode_prems acc_ps rnd vs ps =
+        (case select_mode_prem' thy modes' vs ps of
+          SOME (p, SOME (deriv, [])) => check_mode_prems ((p, deriv) :: acc_ps) rnd (*TODO: uses random? *)
+            (case p of
+                Prem t => union (op =) vs (term_vs t)
+              | Sidecond t => vs
+              | Negprem t => union (op =) vs (term_vs t)
+              | _ => error "I do not know")
+            (filter_out (equal p) ps)
+        | SOME (p, SOME (deriv, missing_vars)) =>
+          if use_random then
+            check_mode_prems ((p, deriv) :: (map
+              (fn v => (Generator (v, the (AList.lookup (op =) vTs v)), Term Output)) missing_vars)
+                @ acc_ps) true
+            (case p of
+                Prem t => union (op =) vs (term_vs t)
+              | Sidecond t => union (op =) vs (term_vs t)
+              | Negprem t => union (op =) vs (term_vs t)
+              | _ => error "I do not know")
+            (filter_out (equal p) ps)
+          else NONE
+        | SOME (p, NONE) => NONE
+        | NONE => NONE)
+  in
+    case check_mode_prems [] false in_vs ps of
+      NONE => NONE
+    | SOME (acc_ps, vs, rnd) =>
+      if forall (is_constructable thy vs) (in_ts @ out_ts) then
+        SOME (ts, rev acc_ps, rnd)
+      else
+        if use_random then
+          let
+            val generators = map
+              (fn v => (Generator (v, the (AList.lookup (op =) vTs v)), Term Output))
+                (subtract (op =) vs (terms_vs out_ts))
+          in
+            SOME (ts, rev (generators @ acc_ps), true)
+          end
+        else
+          NONE
+  end
+
+datatype result = Success of bool | Error of string
+
+fun check_modes_pred' use_random options thy param_vs clauses modes (p, ms) =
+  let
+    fun split xs =
+      let
+        fun split' [] (ys, zs) = (rev ys, rev zs)
+          | split' ((m, Error z) :: xs) (ys, zs) = split' xs (ys, z :: zs)
+          | split' ((m, Success rnd) :: xs) (ys, zs) = split' xs ((m, rnd) :: ys, zs)
+       in
+         split' xs ([], [])
+       end
+    val rs = these (AList.lookup (op =) clauses p)
+    fun check_mode m =
+      let
+        val res = map (check_mode_clause' use_random thy param_vs modes m) rs
+      in
+        case find_indices is_none res of
+          [] => Success (exists (fn SOME (_, _, true) => true | _ => false) res)
+        | is => (print_failed_mode options thy modes p m rs is; Error (error_of p m is))
+      end
+    val res = map (fn (m, _) => (m, check_mode m)) ms
+    val (ms', errors) = split res
   in
     ((p, ms'), errors)
   end;
 
-fun get_modes_pred with_generator thy param_vs clauses modes gen_modes (p, ms) =
+fun get_modes_pred' use_random thy param_vs clauses modes (p, ms) =
   let
-    val rs = case AList.lookup (op =) clauses p of SOME rs => rs | NONE => []
+    val rs = these (AList.lookup (op =) clauses p)
   in
-    (p, map (fn m =>
-      (m, map (the o check_mode_clause with_generator thy param_vs modes gen_modes m) rs)) ms)
+    (p, map (fn (m, rnd) =>
+      (m, map ((fn (ts, ps, rnd) => (ts, ps)) o the o check_mode_clause' use_random thy param_vs modes m) rs)) ms)
   end;
 
-fun fixp f (x : (string * mode list) list) =
+fun fixp f x =
   let val y = f x
   in if x = y then x else fixp f y end;
 
-fun fixp_with_state f ((x : (string * mode list) list), state) =
+fun fixp_with_state f (x, state) =
   let
     val (y, state') = f (x, state)
   in
     if x = y then (y, state') else fixp_with_state f (y, state')
   end
 
-fun infer_modes options thy extra_modes all_modes param_vs clauses =
+fun infer_modes use_random options preds extra_modes param_vs clauses thy =
   let
+    val all_modes = map (fn (s, T) => (s, map (rpair false) (all_modes_of_typ T))) preds
+    fun needs_random s m = (m, member (op =) (#needs_random (the_pred_data thy s)) m)
+    val extra_modes = map (fn (s, ms) => (s, map (needs_random s) ms)) extra_modes
     val (modes, errors) =
       fixp_with_state (fn (modes, errors) =>
         let
           val res = map
-            (check_modes_pred options false thy param_vs clauses (modes @ extra_modes) []) modes
+            (check_modes_pred' use_random options thy param_vs clauses (modes @ extra_modes)) modes
         in (map fst res, errors @ maps snd res) end)
           (all_modes, [])
+    val thy' = fold (fn (s, ms) => if member (op =) (map fst preds) s then
+      set_needs_random s (map fst (filter (fn (_, rnd) => rnd = true) ms)) else I) modes thy
   in
-    (map (get_modes_pred false thy param_vs clauses (modes @ extra_modes) []) modes, errors)
-  end;
-
-fun remove_from rem [] = []
-  | remove_from rem ((k, vs) :: xs) =
-    (case AList.lookup (op =) rem k of
-      NONE => (k, vs)
-    | SOME vs' => (k, subtract (op =) vs' vs))
-    :: remove_from rem xs
-
-fun infer_modes_with_generator options thy extra_modes all_modes param_vs clauses =
-  let
-    val prednames = map fst clauses
-    val extra_modes' = all_modes_of thy
-    val gen_modes = all_random_modes_of thy
-      |> filter_out (fn (name, _) => member (op =) prednames name)
-    val starting_modes = remove_from extra_modes' all_modes
-    fun eq_mode (m1, m2) = (m1 = m2)
-    val (modes, errors) =
-      fixp_with_state (fn (modes, errors) =>
-        let
-          val res = map
-            (check_modes_pred options true thy param_vs clauses extra_modes'
-              (gen_modes @ modes)) modes
-        in (map fst res, errors @ maps snd res) end) (starting_modes, [])
-    val moded_clauses =
-      map (get_modes_pred true thy param_vs clauses extra_modes (gen_modes @ modes)) modes
-    val (moded_clauses', _) = infer_modes options thy extra_modes all_modes param_vs clauses
-    val join_moded_clauses_table = AList.join (op =)
-      (fn _ => fn ((mps1, mps2)) =>
-        merge (fn ((m1, _), (m2, _)) => eq_mode (m1, m2)) (mps1, mps2))
-  in
-    (join_moded_clauses_table (moded_clauses', moded_clauses), errors)
+    ((map (get_modes_pred' use_random thy param_vs clauses (modes @ extra_modes)) modes, errors), thy')
   end;
 
 (* term construction *)
@@ -1231,10 +1353,9 @@
 
 datatype comp_modifiers = Comp_Modifiers of
 {
-  function_name_of : theory -> string -> Predicate_Compile_Aux.mode -> string,
-  set_function_name : string -> Predicate_Compile_Aux.mode -> string -> theory -> theory,
+  compilation : compilation,
   function_name_prefix : string,
-  funT_of : compilation_funs -> mode -> typ -> typ,
+  compfuns : compilation_funs,
   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
@@ -1242,25 +1363,27 @@
 
 fun dest_comp_modifiers (Comp_Modifiers c) = c
 
-val function_name_of = #function_name_of o dest_comp_modifiers
-val set_function_name = #set_function_name o dest_comp_modifiers
+val compilation = #compilation o dest_comp_modifiers
 val function_name_prefix = #function_name_prefix o dest_comp_modifiers
-val funT_of = #funT_of o dest_comp_modifiers
+val compfuns = #compfuns o dest_comp_modifiers
+val funT_of = funT_of o compfuns
 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
 
 end;
 
+(* TODO: uses param_vs -- change necessary for compilation with new modes *)
 fun compile_arg compilation_modifiers compfuns additional_arguments thy param_vs iss arg = 
   let
     fun map_params (t as Free (f, T)) =
       if member (op =) param_vs f then
-        case (the (AList.lookup (op =) (param_vs ~~ iss) f)) of
+        case (AList.lookup (op =) (param_vs ~~ iss) f) of
           SOME is =>
             let
-              val T' = Comp_Mod.funT_of compilation_modifiers compfuns ([], is) T
-            in fst (mk_Eval_of additional_arguments ((Free (f, T'), T), SOME is) []) end
+              val _ = error "compile_arg: A parameter in a input position -- do we have a test case?"
+              val T' = Comp_Mod.funT_of compilation_modifiers is T
+            in t(*fst (mk_Eval_of additional_arguments ((Free (f, T'), T), is) [])*) end
         | NONE => t
       else t
       | map_params t = t
@@ -1291,104 +1414,83 @@
        (v', mk_bot compfuns U')]))
   end;
 
-(*FIXME function can be removed*)
-fun mk_funcomp f t =
+fun compile_expr compilation_modifiers compfuns thy (t, deriv) additional_arguments =
   let
-    val names = Term.add_free_names t [];
-    val Ts = binder_types (fastype_of t);
-    val vs = map2 (curry Free)
-      (Name.variant_list names (replicate (length Ts) "x")) Ts
+    fun expr_of (t, deriv) =
+      (case (t, deriv) of
+        (t, Term Input) => SOME t
+      | (t, Term Output) => NONE
+      | (Const (name, T), Context mode) =>
+        SOME (Const (function_name_of (Comp_Mod.compilation compilation_modifiers) thy name mode,
+          Comp_Mod.funT_of compilation_modifiers mode T))
+      | (Free (s, T), Context m) =>
+        SOME (Free (s, Comp_Mod.funT_of compilation_modifiers m T))
+      | (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 ("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
-    fold_rev lambda vs (f (list_comb (t, vs)))
-  end;
-
-fun compile_param compilation_modifiers compfuns thy NONE t = t
-  | compile_param compilation_modifiers compfuns thy (m as SOME (Mode (mode, _, ms))) t =
-   let
-     val (f, args) = strip_comb (Envir.eta_contract t)
-     val (params, args') = chop (length ms) args
-     val params' = map2 (compile_param compilation_modifiers compfuns thy) ms params
-     val f' =
-       case f of
-         Const (name, T) => Const (Comp_Mod.function_name_of compilation_modifiers thy name mode,
-           Comp_Mod.funT_of compilation_modifiers compfuns mode T)
-       | Free (name, T) => Free (name, Comp_Mod.funT_of compilation_modifiers compfuns mode T)
-       | _ => error ("PredicateCompiler: illegal parameter term")
-   in
-     list_comb (f', params' @ args')
-   end
-
-fun compile_expr compilation_modifiers compfuns thy ((Mode (mode, _, ms)), t)
-  inargs additional_arguments =
-  case strip_comb t of
-    (Const (name, T), params) =>
-       let
-         val params' = map2 (compile_param compilation_modifiers compfuns thy) ms params
-         val name' = Comp_Mod.function_name_of compilation_modifiers thy name mode
-         val T' = Comp_Mod.funT_of compilation_modifiers compfuns mode T
-       in
-         (list_comb (Const (name', T'), params' @ inargs @ additional_arguments))
-       end
-  | (Free (name, T), params) =>
-    list_comb (Free (name, Comp_Mod.funT_of compilation_modifiers compfuns mode T),
-      params @ inargs @ additional_arguments)
+    the (expr_of (t, deriv))
+  end
 
 fun compile_clause compilation_modifiers compfuns thy all_vs param_vs additional_arguments
-  (iss, is) inp (ts, moded_ps) =
+  mode inp (ts, moded_ps) =
   let
+    val iss = ho_arg_modes_of mode
     val compile_match = compile_match compilation_modifiers compfuns
       additional_arguments param_vs iss thy
-    fun check_constrt t (names, eqs) =
-      if is_constrt thy t then (t, (names, eqs)) else
-        let
-          val s = Name.variant names "x"
-          val v = Free (s, fastype_of t)
-        in (v, (s::names, HOLogic.mk_eq (v, t)::eqs)) end;
-
-    val (in_ts, out_ts) = split_smode is ts;
+    val (in_ts, out_ts) = split_mode mode ts;
     val (in_ts', (all_vs', eqs)) =
-      fold_map check_constrt in_ts (all_vs, []);
-
+      fold_map (collect_non_invertible_subterms thy) in_ts (all_vs, []);
     fun compile_prems out_ts' vs names [] =
           let
             val (out_ts'', (names', eqs')) =
-              fold_map check_constrt out_ts' (names, []);
+              fold_map (collect_non_invertible_subterms thy) out_ts' (names, []);
             val (out_ts''', (names'', constr_vs)) = fold_map distinct_v
               out_ts'' (names', map (rpair []) vs);
           in
             compile_match constr_vs (eqs @ eqs') out_ts'''
               (mk_single compfuns (HOLogic.mk_tuple out_ts))
           end
-      | compile_prems out_ts vs names ((p, mode as Mode ((_, is), _, _)) :: ps) =
+      | 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 check_constrt out_ts (names, [])
+              fold_map (collect_non_invertible_subterms thy) 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 (us, t) =>
+               Prem t =>
                  let
-                   val (in_ts, out_ts''') = split_smode is us;
-                   val in_ts = map (compile_arg compilation_modifiers compfuns
-                     additional_arguments thy param_vs iss) in_ts
                    val u =
                      compile_expr compilation_modifiers compfuns thy
-                       (mode, t) in_ts additional_arguments'
+                       (t, deriv) 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 (us, t) =>
+             | Negprem t =>
                  let
-                   val (in_ts, out_ts''') = split_smode is us
-                   val in_ts = map (compile_arg compilation_modifiers compfuns
-                     additional_arguments thy param_vs iss) in_ts
                    val u = mk_not compfuns
                      (compile_expr compilation_modifiers compfuns thy
-                       (mode, t) in_ts additional_arguments')
+                       (t, deriv) additional_arguments')
+                   val (_, out_ts''') = split_mode mode (snd (strip_comb t))
                    val rest = compile_prems out_ts''' vs' names'' ps
                  in
                    (u, rest)
@@ -1403,8 +1505,7 @@
                  end
              | Generator (v, T) =>
                  let
-                   val [size] = additional_arguments
-                   val u = lift_random (HOLogic.mk_random T size)
+                   val u = mk_random T
                    val rest = compile_prems [Free (v, T)]  vs' names'' ps;
                  in
                    (u, rest)
@@ -1418,47 +1519,45 @@
     mk_bind compfuns (mk_single compfuns inp, prem_t)
   end
 
-fun compile_pred compilation_modifiers compfuns thy all_vs param_vs s T mode moded_cls =
+fun compile_pred compilation_modifiers thy all_vs param_vs s T mode moded_cls =
   let
-    val (Ts1, Ts2) = chop (length (fst mode)) (binder_types T)
-    val (Us1, Us2) = split_smodeT (snd mode) Ts2
-    val Ts1' =
-      map2 (fn NONE => I | SOME is => Comp_Mod.funT_of compilation_modifiers compfuns ([], is))
-        (fst mode) Ts1
-    fun mk_input_term (i, NONE) =
-        [Free (Name.variant (all_vs @ param_vs) ("x" ^ string_of_int i), nth Ts2 (i - 1))]
-      | mk_input_term (i, SOME pis) = case HOLogic.strip_tupleT (nth Ts2 (i - 1)) of
-               [] => error "strange unit input"
-             | [T] => [Free (Name.variant (all_vs @ param_vs)
-               ("x" ^ string_of_int i), nth Ts2 (i - 1))]
-             | Ts => let
-               val vnames = Name.variant_list (all_vs @ param_vs)
-                (map (fn j => "x" ^ string_of_int i ^ "p" ^ string_of_int j)
-                  pis)
-             in
-               if null pis then
-                 []
-               else
-                 [HOLogic.mk_tuple (map2 (curry Free) vnames (map (fn j => nth Ts (j - 1)) pis))]
-             end
-    val in_ts = maps mk_input_term (snd mode)
-    val params = map2 (fn s => fn T => Free (s, T)) param_vs Ts1'
-    val additional_arguments = Comp_Mod.additional_arguments compilation_modifiers
+    (* TODO: 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 additional_arguments = []
+    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 = Name.variant 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 cl_ts =
       map (compile_clause compilation_modifiers compfuns
-        thy all_vs param_vs additional_arguments mode (HOLogic.mk_tuple in_ts)) moded_cls;
+        thy all_vs param_vs additional_arguments mode (HOLogic.mk_tuple in_ts')) moded_cls;
     val compilation = Comp_Mod.wrap_compilation compilation_modifiers compfuns
       s T mode additional_arguments
       (if null cl_ts then
-        mk_bot compfuns (HOLogic.mk_tupleT Us2)
+        mk_bot compfuns (HOLogic.mk_tupleT outTs)
       else foldr1 (mk_sup compfuns) cl_ts)
     val fun_const =
-      Const (Comp_Mod.function_name_of compilation_modifiers thy s mode,
-        Comp_Mod.funT_of compilation_modifiers compfuns mode T)
+      Const (function_name_of (Comp_Mod.compilation compilation_modifiers) thy s mode, funT)
   in
     HOLogic.mk_Trueprop
-      (HOLogic.mk_eq (list_comb (fun_const, params @ in_ts @ additional_arguments), compilation))
+      (HOLogic.mk_eq (list_comb (fun_const, in_ts @ additional_arguments), compilation))
   end;
 
 (* special setup for simpset *)                  
@@ -1474,152 +1573,108 @@
       (fn NONE => "X" | SOME k' => string_of_int k')
         (ks @ [SOME k]))) arities));
 
-fun create_intro_elim_rule (mode as (iss, is)) defthm mode_id funT pred thy =
-let
-  val Ts = binder_types (fastype_of pred)
-  val funtrm = Const (mode_id, funT)
-  val (Ts1, Ts2) = chop (length iss) Ts;
-  val Ts1' =
-    map2 (fn NONE => I | SOME is => funT_of (PredicateCompFuns.compfuns) ([], is)) iss Ts1
-  val param_names = Name.variant_list []
-    (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1)));
-  val params = map2 (curry Free) param_names Ts1'
-  fun mk_args (i, T) argnames =
+fun split_lambda (x as Free _) t = lambda x t
+  | split_lambda (Const ("Pair", _) $ t1 $ t2) t =
+    HOLogic.mk_split (split_lambda t1 (split_lambda t2 t))
+  | split_lambda (Const ("Product_Type.Unity", _)) t = Abs ("x", HOLogic.unitT, t)
+  | split_lambda t _ = raise (TERM ("split_lambda", [t]))
+
+fun strip_split_abs (Const ("split", _) $ t) = strip_split_abs t
+  | strip_split_abs (Abs (_, _, t)) = strip_split_abs t
+  | strip_split_abs t = t
+
+fun mk_args is_eval (Pair (m1, m2), Type ("*", [T1, T2])) names =
     let
-      val vname = Name.variant (param_names @ argnames) ("x" ^ string_of_int (length Ts1' + i))
-      val default = (Free (vname, T), vname :: argnames)
+      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 = Name.variant 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 split_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 = Name.variant names "x"
     in
-      case AList.lookup (op =) is i of
-             NONE => default
-           | SOME NONE => default
-           | SOME (SOME pis) =>
-             case HOLogic.strip_tupleT T of
-               [] => default
-             | [_] => default
-             | Ts => 
-            let
-              val vnames = Name.variant_list (param_names @ argnames)
-                (map (fn j => "x" ^ string_of_int (length Ts1' + i) ^ "p" ^ string_of_int j)
-                  (1 upto (length Ts)))
-             in (HOLogic.mk_tuple (map2 (curry Free) vnames Ts), vnames @ argnames) end
+      (Free (x, T), x :: names)
     end
-  val (args, argnames) = fold_map mk_args (1 upto (length Ts2) ~~ Ts2) []
-  val (inargs, outargs) = split_smode is args
-  val param_names' = Name.variant_list (param_names @ argnames)
-    (map (fn i => "p" ^ string_of_int i) (1 upto (length iss)))
-  val param_vs = map2 (curry Free) param_names' Ts1
-  val (params', names) = fold_map (mk_Eval_of []) ((params ~~ Ts1) ~~ iss) []
-  val predpropI = HOLogic.mk_Trueprop (list_comb (pred, param_vs @ args))
-  val predpropE = HOLogic.mk_Trueprop (list_comb (pred, params' @ args))
-  val param_eqs = map2 (HOLogic.mk_Trueprop oo (curry HOLogic.mk_eq)) param_vs params'
-  val funargs = params @ inargs
-  val funpropE = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
-                  if null outargs then Free("y", HOLogic.unitT) else HOLogic.mk_tuple outargs))
-  val funpropI = HOLogic.mk_Trueprop (PredicateCompFuns.mk_Eval (list_comb (funtrm, funargs),
-                   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 (ProofContext.init thy)
-    (argnames @ param_names @ param_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 (ProofContext.init thy)
-    (argnames @ param_names @ param_names' @ ["y", "P"]) [] elimtrm (fn _ => unfolddef_tac)
-in
-  (introthm, elimthm)
-end;
+
+fun create_intro_elim_rule mode defthm mode_id funT pred thy =
+  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 (ProofContext.init thy)
+      (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 (ProofContext.init thy)
+      (argnames @ ["y", "P"]) [] elimtrm (fn _ => unfolddef_tac)
+  in
+    (introthm, elimthm)
+  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' (translate_mode T mode)
-    val name = the_default system_proposal (proposed_names options name (translate_mode T mode))
+      ^ "_" ^ ascii_string_of_mode mode
+    val name = the_default system_proposal (proposed_names options name mode)
   in
     Sign.full_bname thy name
   end;
 
-fun split_tupleT is T =
-  let
-    fun split_tuple' _ _ [] = ([], [])
-      | split_tuple' is i (T::Ts) =
-      (if member (op =) is i then apfst else apsnd) (cons T)
-        (split_tuple' is (i+1) Ts)
-  in
-    split_tuple' is 1 (HOLogic.strip_tupleT T)
-  end
-  
-fun mk_arg xin xout pis T =
-  let
-    val n = length (HOLogic.strip_tupleT T)
-    val ni = length pis
-    fun mk_proj i j t =
-      (if i = j then I else HOLogic.mk_fst)
-        (funpow (i - 1) HOLogic.mk_snd t)
-    fun mk_arg' i (si, so) =
-      if member (op =) pis i then
-        (mk_proj si ni xin, (si+1, so))
-      else
-        (mk_proj so (n - ni) xout, (si, so+1))
-    val (args, _) = fold_map mk_arg' (1 upto n) (1, 1)
-  in
-    HOLogic.mk_tuple args
-  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 as (iss, is)) thy =
+    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 Ts = binder_types T
-        val (Ts1, Ts2) = chop (length iss) Ts
-        val (Us1, Us2) =  split_smodeT is Ts2
-        val Ts1' = map2 (fn NONE => I | SOME is => funT_of compfuns ([], is)) iss Ts1
-        val funT = (Ts1' @ Us1) ---> (mk_predT compfuns (HOLogic.mk_tupleT Us2))
-        val names = Name.variant_list []
-          (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts)));
-        val param_names = Name.variant_list []
-          (map (fn i => "x" ^ string_of_int i) (1 upto (length Ts1')))
-        val xparams = map2 (curry Free) param_names Ts1'
-        fun mk_vars (i, T) names =
+        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 vname = Name.variant names ("x" ^ string_of_int (length Ts1' + i))
-          in
-            case AList.lookup (op =) is i of
-               NONE => ((([], [Free (vname, T)]), Free (vname, T)), vname :: names)
-             | SOME NONE => ((([Free (vname, T)], []), Free (vname, T)), vname :: names)
-             | SOME (SOME pis) =>
-               let
-                 val (Tins, Touts) = split_tupleT pis T
-                 val name_in = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "in")
-                 val name_out = Name.variant names ("x" ^ string_of_int (length Ts1' + i) ^ "out")
-                 val xin = Free (name_in, HOLogic.mk_tupleT Tins)
-                 val xout = Free (name_out, HOLogic.mk_tupleT Touts)
-                 val xarg = mk_arg xin xout pis T
-               in
-                 (((if null Tins then [] else [xin],
-                 if null Touts then [] else [xout]), xarg), name_in :: name_out :: names) end
-               end
-        val (xinoutargs, names) = fold_map mk_vars ((1 upto (length Ts2)) ~~ Ts2) param_names
-        val (xinout, xargs) = split_list xinoutargs
-        val (xins, xouts) = pairself flat (split_list xinout)
-        val (xparams', names') = fold_map (mk_Eval_of []) ((xparams ~~ Ts1) ~~ iss) names
-        fun mk_split_lambda [] t = lambda (Free (Name.variant names' "x", HOLogic.unitT)) t
-          | mk_split_lambda [x] t = lambda x t
-          | mk_split_lambda xs t =
-          let
-            fun mk_split_lambda' (x::y::[]) t = HOLogic.mk_split (lambda x (lambda y t))
-              | mk_split_lambda' (x::xs) t = HOLogic.mk_split (lambda x (mk_split_lambda' xs t))
-          in
-            mk_split_lambda' xs t
-          end;
-        val predterm = PredicateCompFuns.mk_Enum (mk_split_lambda xouts
-          (list_comb (Const (name, T), xparams' @ xargs)))
-        val lhs = list_comb (Const (mode_cname, funT), xparams @ xins)
+            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 split_lambda inargs
+          (PredicateCompFuns.mk_Enum (split_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)] |>
@@ -1627,13 +1682,14 @@
         val (intro, elim) =
           create_intro_elim_rule mode definition mode_cname funT (Const (name, T)) thy'
         in thy'
-          |> add_predfun name mode (mode_cname, definition, intro, elim)
+          |> set_function_name Pred name mode mode_cname
+          |> add_predfun_data name mode (definition, intro, elim)
           |> PureThy.store_thm (Binding.name (mode_cbasename ^ "I"), intro) |> snd
           |> PureThy.store_thm (Binding.name (mode_cbasename ^ "E"), elim)  |> snd
           |> Theory.checkpoint
         end;
   in
-    fold create_definition modes thy
+    thy |> defined_function_of Pred name |> fold create_definition modes
   end;
 
 fun define_functions comp_modifiers compfuns options preds (name, modes) thy =
@@ -1643,13 +1699,15 @@
       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 compfuns mode T
+        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)]
-        |> Comp_Mod.set_function_name comp_modifiers name mode mode_cname
+        |> set_function_name (Comp_Mod.compilation comp_modifiers) name mode mode_cname
       end;
   in
-    fold create_definition modes thy
+    thy
+    |> defined_function_of (Comp_Mod.compilation comp_modifiers) name
+    |> fold create_definition modes
   end;
 
 (* Proving equivalence of term *)
@@ -1674,11 +1732,13 @@
 
 (* MAJOR FIXME:  prove_params should be simple
  - different form of introrule for parameters ? *)
-fun prove_param options thy NONE t = TRY (rtac @{thm refl} 1)
-  | prove_param options thy (m as SOME (Mode (mode, is, ms))) t =
+
+fun prove_param options thy t deriv =
   let
     val  (f, args) = strip_comb (Envir.eta_contract t)
-    val (params, _) = chop (length ms) args
+    val mode = head_mode_of deriv
+    val param_derivations = param_derivations_of deriv
+    val ho_args = ho_args_of mode args
     val f_tac = case f of
       Const (name, T) => simp_tac (HOL_basic_ss addsimps 
          ([@{thm eval_pred}, (predfun_definition_of thy name mode),
@@ -1691,19 +1751,20 @@
     THEN print_tac' options "prove_param"
     THEN f_tac
     THEN print_tac' options "after simplification in prove_args"
-    THEN (EVERY (map2 (prove_param options thy) ms params))
     THEN (REPEAT_DETERM (atac 1))
+    THEN (EVERY (map2 (prove_param options thy) ho_args param_derivations))
   end
 
-fun prove_expr options thy (Mode (mode, is, ms), t, us) (premposition : int) =
+fun prove_expr options thy (premposition : int) (t, deriv) =
   case strip_comb t of
-    (Const (name, T), args) =>  
+    (Const (name, T), args) =>
       let
+        val mode = head_mode_of deriv
         val introrule = predfun_intro_of thy name mode
-        val (args1, args2) = chop (length ms) args
+        val param_derivations = param_derivations_of deriv
+        val ho_args = ho_args_of mode args
       in
-        rtac @{thm bindI} 1
-        THEN print_tac' options "before intro rule:"
+        print_tac' options "before intro rule:"
         (* for the right assumption in first position *)
         THEN rotate_tac premposition 1
         THEN debug_tac (Display.string_of_thm (ProofContext.init thy) introrule)
@@ -1712,39 +1773,58 @@
         (* work with parameter arguments *)
         THEN atac 1
         THEN print_tac' options "parameter goal"
-        THEN (EVERY (map2 (prove_param options thy) ms args1))
+        THEN (EVERY (map2 (prove_param options thy) ho_args param_derivations))
         THEN (REPEAT_DETERM (atac 1))
       end
-  | _ => rtac @{thm bindI} 1
-    THEN asm_full_simp_tac
+  | _ =>
+    asm_full_simp_tac
       (HOL_basic_ss' addsimps [@{thm "split_eta"}, @{thm "split_beta"}, @{thm "fst_conv"},
          @{thm "snd_conv"}, @{thm pair_collapse}]) 1
     THEN (atac 1)
     THEN print_tac' options "after prove parameter call"
-    
+
 
-fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st; 
+fun SOLVED tac st = FILTER (fn st' => nprems_of st' = nprems_of st - 1) tac st;
 
 fun SOLVEDALL tac st = FILTER (fn st' => nprems_of st' = 0) tac st
 
-fun prove_match thy (out_ts : term list) = let
-  fun get_case_rewrite t =
-    if (is_constructor thy t) then let
-      val case_rewrites = (#case_rewrites (Datatype.the_info thy
-        ((fst o dest_Type o fastype_of) t)))
-      in case_rewrites @ maps get_case_rewrite (snd (strip_comb t)) end
-    else []
-  val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: maps get_case_rewrite out_ts
-(* replace TRY by determining if it necessary - are there equations when calling compile match? *)
-in
-   (* make this simpset better! *)
-  asm_full_simp_tac (HOL_basic_ss' addsimps simprules) 1
-  THEN print_tac "after prove_match:"
-  THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1
-         THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss 1))))
-         THEN (SOLVED (asm_simp_tac HOL_basic_ss 1)))))
-  THEN print_tac "after if simplification"
-end;
+fun check_format thy st =
+  let
+    val concl' = Logic.strip_assums_concl (hd (prems_of st))
+    val concl = HOLogic.dest_Trueprop concl'
+    val expr = fst (strip_comb (fst (PredicateCompFuns.dest_Eval concl)))
+    fun valid_expr (Const (@{const_name Predicate.bind}, _)) = true
+      | valid_expr (Const (@{const_name Predicate.single}, _)) = true
+      | valid_expr _ = false
+  in
+    if valid_expr expr then
+      ((*tracing "expression is valid";*) Seq.single st)
+    else
+      ((*tracing "expression is not valid";*) Seq.empty) (*error "check_format: wrong format"*)
+  end
+
+fun prove_match options thy (out_ts : term list) =
+  let
+    fun get_case_rewrite t =
+      if (is_constructor thy t) then let
+        val case_rewrites = (#case_rewrites (Datatype.the_info thy
+          ((fst o dest_Type o fastype_of) t)))
+        in case_rewrites @ maps get_case_rewrite (snd (strip_comb t)) end
+      else []
+    val simprules = @{thm "unit.cases"} :: @{thm "prod.cases"} :: maps get_case_rewrite out_ts
+  (* replace TRY by determining if it necessary - are there equations when calling compile match? *)
+  in
+     (* make this simpset better! *)
+    asm_full_simp_tac (HOL_basic_ss' addsimps simprules) 1
+    THEN print_tac' options "after prove_match:"
+    THEN (DETERM (TRY (EqSubst.eqsubst_tac (ProofContext.init thy) [0] [@{thm "HOL.if_P"}] 1
+           THEN (REPEAT_DETERM (rtac @{thm conjI} 1 THEN (SOLVED (asm_simp_tac HOL_basic_ss' 1))))
+           THEN print_tac' options "if condition to be solved:"
+           THEN (SOLVED (asm_simp_tac HOL_basic_ss' 1 THEN print_tac' options "after if simp; in SOLVED:"))
+           THEN check_format thy
+           THEN print_tac' options "after if simplification - a TRY block")))
+    THEN print_tac' options "after if simplification"
+  end;
 
 (* corresponds to compile_fun -- maybe call that also compile_sidecond? *)
 
@@ -1758,7 +1838,7 @@
     val preds = preds_of t []
     val defs = map
       (fn (pred, T) => predfun_definition_of thy pred
-        ([], map (rpair NONE) (1 upto (length (binder_types T)))))
+        (all_input_of T))
         preds
   in 
     (* remove not_False_eq_True when simpset in prove_match is better *)
@@ -1767,63 +1847,74 @@
     (* need better control here! *)
   end
 
-fun prove_clause options thy nargs modes (iss, is) (_, clauses) (ts, moded_ps) =
+fun prove_clause options thy nargs modes mode (_, clauses) (ts, moded_ps) =
   let
-    val (in_ts, clause_out_ts) = split_smode is ts;
+    val (in_ts, clause_out_ts) = split_mode mode ts;
     fun prove_prems out_ts [] =
-      (prove_match thy out_ts)
+      (prove_match options thy out_ts)
       THEN print_tac' options "before simplifying assumptions"
       THEN asm_full_simp_tac HOL_basic_ss' 1
       THEN print_tac' options "before single intro rule"
       THEN (rtac (if null clause_out_ts then @{thm singleI_unit} else @{thm singleI}) 1)
-    | prove_prems out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
+    | prove_prems out_ts ((p, deriv) :: ps) =
       let
         val premposition = (find_index (equal p) clauses) + nargs
-        val rest_tac = (case p of Prem (us, t) =>
+        val mode = head_mode_of deriv
+        val rest_tac =
+          rtac @{thm bindI} 1
+          THEN (case p of Prem t =>
             let
-              val (_, out_ts''') = split_smode is us
+              val (_, us) = strip_comb t
+              val (_, out_ts''') = split_mode mode us
               val rec_tac = prove_prems out_ts''' ps
             in
               print_tac' options "before clause:"
-              THEN asm_simp_tac HOL_basic_ss 1
+              (*THEN asm_simp_tac HOL_basic_ss 1*)
               THEN print_tac' options "before prove_expr:"
-              THEN prove_expr options thy (mode, t, us) premposition
+              THEN prove_expr options thy premposition (t, deriv)
               THEN print_tac' options "after prove_expr:"
               THEN rec_tac
             end
-          | Negprem (us, t) =>
+          | Negprem t =>
             let
-              val (_, out_ts''') = split_smode is us
+              val (t, args) = strip_comb t
+              val (_, out_ts''') = split_mode mode args
               val rec_tac = prove_prems out_ts''' ps
               val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
-              val (_, params) = strip_comb t
+              val param_derivations = param_derivations_of deriv
+              val params = ho_args_of mode args
             in
-              rtac @{thm bindI} 1
-              THEN print_tac' options "before prove_neg_expr:"
+              print_tac' options "before prove_neg_expr:"
+              THEN full_simp_tac (HOL_basic_ss addsimps
+                [@{thm split_eta}, @{thm split_beta}, @{thm fst_conv},
+                 @{thm snd_conv}, @{thm pair_collapse}, @{thm Product_Type.split_conv}]) 1
               THEN (if (is_some name) then
                   print_tac' options ("before unfolding definition " ^
                     (Display.string_of_thm_global thy
-                      (predfun_definition_of thy (the name) (iss, is))))
+                      (predfun_definition_of thy (the name) mode)))
+                  
                   THEN simp_tac (HOL_basic_ss addsimps
-                    [predfun_definition_of thy (the name) (iss, is)]) 1
+                    [predfun_definition_of thy (the name) mode]) 1
                   THEN rtac @{thm not_predI} 1
                   THEN print_tac' options "after applying rule not_predI"
-                  THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
+                  THEN full_simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True},
+                    @{thm split_eta}, @{thm split_beta}, @{thm fst_conv},
+                    @{thm snd_conv}, @{thm pair_collapse}, @{thm Product_Type.split_conv}]) 1
                   THEN (REPEAT_DETERM (atac 1))
-                  THEN (EVERY (map2 (prove_param options thy) param_modes params))
+                  THEN (EVERY (map2 (prove_param options thy) params param_derivations))
+                  THEN (REPEAT_DETERM (atac 1))
                 else
                   rtac @{thm not_predI'} 1)
                   THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
               THEN rec_tac
             end
           | Sidecond t =>
-           rtac @{thm bindI} 1
-           THEN rtac @{thm if_predI} 1
+           rtac @{thm if_predI} 1
            THEN print_tac' options "before sidecond:"
            THEN prove_sidecond thy modes t
            THEN print_tac' options "after sidecond:"
            THEN prove_prems [] ps)
-      in (prove_match thy out_ts)
+      in (prove_match options thy out_ts)
           THEN rest_tac
       end;
     val prems_tac = prove_prems in_ts moded_ps
@@ -1841,7 +1932,7 @@
 fun prove_one_direction options thy clauses preds modes pred mode moded_clauses =
   let
     val T = the (AList.lookup (op =) preds pred)
-    val nargs = length (binder_types T) - nparams_of thy pred
+    val nargs = length (binder_types T)
     val pred_case_rule = the_elim_of thy pred
   in
     REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"}))
@@ -1893,11 +1984,12 @@
 *)
 (* TODO: remove function *)
 
-fun prove_param2 thy NONE t = all_tac 
-  | prove_param2 thy (m as SOME (Mode (mode, is, ms))) t =
+fun prove_param2 thy t deriv =
   let
-    val  (f, args) = strip_comb (Envir.eta_contract t)
-    val (params, _) = chop (length ms) args
+    val (f, args) = strip_comb (Envir.eta_contract t)
+    val mode = head_mode_of deriv
+    val param_derivations = param_derivations_of deriv
+    val ho_args = ho_args_of mode args
     val f_tac = case f of
         Const (name, T) => full_simp_tac (HOL_basic_ss addsimps 
            (@{thm eval_pred}::(predfun_definition_of thy name mode)
@@ -1908,24 +2000,29 @@
     print_tac "before simplification in prove_args:"
     THEN f_tac
     THEN print_tac "after simplification in prove_args"
-    THEN (EVERY (map2 (prove_param2 thy) ms params))
+    THEN EVERY (map2 (prove_param2 thy) ho_args param_derivations)
   end
 
-
-fun prove_expr2 thy (Mode (mode, is, ms), t) = 
+fun prove_expr2 thy (t, deriv) = 
   (case strip_comb t of
-    (Const (name, T), args) =>
-      etac @{thm bindE} 1
-      THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))
-      THEN print_tac "prove_expr2-before"
-      THEN (debug_tac (Syntax.string_of_term_global thy
-        (prop_of (predfun_elim_of thy name mode))))
-      THEN (etac (predfun_elim_of thy name mode) 1)
-      THEN print_tac "prove_expr2"
-      THEN (EVERY (map2 (prove_param2 thy) ms args))
-      THEN print_tac "finished prove_expr2"      
-    | _ => etac @{thm bindE} 1)
-    
+      (Const (name, T), args) =>
+        let
+          val mode = head_mode_of deriv
+          val param_derivations = param_derivations_of deriv
+          val ho_args = ho_args_of mode args
+        in
+          etac @{thm bindE} 1
+          THEN (REPEAT_DETERM (CHANGED (rewtac @{thm "split_paired_all"})))
+          THEN print_tac "prove_expr2-before"
+          THEN (debug_tac (Syntax.string_of_term_global thy
+            (prop_of (predfun_elim_of thy name mode))))
+          THEN (etac (predfun_elim_of thy name mode) 1)
+          THEN print_tac "prove_expr2"
+          THEN (EVERY (map2 (prove_param2 thy) ho_args param_derivations))
+          THEN print_tac "finished prove_expr2"
+        end
+      | _ => etac @{thm bindE} 1)
+
 (* FIXME: what is this for? *)
 (* replace defined by has_mode thy pred *)
 (* TODO: rewrite function *)
@@ -1938,7 +2035,7 @@
   val preds = preds_of t []
   val defs = map
     (fn (pred, T) => predfun_definition_of thy pred 
-      ([], map (rpair NONE) (1 upto (length (binder_types T)))))
+      (all_input_of T))
       preds
   in
    (* only simplify the one assumption *)
@@ -1947,10 +2044,10 @@
    THEN print_tac "after sidecond2 simplification"
    end
   
-fun prove_clause2 thy modes pred (iss, is) (ts, ps) i =
+fun prove_clause2 thy modes pred mode (ts, ps) i =
   let
     val pred_intro_rule = nth (intros_of thy pred) (i - 1)
-    val (in_ts, clause_out_ts) = split_smode is ts;
+    val (in_ts, clause_out_ts) = split_mode mode ts;
     fun prove_prems2 out_ts [] =
       print_tac "before prove_match2 - last call:"
       THEN prove_match2 thy out_ts
@@ -1969,31 +2066,35 @@
            [@{thm split_eta}, @{thm "split_beta"}, @{thm "fst_conv"},
              @{thm "snd_conv"}, @{thm pair_collapse}]) 1)
           THEN print_tac "state after simp_tac:"))))
-    | prove_prems2 out_ts ((p, mode as Mode ((iss, is), _, param_modes)) :: ps) =
+    | prove_prems2 out_ts ((p, deriv) :: ps) =
       let
+        val mode = head_mode_of deriv
         val rest_tac = (case p of
-          Prem (us, t) =>
+          Prem t =>
           let
-            val (_, out_ts''') = split_smode is us
+            val (_, us) = strip_comb t
+            val (_, out_ts''') = split_mode mode us
             val rec_tac = prove_prems2 out_ts''' ps
           in
-            (prove_expr2 thy (mode, t)) THEN rec_tac
+            (prove_expr2 thy (t, deriv)) THEN rec_tac
           end
-        | Negprem (us, t) =>
+        | Negprem t =>
           let
-            val (_, out_ts''') = split_smode is us
+            val (_, args) = strip_comb t
+            val (_, out_ts''') = split_mode mode args
             val rec_tac = prove_prems2 out_ts''' ps
             val name = (case strip_comb t of (Const (c, _), _) => SOME c | _ => NONE)
-            val (_, params) = strip_comb t
+            val param_derivations = param_derivations_of deriv
+            val ho_args = ho_args_of mode args
           in
             print_tac "before neg prem 2"
             THEN etac @{thm bindE} 1
             THEN (if is_some name then
                 full_simp_tac (HOL_basic_ss addsimps
-                  [predfun_definition_of thy (the name) (iss, is)]) 1
+                  [predfun_definition_of thy (the name) mode]) 1
                 THEN etac @{thm not_predE} 1
                 THEN simp_tac (HOL_basic_ss addsimps [@{thm not_False_eq_True}]) 1
-                THEN (EVERY (map2 (prove_param2 thy) param_modes params))
+                THEN (EVERY (map2 (prove_param2 thy) ho_args param_derivations))
               else
                 etac @{thm not_predE'} 1)
             THEN rec_tac
@@ -2066,10 +2167,10 @@
     
 fun maps_modes preds_modes_table =
   map (fn (pred, modes) =>
-    (pred, map (fn (mode, value) => value) modes)) preds_modes_table  
+    (pred, map (fn (mode, value) => value) modes)) preds_modes_table
     
-fun compile_preds comp_modifiers compfuns thy all_vs param_vs preds moded_clauses =
-  map_preds_modes (fn pred => compile_pred comp_modifiers compfuns thy all_vs param_vs pred
+fun compile_preds comp_modifiers thy all_vs param_vs preds moded_clauses =
+  map_preds_modes (fn pred => compile_pred comp_modifiers thy all_vs param_vs pred
       (the (AList.lookup (op =) preds pred))) moded_clauses
 
 fun prove options thy clauses preds modes moded_clauses compiled_terms =
@@ -2084,89 +2185,58 @@
 
 fun dest_prem thy params t =
   (case strip_comb t of
-    (v as Free _, ts) => if member (op =) params v then Prem (ts, v) else Sidecond t
+    (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 thy params t of
-      Prem (ts, t) => Negprem (ts, t)
+      Prem t => Negprem t
     | Negprem _ => error ("Double negation not allowed in premise: " ^
         Syntax.string_of_term_global thy (c $ t)) 
     | Sidecond t => Sidecond (c $ t))
   | (c as Const (s, _), ts) =>
-    if is_registered thy s then
-      let val (ts1, ts2) = chop (nparams_of thy s) ts
-      in Prem (ts2, list_comb (c, ts1)) end
-    else Sidecond t
+    if is_registered thy s then Prem t else Sidecond t
   | _ => Sidecond t)
-    
-fun prepare_intrs options thy prednames intros =
+
+fun prepare_intrs options compilation thy prednames intros =
   let
     val intrs = map prop_of intros
-    val nparams = nparams_of thy (hd prednames)
     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]
       (ProofContext.init thy)
     val preds = map dest_Const preds
-    val extra_modes = all_modes_of thy
-      |> filter_out (fn (name, _) => member (op =) prednames name)
-    val params = case intrs of
+    val extra_modes =
+      all_modes_of compilation thy |> filter_out (fn (name, _) => member (op =) prednames name)
+    val all_vs = terms_vs intrs
+    val params =
+      case intrs of
         [] =>
           let
-            val (paramTs, _) = chop nparams (binder_types (snd (hd preds)))
+            val T = snd (hd preds)
+            val paramTs =
+              ho_argsT_of (hd (all_modes_of_typ T)) (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 :: _ => fst (chop nparams
-        (snd (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr)))))
-    val param_vs = maps term_vs params
-    val all_vs = terms_vs intrs
-    fun add_clause intr (clauses, arities) =
-    let
-      val _ $ t = Logic.strip_imp_concl intr;
-      val (Const (name, T), ts) = strip_comb t;
-      val (ts1, ts2) = chop nparams ts;
-      val prems = map (dest_prem thy params o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr);
-      val (Ts, Us) = chop nparams (binder_types T)
-    in
-      (AList.update op = (name, these (AList.lookup op = clauses name) @
-        [(ts2, prems)]) clauses,
-       AList.update op = (name, (map (fn U => (case strip_type U of
-                 (Rs as _ :: _, Type ("bool", [])) => SOME (length Rs)
-               | _ => NONE)) Ts,
-             length Us)) arities)
-    end;
-    val (clauses, arities) = fold add_clause intrs ([], []);
-    fun modes_of_arities arities =
-      (map (fn (s, (ks, k)) => (s, cprod (cprods (map
-            (fn NONE => [NONE]
-              | SOME k' => map SOME (map (map (rpair NONE)) (subsets 1 k'))) ks),
-       map (map (rpair NONE)) (subsets 1 k)))) arities)
-    fun modes_of_typ T =
+          in
+            map2 (curry Free) param_names paramTs
+          end
+      | (intr :: _) => maps extract_params
+          (snd (strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))))
+    val param_vs = map (fst o dest_Free) params
+    fun add_clause intr clauses =
       let
-        val (Ts, Us) = chop nparams (binder_types T)
-        fun all_smodes_of_typs Ts = cprods_subset (
-          map_index (fn (i, U) =>
-            case HOLogic.strip_tupleT U of
-              [] => [(i + 1, NONE)]
-            | [U] => [(i + 1, NONE)]
-            | Us =>  (i + 1, NONE) ::
-              (map (pair (i + 1) o SOME)
-                (subtract (op =) [[], 1 upto (length Us)] (subsets 1 (length Us)))))
-          Ts)
+        val (Const (name, T), ts) = strip_comb (HOLogic.dest_Trueprop (Logic.strip_imp_concl intr))
+        val prems = map (dest_prem thy params o HOLogic.dest_Trueprop) (Logic.strip_imp_prems intr)
       in
-        cprod (cprods (map (fn T => case strip_type T of
-          (Rs as _ :: _, Type ("bool", [])) =>
-            map SOME (all_smodes_of_typs Rs) | _ => [NONE]) Ts), all_smodes_of_typs Us)
-      end
-    val all_modes = map (fn (s, T) =>
-      case proposed_modes options of
-        NONE => (s, modes_of_typ T)
-      | SOME (s', modes') =>
-          if s = s' then (s, map (translate_mode' nparams) modes') else (s, modes_of_typ T))
-        preds
-  in (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) end;
+        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, extra_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)
@@ -2182,14 +2252,14 @@
           (Display.string_of_thm_global thy intro)) 
       | _ => true
     val prems = Logic.strip_imp_prems (prop_of intro)
-    fun check_prem (Prem (args, _)) = forall check_arg args
-      | check_prem (Negprem (args, _)) = forall check_arg args
+    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
@@ -2211,20 +2281,19 @@
 
 (* create code equation *)
 
-fun add_code_equations thy nparams preds result_thmss =
+fun add_code_equations thy preds result_thmss =
   let
     fun add_code_equation (predname, T) (pred, result_thms) =
       let
-        val full_mode = (replicate nparams NONE,
-          map (rpair NONE) (1 upto (length (binder_types T) - nparams)))
+        val full_mode = fold_rev (curry Fun) (map (K Input) (binder_types T)) Bool
       in
-        if member (op =) (modes_of thy predname) full_mode then
+        if member (op =) (modes_of Pred thy 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 (predfun_name_of thy predname full_mode,
+            val predfun = Const (function_name_of Pred thy predname full_mode,
               Ts ---> PredicateCompFuns.mk_predT @{typ unit})
             val rhs = @{term Predicate.holds} $ (list_comb (predfun, args))
             val eq_term = HOLogic.mk_Trueprop
@@ -2247,22 +2316,19 @@
 
 datatype steps = Steps of
   {
-  compile_preds : theory -> string list -> string list -> (string * typ) list
-    -> (moded_clause list) pred_mode_table -> term pred_mode_table,
   define_functions : options -> (string * typ) list -> string * mode list -> theory -> theory,
-  infer_modes : options -> theory -> (string * mode list) list -> (string * mode list) list
+  infer_modes : options -> (string * typ) list -> (string * mode list) list
     -> string list -> (string * (term list * indprem list) list) list
-    -> moded_clause list pred_mode_table * string list,
+    -> theory -> ((moded_clause list pred_mode_table * string list) * theory),
   prove : options -> theory -> (string * (term list * indprem list) list) list
     -> (string * typ) list -> (string * mode list) list
     -> moded_clause list pred_mode_table -> term pred_mode_table -> thm pred_mode_table,
-  add_code_equations : theory -> int -> (string * typ) list
+  add_code_equations : theory -> (string * typ) list
     -> (string * thm list) list -> (string * thm list) list,
-  defined : theory -> string -> bool,
+  comp_modifiers : Comp_Mod.comp_modifiers,
   qname : bstring
   }
 
-
 fun add_equations_of steps options prednames thy =
   let
     fun dest_steps (Steps s) = s
@@ -2270,37 +2336,37 @@
       ("Starting predicate compiler 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 (preds, nparams, all_vs, param_vs, extra_modes, clauses, all_modes) =
-      prepare_intrs options thy prednames (maps (intros_of thy) prednames)
+    val compilation = Comp_Mod.compilation (#comp_modifiers (dest_steps steps))
+    val (preds, all_vs, param_vs, extra_modes, clauses) =
+      prepare_intrs options compilation thy prednames (maps (intros_of thy) prednames)
     val _ = print_step options "Infering modes..."
-    val (moded_clauses, errors) =
-      #infer_modes (dest_steps steps) options thy extra_modes all_modes param_vs clauses
+    val ((moded_clauses, errors), thy') =
+      #infer_modes (dest_steps steps) options preds extra_modes param_vs clauses thy
     val modes = map (fn (p, mps) => (p, map fst mps)) moded_clauses
     val _ = check_expected_modes preds options modes
     val _ = check_proposed_modes preds options modes extra_modes errors
-    val _ = print_modes options thy modes
-      (*val _ = print_moded_clauses thy moded_clauses*)
+    val _ = print_modes options thy' modes
     val _ = print_step options "Defining executable functions..."
-    val thy' = fold (#define_functions (dest_steps steps) options preds) modes thy
+    val thy'' = fold (#define_functions (dest_steps steps) options preds) modes thy'
       |> Theory.checkpoint
     val _ = print_step options "Compiling equations..."
     val compiled_terms =
-      #compile_preds (dest_steps steps) thy' all_vs param_vs preds moded_clauses
-    val _ = print_compiled_terms options thy' compiled_terms
+      compile_preds (#comp_modifiers (dest_steps steps)) thy'' all_vs param_vs preds moded_clauses
+    val _ = print_compiled_terms options thy'' compiled_terms
     val _ = print_step options "Proving equations..."
-    val result_thms = #prove (dest_steps steps) options thy' clauses preds (extra_modes @ modes)
+    val result_thms = #prove (dest_steps steps) options thy'' clauses preds (extra_modes @ modes)
       moded_clauses compiled_terms
-    val result_thms' = #add_code_equations (dest_steps steps) thy' nparams preds
+    val result_thms' = #add_code_equations (dest_steps steps) thy'' 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'' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss
+    val thy''' = fold (fn (name, result_thms) => fn thy => snd (PureThy.add_thmss
       [((Binding.qualify true (Long_Name.base_name name) (Binding.name qname), result_thms),
         [attrib thy ])] thy))
-      result_thms' thy' |> Theory.checkpoint
+      result_thms' thy'' |> Theory.checkpoint
   in
-    thy''
+    thy'''
   end
 
 fun extend' value_of edges_of key (G, visited) =
@@ -2320,36 +2386,27 @@
 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' = thy
       |> PredData.map (fold (extend (fetch_pred_data thy) (depending_preds_of thy)) names)
       |> 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_rev
       (fn preds => fn thy =>
-        if not (forall (#defined (dest_steps steps) thy) preds) then
+        if not (forall (defined thy) preds) then
           add_equations_of steps options preds thy
         else thy)
       scc thy' |> Theory.checkpoint
   in thy'' end
-
-(* different instantiantions of the predicate compiler *)
-
-val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers
-  {function_name_of = predfun_name_of : (theory -> string -> mode -> string),
-  set_function_name = (fn _ => fn _ => fn _ => I),
-  function_name_prefix = "",
-  funT_of = funT_of : (compilation_funs -> mode -> typ -> typ),
-  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 depth_limited_comp_modifiers = Comp_Mod.Comp_Modifiers
-  {function_name_of = depth_limited_function_name_of,
-  set_function_name = set_depth_limited_function_name,
+  {
+  compilation = Depth_Limited,
+  function_name_of = function_name_of Depth_Limited,
+  set_function_name = set_function_name Depth_Limited,
   funT_of = depth_limited_funT_of : (compilation_funs -> mode -> typ -> typ),
   function_name_prefix = "depth_limited_",
   additional_arguments = fn names =>
@@ -2384,8 +2441,10 @@
   }
 
 val random_comp_modifiers = Comp_Mod.Comp_Modifiers
-  {function_name_of = random_function_name_of,
-  set_function_name = set_random_function_name,
+  {
+  compilation = Random,
+  function_name_of = function_name_of Random,
+  set_function_name = set_function_name Random,
   function_name_prefix = "random_",
   funT_of = K random_function_funT_of : (compilation_funs -> mode -> typ -> typ),
   additional_arguments = fn names => [Free (Name.variant names "size", @{typ code_numeral})],
@@ -2393,55 +2452,106 @@
     : (compilation_funs -> string -> typ -> mode -> term list -> term -> term),
   transform_additional_arguments = K I : (indprem -> term list -> term list)
   }
+*)
+(* different instantiantions of the predicate compiler *)
+
+val predicate_comp_modifiers = Comp_Mod.Comp_Modifiers
+  {
+  compilation = Pred,
+  function_name_prefix = "",
+  compfuns = PredicateCompFuns.compfuns,
+  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 add_equations = gen_add_equations
+  (Steps {infer_modes = infer_modes false,
+  define_functions = create_definitions,
+  prove = prove,
+  add_code_equations = add_code_equations,
+  comp_modifiers = predicate_comp_modifiers,
+  qname = "equation"})
 
 val annotated_comp_modifiers = Comp_Mod.Comp_Modifiers
-  {function_name_of = annotated_function_name_of,
-  set_function_name = set_annotated_function_name,
+  {
+  compilation = Annotated,
   function_name_prefix = "annotated_",
-  funT_of = funT_of : (compilation_funs -> mode -> typ -> typ),
+  compfuns = PredicateCompFuns.compfuns,
   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' (translate_mode T mode)) compilation,
+        " with mode " ^ string_of_mode mode) compilation,
   transform_additional_arguments = K I : (indprem -> term list -> term list)
   }
 
-val add_equations = gen_add_equations
-  (Steps {infer_modes = infer_modes,
-  define_functions = create_definitions,
-  compile_preds = compile_preds predicate_comp_modifiers PredicateCompFuns.compfuns,
-  prove = prove,
-  add_code_equations = add_code_equations,
-  defined = defined_functions,
-  qname = "equation"})
+val dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
+  {
+  compilation = DSeq,
+  function_name_prefix = "dseq_",
+  compfuns = DSequence_CompFuns.compfuns,
+  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 random_dseq_comp_modifiers = Comp_Mod.Comp_Modifiers
+  {
+  compilation = Random_DSeq,
+  function_name_prefix = "random_dseq_",
+  compfuns = Random_Sequence_CompFuns.compfuns,
+  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 add_depth_limited_equations = gen_add_equations
   (Steps {infer_modes = infer_modes,
   define_functions = define_functions depth_limited_comp_modifiers PredicateCompFuns.compfuns,
   compile_preds = compile_preds depth_limited_comp_modifiers PredicateCompFuns.compfuns,
   prove = prove_by_skip,
-  add_code_equations = K (K (K I)),
-  defined = defined_depth_limited_functions,
+  add_code_equations = K (K I),
+  defined = defined_functions Depth_Limited,
   qname = "depth_limited_equation"})
-
+*)
 val add_annotated_equations = gen_add_equations
-  (Steps {infer_modes = infer_modes,
+  (Steps {infer_modes = infer_modes false,
   define_functions = define_functions annotated_comp_modifiers PredicateCompFuns.compfuns,
-  compile_preds = compile_preds annotated_comp_modifiers PredicateCompFuns.compfuns,
   prove = prove_by_skip,
-  add_code_equations = K (K (K I)),
-  defined = defined_annotated_functions,
+  add_code_equations = K (K I),
+  comp_modifiers = annotated_comp_modifiers,
   qname = "annotated_equation"})
-
+(*
 val add_quickcheck_equations = gen_add_equations
   (Steps {infer_modes = infer_modes_with_generator,
   define_functions = define_functions random_comp_modifiers RandomPredCompFuns.compfuns,
   compile_preds = compile_preds random_comp_modifiers RandomPredCompFuns.compfuns,
   prove = prove_by_skip,
-  add_code_equations = K (K (K I)),
-  defined = defined_random_functions,
+  add_code_equations = K (K I),
+  defined = defined_functions Random,
   qname = "random_equation"})
+*)
+val add_dseq_equations = gen_add_equations
+  (Steps {infer_modes = infer_modes false,
+  define_functions = define_functions dseq_comp_modifiers DSequence_CompFuns.compfuns,
+  prove = prove_by_skip,
+  add_code_equations = K (K I),
+  comp_modifiers = dseq_comp_modifiers,
+  qname = "dseq_equation"})
+
+val add_random_dseq_equations = gen_add_equations
+  (Steps {infer_modes = infer_modes true,
+  define_functions = define_functions random_dseq_comp_modifiers Random_Sequence_CompFuns.compfuns,
+  prove = prove_by_skip,
+  add_code_equations = K (K I),
+  comp_modifiers = random_dseq_comp_modifiers,
+  qname = "random_dseq_equation"})
+
 
 (** user interface **)
 
@@ -2474,9 +2584,8 @@
       let
         val T = Sign.the_const_type thy const
         val pred = Const (const, T)
-        val nparams = nparams_of thy' const
         val intros = intros_of thy' const
-      in mk_casesrule lthy' pred nparams intros end  
+      in mk_casesrule lthy' pred intros end  
     val cases_rules = map mk_cases preds
     val cases =
       map (fn case_rule => Rule_Cases.Case {fixes = [],
@@ -2492,15 +2601,15 @@
           (ProofContext.init (ProofContext.theory_of goal_ctxt)) (map the_single thms)
       in
         goal_ctxt |> Local_Theory.theory (fold set_elim global_thms #>
-          (if is_random options then
-            (add_equations options [const] #>
-            add_quickcheck_equations options [const])
-           else if is_depth_limited options then
-             add_depth_limited_equations options [const]
-           else if is_annotated options then
-             add_annotated_equations options [const]
-           else
-             add_equations options [const]))
+          ((case compilation options of
+             Pred => add_equations
+           | DSeq => add_dseq_equations
+           | Random_DSeq => add_random_dseq_equations
+           | compilation => error ("Compilation not supported")
+           (*| Random => (fn opt => fn cs => add_equations opt cs #> add_quickcheck_equations opt cs)
+           | Depth_Limited => add_depth_limited_equations
+           | Annotated => add_annotated_equations*)
+           ) options [const]))
       end
   in
     Proof.theorem_i NONE after_qed (map (single o (rpair [])) cases_rules) lthy''
@@ -2514,104 +2623,161 @@
 val eval_ref = Unsynchronized.ref (NONE : (unit -> term Predicate.pred) option);
 val random_eval_ref =
   Unsynchronized.ref (NONE : (unit -> int * int -> term Predicate.pred * (int * int)) option);
+val dseq_eval_ref = Unsynchronized.ref (NONE : (unit -> term DSequence.dseq) option);
+val random_dseq_eval_ref =
+  Unsynchronized.ref (NONE : (unit -> int -> int -> int * int -> term DSequence.dseq * (int * int)) option);
 
 (*FIXME turn this into an LCF-guarded preprocessor for comprehensions*)
-(* TODO: make analyze_compr generic with respect to the compilation modifiers*)
-fun analyze_compr thy compfuns param_user_modes (depth_limit, (random, annotated)) t_compr =
+fun analyze_compr thy compfuns param_user_modes (compilation, arguments) t_compr =
   let
+    val all_modes_of = all_modes_of compilation
     val split = case t_compr of (Const (@{const_name Collect}, _) $ t) => t
       | _ => error ("Not a set comprehension: " ^ Syntax.string_of_term_global thy t_compr);
     val (body, Ts, fp) = HOLogic.strip_psplits split;
-    val (pred as Const (name, T), all_args) = strip_comb body;
-    val (params, args) = chop (nparams_of thy name) all_args;
-    val user_mode = map_filter I (map_index
-      (fn (i, t) => case t of Bound j => if j < length Ts then NONE
-        else SOME (i+1) | _ => SOME (i+1)) args); (*FIXME dangling bounds should not occur*)
-    val user_mode' = map (rpair NONE) user_mode
-    val all_modes_of = if random then all_random_modes_of else all_modes_of
-    fun fits_to is NONE = true
-      | fits_to is (SOME pm) = (is = (snd (translate_mode' 0 pm)))
-    fun valid ((SOME (Mode (_, is, ms))) :: ms') (pm :: pms) =
-        fits_to is pm andalso valid (ms @ ms') pms
-      | valid (NONE :: ms') pms = valid ms' pms
-      | valid [] [] = true
-      | valid [] _ = error "Too many mode annotations"
-      | valid (SOME _ :: _) [] = error "Not enough mode annotations"
-    val modes = filter (fn Mode (_, is, ms) => is = user_mode'
-        andalso (the_default true (Option.map (valid ms) param_user_modes)))
-      (modes_of_term (all_modes_of thy) (list_comb (pred, params)));
-    val m = case modes
-     of [] => error ("No mode possible for comprehension "
-                ^ Syntax.string_of_term_global thy t_compr)
-      | [m] => m
-      | m :: _ :: _ => (warning ("Multiple modes possible for comprehension "
-                ^ Syntax.string_of_term_global thy t_compr); m);
-    val (inargs, outargs) = split_smode user_mode' args;
-    val additional_arguments =
-      case depth_limit of
-        NONE => (if random then [@{term "5 :: code_numeral"}] else [])
-      | SOME d => [@{term "True"}, HOLogic.mk_number @{typ "code_numeral"} d]
-    val comp_modifiers =
-      case depth_limit of
-        NONE =>
-          (if random then random_comp_modifiers else
-           if annotated then annotated_comp_modifiers else predicate_comp_modifiers)
-      | SOME _ => depth_limited_comp_modifiers
-    val t_pred = compile_expr comp_modifiers compfuns thy
-      (m, list_comb (pred, params)) inargs additional_arguments;
-    val t_eval = if null outargs then t_pred else
+    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 Ts
+    val body = subst_bounds (output_frees, body)
+    val T_compr = HOLogic.mk_ptupleT fp (rev Ts)
+    val output_tuple = HOLogic.mk_ptuple fp T_compr (rev output_frees)
+    val (pred as Const (name, T), all_args) = strip_comb body
+  in
+    if defined_functions compilation thy name then
       let
-        val outargs_bounds = map (fn Bound i => i) outargs;
-        val outargsTs = map (nth Ts) outargs_bounds;
-        val T_pred = HOLogic.mk_tupleT outargsTs;
-        val T_compr = HOLogic.mk_ptupleT fp (rev Ts);
-        val k = length outargs - 1;
-        val arrange_bounds = map_index (fn (i, j) => (k-i, k-j)) outargs_bounds
-          |> sort (prod_ord (K EQUAL) int_ord)
-          |> map fst;
-        val (outargsTs', outargsT) = split_last outargsTs;
-        val (arrange, _) = fold_rev (fn U => fn (t, T) =>
-            (HOLogic.split_const (U, T, T_compr) $ Abs ("", U, t),
-             HOLogic.mk_prodT (U, T)))
-          outargsTs' (Abs ("", outargsT,
-            HOLogic.mk_ptuple fp T_compr (map Bound arrange_bounds)), outargsT)
-      in mk_map compfuns T_pred T_compr arrange t_pred end
-  in t_eval end;
+        fun extract_mode (Const ("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 _ = false
+          in forall instance_of (strip_fun_mode m1 ~~ strip_fun_mode m2) end
+        val derivs = all_derivations_of thy (all_modes_of thy) [] 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_global thy t_compr)
+          | [d] => d
+          | d :: _ :: _ => (warning ("Multiple modes possible for comprehension "
+                    ^ Syntax.string_of_term_global thy t_compr); d);
+        val (_, outargs) = split_mode (head_mode_of deriv) all_args
+        val additional_arguments =
+          case compilation of
+            Pred => []
+          | Random => [@{term "5 :: code_numeral"}]
+          | Annotated => []
+          | Depth_Limited => [@{term "True"}, HOLogic.mk_number @{typ "code_numeral"} (hd arguments)]
+          | DSeq => []
+          | Random_DSeq => []
+        val comp_modifiers =
+          case compilation of
+            Pred => predicate_comp_modifiers
+          (*| Random => random_comp_modifiers
+          | Depth_Limited => depth_limited_comp_modifiers
+          | Annotated => annotated_comp_modifiers*)
+          | DSeq => dseq_comp_modifiers
+          | Random_DSeq => random_dseq_comp_modifiers
+        val t_pred = compile_expr comp_modifiers compfuns thy (body, deriv) additional_arguments;
+        val T_pred = dest_predT compfuns (fastype_of t_pred)
+        val arrange = split_lambda (HOLogic.mk_tuple outargs) output_tuple
+      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 thy param_user_modes (options as (depth_limit, (random, annotated))) t_compr =
+fun eval thy param_user_modes (options as (compilation, arguments)) k t_compr =
   let
-    val compfuns = if random then RandomPredCompFuns.compfuns else PredicateCompFuns.compfuns
+    val compfuns =
+      case compilation of
+        Random => RandomPredCompFuns.compfuns
+      | DSeq => DSequence_CompFuns.compfuns
+      | Random_DSeq => Random_Sequence_CompFuns.compfuns
+      | _ => PredicateCompFuns.compfuns
     val t = analyze_compr thy compfuns param_user_modes options t_compr;
     val T = dest_predT compfuns (fastype_of t);
     val t' = mk_map compfuns T HOLogic.termT (HOLogic.term_of_const T) t;
-    val eval =
-      if random then
-        Code_Eval.eval NONE ("Predicate_Compile_Core.random_eval_ref", random_eval_ref)
+    val ts =
+      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
-      else
-        Code_Eval.eval NONE ("Predicate_Compile_Core.eval_ref", eval_ref) Predicate.map thy t' []
-  in (T, eval) end;
+            |> Random_Engine.run))
+      | Random_DSeq =>
+          let
+            val [nrandom, size, depth] = arguments
+          in
+            fst (DSequence.yieldn k
+              (Code_Eval.eval NONE ("Predicate_Compile_Core.random_dseq_eval_ref", random_dseq_eval_ref)
+                (fn proc => fn g => fn nrandom => fn size => fn s => g nrandom size s |>> DSequence.map proc)
+                  thy t' [] nrandom size
+                |> Random_Engine.run)
+              depth true)
+          end
+      | DSeq =>
+          fst (DSequence.yieldn k
+            (Code_Eval.eval NONE ("Predicate_Compile_Core.dseq_eval_ref", dseq_eval_ref)
+              DSequence.map thy t' []) (the_single arguments) true)
+      | _ =>
+          fst (Predicate.yieldn k
+            (Code_Eval.eval NONE ("Predicate_Compile_Core.eval_ref", eval_ref)
+              Predicate.map thy t' []))
+  in (T, ts) end;
 
-fun values ctxt param_user_modes options k t_compr =
+fun values ctxt param_user_modes (raw_expected, comp_options) k t_compr =
   let
-    val thy = ProofContext.theory_of ctxt;
-    val (T, ts) = eval thy param_user_modes options t_compr;
-    val (ts, _) = Predicate.yieldn k ts;
-    val setT = HOLogic.mk_setT T;
-    val elemsT = HOLogic.mk_set T ts;
+    val thy = ProofContext.theory_of ctxt
+    val (T, ts) = eval thy param_user_modes comp_options k t_compr
+    val setT = HOLogic.mk_setT T
+    val elems = HOLogic.mk_set T ts
     val cont = Free ("...", setT)
-  in if k = ~1 orelse length ts < k then elemsT
-    else Const (@{const_name Set.union}, setT --> setT --> setT) $ elemsT $ cont
+    (* check expected values *)
+    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 Const (@{const_name Set.union}, setT --> setT --> setT) $ elems $ cont
   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' = values ctxt param_user_modes options k t;
-    val ty' = Term.type_of t';
-    val ctxt' = Variable.auto_fixes t' ctxt;
+    val ctxt = Toplevel.context_of state
+    val t = Syntax.read_term ctxt raw_t
+    val t' = values ctxt param_user_modes options k t
+    val ty' = Term.type_of t'
+    val ctxt' = Variable.auto_fixes t' ctxt
     val p = PrintMode.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')]) ();

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_data.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_data.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -7,10 +7,10 @@
 signature PREDICATE_COMPILE_DATA =
 sig
   type specification_table;
-  val make_const_spec_table : Predicate_Compile_Aux.options -> theory -> specification_table
-  val get_specification :  specification_table -> string -> thm list
-  val obtain_specification_graph : Predicate_Compile_Aux.options -> theory ->
-    specification_table -> string -> thm list Graph.T
+  (*val make_const_spec_table : Predicate_Compile_Aux.options -> theory -> specification_table*)
+  val get_specification : theory -> term -> thm list
+  val obtain_specification_graph :
+    Predicate_Compile_Aux.options -> theory -> term -> thm list TermGraph.T
   val normalize_equation : theory -> thm -> thm
 end;
 
@@ -37,16 +37,17 @@
 
 type specification_table = thm list Symtab.table
 
-fun defining_const_of_introrule_term t =
+fun defining_term_of_introrule_term t =
   let
     val _ $ u = Logic.strip_imp_concl t
-    val (pred, all_args) = strip_comb u
+  in fst (strip_comb u) end
+(*  
   in case pred of
     Const (c, T) => c
     | _ => raise TERM ("defining_const_of_introrule_term failed: Not a constant", [t])
   end
-
-val defining_const_of_introrule = defining_const_of_introrule_term o prop_of
+*)
+val defining_term_of_introrule = defining_term_of_introrule_term o prop_of
 
 (*TODO*)
 fun is_introlike_term t = true
@@ -66,14 +67,20 @@
 
 val check_equation_format = check_equation_format_term o prop_of
 
-fun defining_const_of_equation_term (t as (Const ("==", _) $ u $ v)) =
-  (case fst (strip_comb u) of
-    Const (c, _) => c
-  | _ => raise TERM ("defining_const_of_equation_term failed: Not a constant", [t]))
-  | defining_const_of_equation_term t =
+
+fun defining_term_of_equation_term (t as (Const ("==", _) $ u $ v)) = fst (strip_comb u)
+  | defining_term_of_equation_term t =
     raise TERM ("defining_const_of_equation_term failed: Not an equation", [t])
 
-val defining_const_of_equation = defining_const_of_equation_term o prop_of
+val defining_term_of_equation = defining_term_of_equation_term o prop_of
+
+fun defining_const_of_equation th =
+  case defining_term_of_equation th
+   of Const (c, _) => c
+    | _ => raise TERM ("defining_const_of_equation failed: Not a constant", [prop_of th])
+
+
+
 
 (* Normalizing equations *)
 
@@ -125,7 +132,7 @@
   |> split_all_pairs thy
   |> tap check_equation_format
 
-fun inline_equations options thy th =
+fun inline_equations thy th =
   let
     val inline_defs = Predicate_Compile_Inline_Defs.get (ProofContext.init thy)
     val th' = (Simplifier.full_simplify (HOL_basic_ss addsimps inline_defs)) th
@@ -136,7 +143,7 @@
   in
     th'
   end
-
+(*
 fun store_thm_in_table options ignore thy th=
   let
     val th = th
@@ -150,7 +157,7 @@
         in
           (defining_const_of_equation eq, eq)
         end
-      else if (is_introlike th) then (defining_const_of_introrule th, th)
+      else if is_introlike th then (defining_const_of_introrule th, th)
       else error "store_thm: unexpected definition format"
   in
     if ignore const then I else Symtab.cons_list (const, th)
@@ -160,15 +167,15 @@
   let
     fun store ignore f =
       fold (store_thm_in_table options ignore thy)
-        (map (Thm.transfer thy) (f (ProofContext.init thy)))
+        (map (Thm.transfer thy) (f ))
     val table = Symtab.empty
       |> store (K false) Predicate_Compile_Alternative_Defs.get
     val ignore = Symtab.defined table
   in
     table
     |> store ignore (fn ctxt => maps
-      (fn (roughly, (ts, ths)) => if roughly = Spec_Rules.Equational then ths else [])
-        (Spec_Rules.get ctxt))
+      else [])
+        
     |> store ignore Nitpick_Simps.get
     |> store ignore Nitpick_Intros.get
   end
@@ -177,28 +184,62 @@
   case Symtab.lookup table constname of
     SOME thms => thms                  
   | NONE => error ("get_specification: lookup of constant " ^ quote constname ^ " failed")
+*)
+
+fun get_specification thy t =
+  Output.cond_timeit true "get_specification" (fn () =>
+  let
+    val ctxt = ProofContext.init thy
+    fun filtering th =
+      if is_equationlike th andalso
+        defining_const_of_equation (normalize_equation thy th) = (fst (dest_Const t)) then
+        SOME (normalize_equation thy th)
+      else
+        if is_introlike th andalso defining_term_of_introrule th = t then
+          SOME th
+        else
+          NONE
+  in
+    case map_filter filtering (map (Thm.transfer thy) (Predicate_Compile_Alternative_Defs.get ctxt))
+     of [] => (case map_filter
+       (fn (roughly, (ts, ths)) =>
+         if roughly = Spec_Rules.Equational andalso member (op =) ts t then SOME ths else NONE)
+         (map ((apsnd o apsnd) (map (Thm.transfer thy))) (Spec_Rules.retrieve ctxt t))
+       of [] => Output.cond_timeit true "Nitpick get_spec"
+         (fn () => (case map_filter filtering (map (Thm.transfer thy) (Nitpick_Simps.get ctxt))
+         of [] => map_filter filtering (map (Thm.transfer thy) (Nitpick_Intros.get ctxt))
+         | ths => ths))
+       | thss => flat thss)
+     | ths => ths
+  end)
 
 val logic_operator_names =
-  [@{const_name "=="}, @{const_name "op ="}, @{const_name "op -->"}, @{const_name "All"}, @{const_name "Ex"}, 
+  [@{const_name "=="}, 
+   @{const_name "==>"},
+   @{const_name "Trueprop"},
+   @{const_name "Not"},
+   @{const_name "op ="},
+   @{const_name "op -->"},
+   @{const_name "All"},
+   @{const_name "Ex"}, 
    @{const_name "op &"}]
 
-val special_cases = member (op =) [
-    @{const_name "False"},
-    @{const_name "Suc"}, @{const_name Nat.zero_nat_inst.zero_nat},
-    @{const_name Nat.one_nat_inst.one_nat},
-@{const_name "HOL.ord_class.less"}, @{const_name "HOL.ord_class.less_eq"},
-@{const_name "HOL.zero_class.zero"},
-@{const_name "HOL.one_class.one"},  @{const_name HOL.plus_class.plus},
-@{const_name Nat.ord_nat_inst.less_eq_nat},
-@{const_name Nat.ord_nat_inst.less_nat},
-@{const_name number_nat_inst.number_of_nat},
+fun special_cases (c, T) = member (op =) [
+  @{const_name "Product_Type.Unity"},
+  @{const_name "False"},
+  @{const_name "Suc"}, @{const_name Nat.zero_nat_inst.zero_nat},
+  @{const_name Nat.one_nat_inst.one_nat},
+  @{const_name "HOL.ord_class.less"}, @{const_name "HOL.ord_class.less_eq"},
+  @{const_name "HOL.zero_class.zero"},
+  @{const_name "HOL.one_class.one"},  @{const_name HOL.plus_class.plus},
+  @{const_name Nat.ord_nat_inst.less_eq_nat},
+  @{const_name Nat.ord_nat_inst.less_nat},
+  @{const_name number_nat_inst.number_of_nat},
   @{const_name Int.Bit0},
   @{const_name Int.Bit1},
   @{const_name Int.Pls},
-@{const_name "Int.zero_int_inst.zero_int"},
-@{const_name "List.filter"}]
-
-fun case_consts thy s = is_some (Datatype.info_of_case thy s)
+  @{const_name "Int.zero_int_inst.zero_int"},
+  @{const_name "List.filter"}] c
 
 fun print_specification options thy constname specs = 
   if show_intermediate_results options then
@@ -206,26 +247,32 @@
       cat_lines (map (Display.string_of_thm_global thy) specs))
   else ()
 
-fun obtain_specification_graph options thy table constname =
+fun obtain_specification_graph options thy t =
   let
-    fun is_nondefining_constname c = member (op =) logic_operator_names c
-    val is_defining_constname = member (op =) (Symtab.keys table)
-    fun has_code_pred_intros c = is_some (try (Predicate_Compile_Core.intros_of thy) c)
+    fun is_nondefining_const (c, T) = member (op =) logic_operator_names c
+    fun has_code_pred_intros (c, T) = is_some (try (Predicate_Compile_Core.intros_of thy) c)
+    fun case_consts (c, T) = is_some (Datatype.info_of_case thy c)
+    fun is_datatype_constructor (c, T) = is_some (Datatype.info_of_constr thy (c, T))
     fun defiants_of specs =
-      fold (Term.add_const_names o prop_of) specs []
-      |> filter is_defining_constname
-      |> filter_out is_nondefining_constname
+      fold (Term.add_consts o prop_of) specs []
+      |> filter_out is_datatype_constructor
+      |> filter_out is_nondefining_const
       |> filter_out has_code_pred_intros
-      |> filter_out (case_consts thy)
+      |> filter_out case_consts
       |> filter_out special_cases
-    fun extend constname =
+      |> map Const
+      (*
+      |> filter is_defining_constname*)
+    fun extend t =
       let
-        val specs = get_specification table constname
-        val _ = print_specification options thy constname specs
+        val specs = rev (get_specification thy t)
+          |> map (inline_equations thy)
+          (*|> Predicate_Compile_Set.unfold_set_notation*)
+        (*val _ = print_specification options thy constname specs*)
       in (specs, defiants_of specs) end;
   in
-    Graph.extend extend constname Graph.empty
+    TermGraph.extend extend t TermGraph.empty
   end;
   
-  
+
 end;

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_fun.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_fun.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -14,31 +14,7 @@
 structure Predicate_Compile_Fun : PREDICATE_COMPILE_FUN =
 struct
 
-fun is_funtype (Type ("fun", [_, _])) = true
-  | is_funtype _ = false;
-
-fun is_Type (Type _) = true
-  | is_Type _ = false
-
-(* returns true if t is an application of an datatype constructor *)
-(* which then consequently would be splitted *)
-(* else false *)
-(*
-fun is_constructor thy t =
-  if (is_Type (fastype_of t)) then
-    (case DatatypePackage.get_datatype thy ((fst o dest_Type o fastype_of) t) of
-      NONE => false
-    | SOME info => (let
-      val constr_consts = maps (fn (_, (_, _, constrs)) => map fst constrs) (#descr info)
-      val (c, _) = strip_comb t
-      in (case c of
-        Const (name, _) => name mem_string constr_consts
-        | _ => false) end))
-  else false
-*)
-
-(* must be exported in code.ML *)
-fun is_constr thy = is_some o Code.get_datatype_of_constr thy;
+open Predicate_Compile_Aux;
 
 (* Table from constant name (string) to term of inductive predicate *)
 structure Pred_Compile_Preproc = Theory_Data

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_pred.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_pred.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -112,8 +112,9 @@
   #> Simplifier.simplify (HOL_basic_ss addsimps [@{thm ex_disj_distrib}])
 
 val rewrite_intros =
-  Simplifier.simplify (HOL_basic_ss addsimps @{thms HOL.simp_thms(9)})
-
+(*  Simplifier.simplify (HOL_basic_ss addsimps @{thms HOL.simp_thms(9)}) *)
+  Simplifier.full_simplify (HOL_basic_ss addsimps [@{thm not_not}])
+  
 fun preprocess (constname, specs) thy =
   let
     val ctxt = ProofContext.init thy

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_quickcheck.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_quickcheck.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -8,7 +8,8 @@
 sig
   val quickcheck : Proof.context -> term -> int -> term list option
   val test_ref :
-    ((unit -> int -> int * int -> term list Predicate.pred * (int * int)) option) Unsynchronized.ref
+    ((unit -> int -> int -> int * int -> term list DSequence.dseq * (int * int)) option) Unsynchronized.ref
+  val tracing : bool Unsynchronized.ref;
 end;
 
 structure Predicate_Compile_Quickcheck : PREDICATE_COMPILE_QUICKCHECK =
@@ -17,7 +18,9 @@
 open Predicate_Compile_Aux;
 
 val test_ref =
-  Unsynchronized.ref (NONE : (unit -> int -> int * int -> term list Predicate.pred * (int * int)) option)
+  Unsynchronized.ref (NONE : (unit -> int -> int -> int * int -> term list DSequence.dseq * (int * int)) option);
+
+val tracing = Unsynchronized.ref false;
 
 val target = "Quickcheck"
 
@@ -28,15 +31,12 @@
   show_steps = true,
   show_intermediate_results = true,
   show_proof_trace = false,
-  show_modes = true,
+  show_modes = false,
   show_mode_inference = false,
-  show_compilation = true,
+  show_compilation = false,
   skip_proof = false,
-  
-  inductify = false,
-  random = false,
-  depth_limited = false,
-  annotated = false
+  compilation = Random,
+  inductify = false
 }
 
 fun dest_compfuns (Predicate_Compile_Core.CompilationFuns funs) = funs
@@ -65,7 +65,11 @@
 
 fun quickcheck ctxt t =
   let
-    val _ = tracing ("Starting quickcheck with " ^ (Syntax.string_of_term ctxt t))
+    (*val () =
+      if !tracing then
+        tracing ("Starting quickcheck with " ^ (Syntax.string_of_term ctxt t))
+      else
+        ()*)
     val ctxt' = ProofContext.theory (Context.copy_thy) ctxt
     val thy = (ProofContext.theory_of ctxt') 
     val (vs, t') = strip_abs t
@@ -75,42 +79,47 @@
     val constname = "pred_compile_quickcheck"
     val full_constname = Sign.full_bname thy constname
     val constT = map snd vs' ---> @{typ bool}
-    val thy' = Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] thy
+    val thy1 = Sign.add_consts_i [(Binding.name constname, constT, NoSyn)] thy
+    val const = Const (full_constname, constT)
     val t = Logic.list_implies
-      (map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),
+      (map HOLogic.mk_Trueprop (prems @ [HOLogic.mk_not concl]),                               
        HOLogic.mk_Trueprop (list_comb (Const (full_constname, constT), map Free vs')))
-    val tac = fn _ => Skip_Proof.cheat_tac thy'
-    val intro = Goal.prove (ProofContext.init thy') (map fst vs') [] t tac
-    val _ = tracing (Display.string_of_thm ctxt' intro)
-    val thy'' = thy'
-      |> Context.theory_map (Predicate_Compile_Alternative_Defs.add_thm intro)
-      |> Predicate_Compile.preprocess options full_constname
-      |> Predicate_Compile_Core.add_equations options [full_constname]
-      (*  |> Predicate_Compile_Core.add_depth_limited_equations Predicate_Compile_Aux.default_options [full_constname]*)
-      |> Predicate_Compile_Core.add_quickcheck_equations options [full_constname]
-    val depth_limited_modes = Predicate_Compile_Core.depth_limited_modes_of thy'' full_constname
-    val modes = Predicate_Compile_Core.random_modes_of thy'' full_constname  
+    val tac = fn _ => Skip_Proof.cheat_tac thy1
+    val intro = Goal.prove (ProofContext.init thy1) (map fst vs') [] t tac
+    (*val _ = tracing (Display.string_of_thm ctxt' intro)*)
+    val thy2 = (*Output.cond_timeit (!Quickcheck.timing) "predicate intros"
+      (fn () => *)(Context.theory_map (Predicate_Compile_Alternative_Defs.add_thm intro) thy1)
+    val thy3 = (*Output.cond_timeit (!Quickcheck.timing) "predicate preprocessing"
+        (fn () =>*) (Predicate_Compile.preprocess options const thy2)
+    val thy4 = Output.cond_timeit (!Quickcheck.timing) "random_dseq compilation"
+        (fn () => Predicate_Compile_Core.add_random_dseq_equations options [full_constname] thy3)
+    (*val depth_limited_modes = Predicate_Compile_Core.modes_of Depth_Limited thy'' full_constname*)
+    val modes = Predicate_Compile_Core.modes_of Random_DSeq thy4 full_constname
+    val output_mode = fold_rev (curry Fun) (map (K Output) (binder_types constT)) Bool
     val prog =
-      if member (op =) modes ([], []) then
+      if member eq_mode modes output_mode then
         let
-          val name = Predicate_Compile_Core.random_function_name_of thy'' full_constname ([], [])
-          val T = [@{typ code_numeral}] ---> (mk_randompredT (HOLogic.mk_tupleT (map snd vs')))
-          in Const (name, T) $ Bound 0 end
+          val name = Predicate_Compile_Core.function_name_of Random_DSeq thy4 full_constname output_mode
+          val T = (mk_randompredT (HOLogic.mk_tupleT (map snd vs')))
+        in
+          Const (name, T)
+        end
       (*else if member (op =) depth_limited_modes ([], []) then
         let
           val name = Predicate_Compile_Core.depth_limited_function_name_of thy'' full_constname ([], [])
           val T = @{typ code_numeral} --> (mk_predT (HOLogic.mk_tupleT (map snd vs')))
         in lift_pred (Const (name, T) $ Bound 0) end*)
       else error "Predicate Compile Quickcheck failed"
-    val qc_term = Abs ("size", @{typ code_numeral}, mk_bind (prog,
+    val qc_term = mk_bind (prog,
       mk_split_lambda (map Free vs') (mk_return (HOLogic.mk_list @{typ term}
-      (map2 HOLogic.mk_term_of (map snd vs') (map Free vs'))))))
-    val _ = tracing (Syntax.string_of_term ctxt' qc_term)
-    val compile = Code_Eval.eval (SOME target) ("Predicate_Compile_Quickcheck.test_ref", test_ref)
-      (fn proc => fn g => fn s => g s #>> (Predicate.map o map) proc)
-      thy'' qc_term []
+      (map2 HOLogic.mk_term_of (map snd vs') (map Free vs')))))
+    val compilation =
+      Code_Eval.eval NONE ("Predicate_Compile_Quickcheck.test_ref", test_ref)
+        (fn proc => fn g => fn n => fn size => fn s => g n size s |>> (DSequence.map o map) proc)
+        thy4 qc_term []
   in
-    ((compile #> Random_Engine.run) #> (Option.map fst o Predicate.yield))
+    (fn size =>
+      Option.map fst (DSequence.yield (compilation size size |> Random_Engine.run) size true))
   end
 
 end;

--- a/src/HOL/Word/WordBitwise.thy	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/Word/WordBitwise.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -204,7 +204,7 @@
 
 lemma bl_word_not: "to_bl (NOT w) = map Not (to_bl w)" 
   unfolding to_bl_def word_log_defs
-  by (simp add: bl_not_bin number_of_is_id word_no_wi [symmetric])
+  by (simp add: bl_not_bin number_of_is_id word_no_wi [symmetric] bin_to_bl_def[symmetric])
 
 lemma bl_word_xor: "to_bl (v XOR w) = map2 op ~= (to_bl v) (to_bl w)" 
   unfolding to_bl_def word_log_defs bl_xor_bin

--- a/src/HOL/ex/Predicate_Compile_Alternative_Defs.thy	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/ex/Predicate_Compile_Alternative_Defs.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -1,13 +1,19 @@
 theory Predicate_Compile_Alternative_Defs
-imports Main
+imports "../Predicate_Compile"
 begin
 
 section {* Set operations *}
 
-declare eq_reflection[OF empty_def, code_pred_inline] 
+declare Collect_def[code_pred_inline]
+declare mem_def[code_pred_inline]
+
+declare eq_reflection[OF empty_def, code_pred_inline]
+declare insert_code[code_pred_def]
 declare eq_reflection[OF Un_def, code_pred_inline]
 declare eq_reflection[OF UNION_def, code_pred_inline]
 
+
+
 section {* Alternative list definitions *}
  
 subsection {* Alternative rules for set *}
@@ -22,13 +28,13 @@
 unfolding mem_def[symmetric, of _ x]
 by auto
 
-code_pred set
+code_pred [skip_proof] set
 proof -
   case set
   from this show thesis
-    apply (case_tac a1)
+    apply (case_tac xb)
     apply auto
-    unfolding mem_def[symmetric, of _ a2]
+    unfolding mem_def[symmetric, of _ xc]
     apply auto
     unfolding mem_def
     apply fastsimp
@@ -43,15 +49,15 @@
 lemma list_all2_ConsI [code_pred_intro]: "list_all2 P xs ys ==> P x y ==> list_all2 P (x#xs) (y#ys)"
 by auto
 
-code_pred list_all2
+code_pred [skip_proof] list_all2
 proof -
   case list_all2
   from this show thesis
     apply -
-    apply (case_tac a1)
-    apply (case_tac a2)
+    apply (case_tac xa)
+    apply (case_tac xb)
     apply auto
-    apply (case_tac a2)
+    apply (case_tac xb)
     apply auto
     done
 qed

--- a/src/HOL/ex/Predicate_Compile_Quickcheck.thy	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/ex/Predicate_Compile_Quickcheck.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -3,10 +3,34 @@
 header {* A Prototype of Quickcheck based on the Predicate Compiler *}
 
 theory Predicate_Compile_Quickcheck
-imports Main
+imports "../Predicate_Compile"
 uses "../Tools/Predicate_Compile/predicate_compile_quickcheck.ML"
 begin
 
 setup {* Quickcheck.add_generator ("predicate_compile", Predicate_Compile_Quickcheck.quickcheck) *}
+(*
+datatype alphabet = a | b
 
+inductive_set S\<^isub>1 and A\<^isub>1 and B\<^isub>1 where
+  "[] \<in> S\<^isub>1"
+| "w \<in> A\<^isub>1 \<Longrightarrow> b # w \<in> S\<^isub>1"
+| "w \<in> B\<^isub>1 \<Longrightarrow> a # w \<in> S\<^isub>1"
+| "w \<in> S\<^isub>1 \<Longrightarrow> a # w \<in> A\<^isub>1"
+| "w \<in> S\<^isub>1 \<Longrightarrow> b # w \<in> S\<^isub>1"
+| "\<lbrakk>v \<in> B\<^isub>1; v \<in> B\<^isub>1\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>1"
+
+ML {* set Toplevel.debug *}
+
+declare mem_def[code_pred_inline] Collect_def[code_pred_inline]
+
+lemma
+  "w \<in> S\<^isub>1p \<Longrightarrow> w = []"
+quickcheck[generator = predicate_compile, iterations=1]
+oops
+
+theorem S\<^isub>1_sound:
+"w \<in> S\<^isub>1p \<Longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
+quickcheck[generator=predicate_compile, size=15]
+oops
+*)
 end
\ No newline at end of file

--- a/src/HOL/ex/Predicate_Compile_Quickcheck_ex.thy	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/ex/Predicate_Compile_Quickcheck_ex.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -3,39 +3,43 @@
   Predicate_Compile_Alternative_Defs
 begin
 
-section {* Sets *}
+ML {* Predicate_Compile_Alternative_Defs.get *}
 
+section {* Sets *}
+(*
 lemma "x \<in> {(1::nat)} ==> False"
+quickcheck[generator=predicate_compile, iterations=10]
+oops
+*)
+(* TODO: some error with doubled negation *)
+(*
+lemma "x \<in> {Suc 0, Suc (Suc 0)} ==> x \<noteq> Suc 0"
 quickcheck[generator=predicate_compile]
 oops
-
-(* TODO: some error with doubled negation *)
-lemma "x \<in> {Suc 0, Suc (Suc 0)} ==> x \<noteq> Suc 0"
+*)
+(*
+lemma "x \<in> {Suc 0, Suc (Suc 0)} ==> x = Suc 0"
+quickcheck[generator=predicate_compile]
+oops
+*) 
+lemma "x \<in> {Suc 0, Suc (Suc 0)} ==> x <= Suc 0"
 (*quickcheck[generator=predicate_compile]*)
 oops
 
-lemma "x \<in> {Suc 0, Suc (Suc 0)} ==> x = Suc 0"
-quickcheck[generator=predicate_compile]
-oops
- 
-lemma "x \<in> {Suc 0, Suc (Suc 0)} ==> x <= Suc 0"
-quickcheck[generator=predicate_compile]
-oops
-
 section {* Numerals *}
-
+(*
 lemma
   "x \<in> {1, 2, (3::nat)} ==> x = 1 \<or> x = 2"
 quickcheck[generator=predicate_compile]
 oops
-
+*)
 lemma "x \<in> {1, 2, (3::nat)} ==> x < 3"
 (*quickcheck[generator=predicate_compile]*)
 oops
 
 lemma
   "x \<in> {1, 2} \<union> {3, 4} ==> x = (1::nat) \<or> x = (2::nat)"
-quickcheck[generator=predicate_compile]
+(*quickcheck[generator=predicate_compile]*)
 oops
 
 section {* Context Free Grammar *}
@@ -49,10 +53,33 @@
 | "w \<in> S\<^isub>1 \<Longrightarrow> a # w \<in> A\<^isub>1"
 | "w \<in> S\<^isub>1 \<Longrightarrow> b # w \<in> S\<^isub>1"
 | "\<lbrakk>v \<in> B\<^isub>1; v \<in> B\<^isub>1\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>1"
+(*
+code_pred [random_dseq inductify] "S\<^isub>1p" .
+*)
+(*thm B\<^isub>1p.random_dseq_equation*)
+(*
+values [random_dseq 2, 2, 4] 10 "{x. S\<^isub>1p x}"
+values [random_dseq 1, 1, 5] 20 "{x. S\<^isub>1p x}"
+
+ML {* set ML_Context.trace *}
+*)
+ML {* set Toplevel.debug *}
+(*
+quickcheck[generator = predicate_compile, size = 10, iterations = 1]
+oops
+*)
+ML {* Spec_Rules.get *}
+ML {* Item_Net.retrieve *}
+local_setup {* Local_Theory.checkpoint *}
+ML {* Predicate_Compile_Data.get_specification @{theory} @{term "append"} *}
+lemma
+  "w \<in> S\<^isub>1p \<Longrightarrow> w = []"
+quickcheck[generator = predicate_compile, iterations=1]
+oops
 
 theorem S\<^isub>1_sound:
 "w \<in> S\<^isub>1p \<Longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
-(*quickcheck[generator=predicate_compile, size=15]*)
+quickcheck[generator=predicate_compile, size=15]
 oops
 
 
@@ -64,37 +91,37 @@
 | "w \<in> S\<^isub>2 \<Longrightarrow> b # w \<in> B\<^isub>2"
 | "\<lbrakk>v \<in> B\<^isub>2; v \<in> B\<^isub>2\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>2"
 
-code_pred [inductify, random] S\<^isub>2 .
-thm S\<^isub>2.random_equation
-thm A\<^isub>2.random_equation
-thm B\<^isub>2.random_equation
+code_pred [random_dseq inductify] S\<^isub>2 .
+thm S\<^isub>2.random_dseq_equation
+thm A\<^isub>2.random_dseq_equation
+thm B\<^isub>2.random_dseq_equation
 
-values [random] 10 "{x. S\<^isub>2 x}"
+values [random_dseq 1, 2, 8] 10 "{x. S\<^isub>2 x}"
 
 lemma "w \<in> S\<^isub>2 ==> w \<noteq> [] ==> w \<noteq> [b, a] ==> w \<in> {}"
-quickcheck[generator=predicate_compile]
+quickcheck[generator=predicate_compile, size=8]
 oops
 
 lemma "[x <- w. x = a] = []"
 quickcheck[generator=predicate_compile]
 oops
 
+declare list.size(3,4)[code_pred_def]
 
+(*
 lemma "length ([x \<leftarrow> w. x = a]) = (0::nat)"
-(*quickcheck[generator=predicate_compile]*)
+quickcheck[generator=predicate_compile]
 oops
-
-
+*)
 
 lemma
-"w \<in> S\<^isub>2 ==> length [x \<leftarrow> w. x = a] < Suc (Suc 0)"
-(*quickcheck[generator=predicate_compile]*)
+"w \<in> S\<^isub>2 ==> length [x \<leftarrow> w. x = a] <= Suc (Suc 0)"
+quickcheck[generator=predicate_compile, size = 10, iterations = 1]
 oops
 
-
 theorem S\<^isub>2_sound:
 "w \<in> S\<^isub>2 \<longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
-(*quickcheck[generator=predicate_compile, size=15, iterations=100]*)
+quickcheck[generator=predicate_compile, size=15, iterations=1]
 oops
 
 inductive_set S\<^isub>3 and A\<^isub>3 and B\<^isub>3 where
@@ -107,23 +134,24 @@
 
 code_pred [inductify] S\<^isub>3 .
 thm S\<^isub>3.equation
+(*
+values 10 "{x. S\<^isub>3 x}"
+*)
 
-values 10 "{x. S\<^isub>3 x}"
 
 lemma S\<^isub>3_sound:
 "w \<in> S\<^isub>3 \<longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
-(*quickcheck[generator=predicate_compile, size=10, iterations=1]*)
+quickcheck[generator=predicate_compile, size=10, iterations=10]
 oops
 
-
 lemma "\<not> (length w > 2) \<or> \<not> (length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b])"
-(*quickcheck[size=10, generator = pred_compile]*)
+quickcheck[size=10, generator = predicate_compile]
 oops
 
 theorem S\<^isub>3_complete:
 "length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. b = x] \<longrightarrow> w \<in> S\<^isub>3"
 (*quickcheck[generator=SML]*)
-(*quickcheck[generator=predicate_compile, size=10, iterations=100]*)
+quickcheck[generator=predicate_compile, size=10, iterations=100]
 oops
 
 
@@ -138,13 +166,205 @@
 
 theorem S\<^isub>4_sound:
 "w \<in> S\<^isub>4 \<longrightarrow> length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b]"
-(*quickcheck[generator = predicate_compile, size=2, iterations=1]*)
+quickcheck[generator = predicate_compile, size=5, iterations=1]
 oops
 
 theorem S\<^isub>4_complete:
 "length [x \<leftarrow> w. x = a] = length [x \<leftarrow> w. x = b] \<longrightarrow> w \<in> S\<^isub>4"
-(*quickcheck[generator = pred_compile, size=5, iterations=1]*)
+quickcheck[generator = predicate_compile, size=5, iterations=1]
+oops
+
+hide const b
+
+subsection {* Lexicographic order *}
+lemma
+  "(u, v) : lexord r ==> (x @ u, y @ v) : lexord r"
+
+subsection {* IMP *}
+
+types
+  var = nat
+  state = "int list"
+
+datatype com =
+  Skip |
+  Ass var "int" |
+  Seq com com |
+  IF "state list" com com |
+  While "state list" com
+
+inductive exec :: "com => state => state => bool" where
+  "exec Skip s s" |
+  "exec (Ass x e) s (s[x := e])" |
+  "exec c1 s1 s2 ==> exec c2 s2 s3 ==> exec (Seq c1 c2) s1 s3" |
+  "s \<in> set b ==> exec c1 s t ==> exec (IF b c1 c2) s t" |
+  "s \<notin> set b ==> exec c2 s t ==> exec (IF b c1 c2) s t" |
+  "s \<notin> set b ==> exec (While b c) s s" |
+  "s1 \<in> set b ==> exec c s1 s2 ==> exec (While b c) s2 s3 ==> exec (While b c) s1 s3"
+
+code_pred [random_dseq] exec .
+
+values [random_dseq 1, 2, 3] 10 "{(c, s, s'). exec c s s'}"
+
+lemma
+  "exec c s s' ==> exec (Seq c c) s s'"
+quickcheck[generator = predicate_compile, size=3, iterations=1]
+oops
+
+subsection {* Lambda *}
+
+datatype type =
+    Atom nat
+  | Fun type type    (infixr "\<Rightarrow>" 200)
+
+datatype dB =
+    Var nat
+  | App dB dB (infixl "\<degree>" 200)
+  | Abs type dB
+
+primrec
+  nth_el :: "'a list \<Rightarrow> nat \<Rightarrow> 'a option" ("_\<langle>_\<rangle>" [90, 0] 91)
+where
+  "[]\<langle>i\<rangle> = None"
+| "(x # xs)\<langle>i\<rangle> = (case i of 0 \<Rightarrow> Some x | Suc j \<Rightarrow> xs \<langle>j\<rangle>)"
+
+inductive nth_el' :: "'a list \<Rightarrow> nat \<Rightarrow> 'a \<Rightarrow> bool"
+where
+  "nth_el' (x # xs) 0 x"
+| "nth_el' xs i y \<Longrightarrow> nth_el' (x # xs) (Suc i) y"
+
+inductive typing :: "type list \<Rightarrow> dB \<Rightarrow> type \<Rightarrow> bool"  ("_ \<turnstile> _ : _" [50, 50, 50] 50)
+  where
+    Var [intro!]: "nth_el' env x T \<Longrightarrow> env \<turnstile> Var x : T"
+  | Abs [intro!]: "T # env \<turnstile> t : U \<Longrightarrow> env \<turnstile> Abs T t : (T \<Rightarrow> U)"
+  | App [intro!]: "env \<turnstile> s : U \<Rightarrow> T \<Longrightarrow> env \<turnstile> t : T \<Longrightarrow> env \<turnstile> (s \<degree> t) : U"
+
+primrec
+  lift :: "[dB, nat] => dB"
+where
+    "lift (Var i) k = (if i < k then Var i else Var (i + 1))"
+  | "lift (s \<degree> t) k = lift s k \<degree> lift t k"
+  | "lift (Abs T s) k = Abs T (lift s (k + 1))"
+
+primrec
+  subst :: "[dB, dB, nat] => dB"  ("_[_'/_]" [300, 0, 0] 300)
+where
+    subst_Var: "(Var i)[s/k] =
+      (if k < i then Var (i - 1) else if i = k then s else Var i)"
+  | subst_App: "(t \<degree> u)[s/k] = t[s/k] \<degree> u[s/k]"
+  | subst_Abs: "(Abs T t)[s/k] = Abs T (t[lift s 0 / k+1])"
+
+inductive beta :: "[dB, dB] => bool"  (infixl "\<rightarrow>\<^sub>\<beta>" 50)
+  where
+    beta [simp, intro!]: "Abs T s \<degree> t \<rightarrow>\<^sub>\<beta> s[t/0]"
+  | appL [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> s \<degree> u \<rightarrow>\<^sub>\<beta> t \<degree> u"
+  | appR [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> u \<degree> s \<rightarrow>\<^sub>\<beta> u \<degree> t"
+  | abs [simp, intro!]: "s \<rightarrow>\<^sub>\<beta> t ==> Abs T s \<rightarrow>\<^sub>\<beta> Abs T t"
+
+lemma
+  "\<Gamma> \<turnstile> t : U \<Longrightarrow> t \<rightarrow>\<^sub>\<beta> t' \<Longrightarrow> \<Gamma> \<turnstile> t' : U"
+quickcheck[generator = predicate_compile, size = 7, iterations = 10]
 oops
 
+(*
+code_pred (expected_modes: i => i => o => bool, i => i => i => bool) typing .
+thm typing.equation
+
+code_pred (modes: i => i => bool,  i => o => bool as reduce') beta .
+thm beta.equation
+
+values "{x. App (Abs (Atom 0) (Var 0)) (Var 1) \<rightarrow>\<^sub>\<beta> x}"
+
+definition "reduce t = Predicate.the (reduce' t)"
+
+value "reduce (App (Abs (Atom 0) (Var 0)) (Var 1))"
+
+code_pred [random] typing .
+code_pred [random_dseq] typing .
+
+(*values [random] 1 "{(\<Gamma>, t, T). \<Gamma> \<turnstile> t : T}"
+*)*)
+
+subsection {* JAD *}
+
+definition matrix :: "('a :: semiring_0) list list \<Rightarrow> nat \<Rightarrow> nat \<Rightarrow> bool" where
+  "matrix M rs cs \<longleftrightarrow> (\<forall> row \<in> set M. length row = cs) \<and> length M = rs"
+(*
+code_pred [random_dseq inductify] matrix .
+thm matrix.random_dseq_equation
+
+thm matrix_aux.random_dseq_equation
+
+values [random_dseq 3, 2] 10 "{(M, rs, cs). matrix (M:: int list list) rs cs}"
+*)
+lemma [code_pred_intro]:
+  "matrix [] 0 m"
+  "matrix xss n m ==> length xs = m ==> matrix (xs # xss) (Suc n) m"
+sorry
+
+code_pred [random_dseq inductify] matrix sorry
+
+
+values [random_dseq 2, 2, 15] 6 "{(M::int list list, n, m). matrix M n m}"
+
+definition "scalar_product v w = (\<Sum> (x, y)\<leftarrow>zip v w. x * y)"
+
+definition mv :: "('a \<Colon> semiring_0) list list \<Rightarrow> 'a list \<Rightarrow> 'a list"
+  where [simp]: "mv M v = map (scalar_product v) M"
+text {*
+  This defines the matrix vector multiplication. To work properly @{term
+"matrix M m n \<and> length v = n"} must hold.
+*}
+
+subsection "Compressed matrix"
+
+definition "sparsify xs = [i \<leftarrow> zip [0..<length xs] xs. snd i \<noteq> 0]"
+(*
+lemma sparsify_length: "(i, x) \<in> set (sparsify xs) \<Longrightarrow> i < length xs"
+  by (auto simp: sparsify_def set_zip)
+
+lemma listsum_sparsify[simp]:
+  fixes v :: "('a \<Colon> semiring_0) list"
+  assumes "length w = length v"
+  shows "(\<Sum>x\<leftarrow>sparsify w. (\<lambda>(i, x). v ! i) x * snd x) = scalar_product v w"
+    (is "(\<Sum>x\<leftarrow>_. ?f x) = _")
+  unfolding sparsify_def scalar_product_def
+  using assms listsum_map_filter[where f="?f" and P="\<lambda> i. snd i \<noteq> (0::'a)"]
+  by (simp add: listsum_setsum)
+*)
+definition [simp]: "unzip w = (map fst w, map snd w)"
+
+primrec insert :: "('a \<Rightarrow> 'b \<Colon> linorder) => 'a \<Rightarrow> 'a list => 'a list" where
+  "insert f x [] = [x]" |
+  "insert f x (y # ys) = (if f y < f x then y # insert f x ys else x # y # ys)"
+
+primrec sort :: "('a \<Rightarrow> 'b \<Colon> linorder) \<Rightarrow> 'a list => 'a list" where
+  "sort f [] = []" |
+  "sort f (x # xs) = insert f x (sort f xs)"
+
+definition
+  "length_permutate M = (unzip o sort (length o snd)) (zip [0 ..< length M] M)"
+
+definition
+  "transpose M = [map (\<lambda> xs. xs ! i) (takeWhile (\<lambda> xs. i < length xs) M). i \<leftarrow> [0 ..< length (M ! 0)]]"
+
+definition
+  "inflate upds = foldr (\<lambda> (i, x) upds. upds[i := x]) upds (replicate (length upds) 0)"
+
+definition
+  "jad = apsnd transpose o length_permutate o map sparsify"
+
+definition
+  "jad_mv v = inflate o split zip o apsnd (map listsum o transpose o map (map (\<lambda> (i, x). v ! i * x)))"
+ML {* ML_Context.trace := false *}
+
+lemma "matrix (M::int list list) rs cs \<Longrightarrow> False"
+quickcheck[generator = predicate_compile, size = 6]
+oops
+
+lemma
+  "\<lbrakk> matrix M rs cs ; length v = cs \<rbrakk> \<Longrightarrow> jad_mv v (jad M) = mv M v"
+(*quickcheck[generator = predicate_compile]*)
+oops
 
 end
\ No newline at end of file

--- a/src/HOL/ex/Predicate_Compile_ex.thy	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/HOL/ex/Predicate_Compile_ex.thy	Wed Jan 20 14:05:17 2010 +0100
@@ -1,5 +1,5 @@
 theory Predicate_Compile_ex
-imports Main Predicate_Compile_Alternative_Defs
+imports Predicate_Compile_Alternative_Defs
 begin
 
 subsection {* Basic predicates *}
@@ -7,8 +7,35 @@
 inductive False' :: "bool"
 
 code_pred (expected_modes: bool) False' .
-code_pred [depth_limited] False' .
-code_pred [random] False' .
+code_pred [dseq] False' .
+code_pred [random_dseq] False' .
+
+values [expected "{}" pred] "{x. False'}"
+values [expected "{}" dseq 1] "{x. False'}"
+values [expected "{}" random_dseq 1, 1, 1] "{x. False'}"
+
+value "False'"
+
+
+inductive True' :: "bool"
+where
+  "True ==> True'"
+
+code_pred True' .
+code_pred [dseq] True' .
+code_pred [random_dseq] True' .
+
+thm True'.equation
+thm True'.dseq_equation
+thm True'.random_dseq_equation
+values [expected "{()}" ]"{x. True'}"
+values [expected "{}" dseq 0] "{x. True'}"
+values [expected "{()}" dseq 1] "{x. True'}"
+values [expected "{()}" dseq 2] "{x. True'}"
+values [expected "{}" random_dseq 1, 1, 0] "{x. True'}"
+values [expected "{}" random_dseq 1, 1, 1] "{x. True'}"
+values [expected "{()}" random_dseq 1, 1, 2] "{x. True'}"
+values [expected "{()}" random_dseq 1, 1, 3] "{x. True'}"
 
 inductive EmptySet :: "'a \<Rightarrow> bool"
 
@@ -38,6 +65,7 @@
   EmptyClosure .
 
 thm EmptyClosure.equation
+
 (* TODO: inductive package is broken!
 inductive False'' :: "bool"
 where
@@ -53,12 +81,6 @@
 code_pred (expected_modes: [], [1]) [inductify] EmptySet'' .
 *)
 
-inductive True' :: "bool"
-where
-  "True \<Longrightarrow> True'"
-
-code_pred (expected_modes: bool) True' .
-
 consts a' :: 'a
 
 inductive Fact :: "'a \<Rightarrow> 'a \<Rightarrow> bool"
@@ -72,7 +94,30 @@
   "zerozero (0, 0)"
 
 code_pred (expected_modes: i => bool, i * o => bool, o * i => bool, o => bool) zerozero .
-code_pred [random] zerozero .
+code_pred [dseq] zerozero .
+code_pred [random_dseq] zerozero .
+
+thm zerozero.equation
+thm zerozero.dseq_equation
+thm zerozero.random_dseq_equation
+
+text {* We expect the user to expand the tuples in the values command.
+The following values command is not supported. *}
+(*values "{x. zerozero x}" *)
+text {* Instead, the user must type *}
+values "{(x, y). zerozero (x, y)}"
+
+values [expected "{}" dseq 0] "{(x, y). zerozero (x, y)}"
+values [expected "{(0::nat, 0::nat)}" dseq 1] "{(x, y). zerozero (x, y)}"
+values [expected "{(0::nat, 0::nat)}" dseq 2] "{(x, y). zerozero (x, y)}"
+values [expected "{}" random_dseq 1, 1, 2] "{(x, y). zerozero (x, y)}"
+values [expected "{(0::nat, 0:: nat)}" random_dseq 1, 1, 3] "{(x, y). zerozero (x, y)}"
+
+inductive nested_tuples :: "((int * int) * int * int) => bool"
+where
+  "nested_tuples ((0, 1), 2, 3)"
+
+code_pred nested_tuples .
 
 inductive JamesBond :: "nat => int => code_numeral => bool"
 where
@@ -80,16 +125,17 @@
 
 code_pred JamesBond .
 
-values "{(a, b, c). JamesBond a b c}"
-values "{(a, c, b). JamesBond a b c}"
-values "{(b, a, c). JamesBond a b c}"
-values "{(b, c, a). JamesBond a b c}"
-values "{(c, a, b). JamesBond a b c}"
-values "{(c, b, a). JamesBond a b c}"
+values [expected "{(0::nat, 0::int , 7::code_numeral)}"] "{(a, b, c). JamesBond a b c}"
+values [expected "{(0::nat, 7::code_numeral, 0:: int)}"] "{(a, c, b). JamesBond a b c}"
+values [expected "{(0::int, 0::nat, 7::code_numeral)}"] "{(b, a, c). JamesBond a b c}"
+values [expected "{(0::int, 7::code_numeral, 0::nat)}"] "{(b, c, a). JamesBond a b c}"
+values [expected "{(7::code_numeral, 0::nat, 0::int)}"] "{(c, a, b). JamesBond a b c}"
+values [expected "{(7::code_numeral, 0::int, 0::nat)}"] "{(c, b, a). JamesBond a b c}"
 
-values "{(a, b). JamesBond 0 b a}"
-values "{(c, a). JamesBond a 0 c}"
-values "{(a, c). JamesBond a 0 c}"
+values [expected "{(7::code_numeral, 0::int)}"] "{(a, b). JamesBond 0 b a}"
+values [expected "{(7::code_numeral, 0::nat)}"] "{(c, a). JamesBond a 0 c}"
+values [expected "{(0::nat, 7::code_numeral)}"] "{(a, c). JamesBond a 0 c}"
+
 
 subsection {* Alternative Rules *}
 
@@ -119,14 +165,14 @@
   case is_D_or_E
   from this(1) show thesis
   proof
-    fix x
-    assume x: "a1 = x"
-    assume "x = D \<or> x = E"
+    fix xa
+    assume x: "x = xa"
+    assume "xa = D \<or> xa = E"
     from this show thesis
     proof
-      assume "x = D" from this x is_D_or_E(2) show thesis by simp
+      assume "xa = D" from this x is_D_or_E(2) show thesis by simp
     next
-      assume "x = E" from this x is_D_or_E(3) show thesis by simp
+      assume "xa = E" from this x is_D_or_E(3) show thesis by simp
     qed
   qed
 qed
@@ -157,15 +203,15 @@
   case is_F_or_G
   from this(1) show thesis
   proof
-    fix x
-    assume x: "a1 = x"
-    assume "x = F \<or> x = G"
+    fix xa
+    assume x: "x = xa"
+    assume "xa = F \<or> xa = G"
     from this show thesis
     proof
-      assume "x = F"
+      assume "xa = F"
       from this x is_F_or_G(2) show thesis by simp
     next
-      assume "x = G"
+      assume "xa = G"
       from this x is_F_or_G(3) show thesis by simp
     qed
   qed
@@ -200,15 +246,16 @@
 
 code_pred (expected_modes: i * i => bool, i * o => bool, o * i => bool, o => bool) [inductify] zerozero'' .
 
-subsection {* Numerals *}
+subsection {* Sets and Numerals *}
 
 definition
-  "one_or_two == {Suc 0, (Suc (Suc 0))}"
+  "one_or_two = {Suc 0, (Suc (Suc 0))}"
 
-(*code_pred [inductify] one_or_two .*)
-code_pred [inductify, random] one_or_two .
-(*values "{x. one_or_two x}"*)
-values [random] "{x. one_or_two x}"
+code_pred [inductify] one_or_two .
+code_pred [dseq] one_or_two .
+(*code_pred [random_dseq] one_or_two .*)
+values [expected "{Suc 0::nat, 2::nat}"] "{x. one_or_two x}"
+(*values [random_dseq 1,1,2] "{x. one_or_two x}"*)
 
 inductive one_or_two' :: "nat => bool"
 where
@@ -222,13 +269,12 @@
 
 definition one_or_two'':
   "one_or_two'' == {1, (2::nat)}"
-
-code_pred [inductify] one_or_two'' .
+ML {* prop_of @{thm one_or_two''} *}
+(*code_pred [inductify] one_or_two'' .
 thm one_or_two''.equation
 
 values "{x. one_or_two'' x}"
-
-
+*)
 subsection {* even predicate *}
 
 inductive even :: "nat \<Rightarrow> bool" and odd :: "nat \<Rightarrow> bool" where
@@ -237,35 +283,55 @@
   | "odd n \<Longrightarrow> even (Suc n)"
 
 code_pred (expected_modes: i => bool, o => bool) even .
-code_pred [depth_limited] even .
-code_pred [random] even .
+code_pred [dseq] even .
+code_pred [random_dseq] even .
 
 thm odd.equation
 thm even.equation
-thm odd.depth_limited_equation
-thm even.depth_limited_equation
-thm even.random_equation
-thm odd.random_equation
+thm odd.dseq_equation
+thm even.dseq_equation
+thm odd.random_dseq_equation
+thm even.random_dseq_equation
 
 values "{x. even 2}"
 values "{x. odd 2}"
 values 10 "{n. even n}"
 values 10 "{n. odd n}"
-values [depth_limit = 2] "{x. even 6}"
-values [depth_limit = 7] "{x. even 6}"
-values [depth_limit = 2] "{x. odd 7}"
-values [depth_limit = 8] "{x. odd 7}"
-values [depth_limit = 7] 10 "{n. even n}"
+values [expected "{}" dseq 2] "{x. even 6}"
+values [expected "{}" dseq 6] "{x. even 6}"
+values [expected "{()}" dseq 7] "{x. even 6}"
+values [dseq 2] "{x. odd 7}"
+values [dseq 6] "{x. odd 7}"
+values [dseq 7] "{x. odd 7}"
+values [expected "{()}" dseq 8] "{x. odd 7}"
+
+values [expected "{}" dseq 0] 8 "{x. even x}"
+values [expected "{0::nat}" dseq 1] 8 "{x. even x}"
+values [expected "{0::nat, 2}" dseq 3] 8 "{x. even x}"
+values [expected "{0::nat, 2}" dseq 4] 8 "{x. even x}"
+values [expected "{0::nat, 2, 4}" dseq 6] 8 "{x. even x}"
+
+values [random_dseq 1, 1, 0] 8 "{x. even x}"
+values [random_dseq 1, 1, 1] 8 "{x. even x}"
+values [random_dseq 1, 1, 2] 8 "{x. even x}"
+values [random_dseq 1, 1, 3] 8 "{x. even x}"
+values [random_dseq 1, 1, 6] 8 "{x. even x}"
+
+values [expected "{}" random_dseq 1, 1, 7] "{x. odd 7}"
+values [random_dseq 1, 1, 8] "{x. odd 7}"
+values [random_dseq 1, 1, 9] "{x. odd 7}"
 
 definition odd' where "odd' x == \<not> even x"
 
 code_pred (expected_modes: i => bool) [inductify] odd' .
-code_pred [inductify, depth_limited] odd' .
-code_pred [inductify, random] odd' .
+code_pred [dseq inductify] odd' .
+code_pred [random_dseq inductify] odd' .
 
-thm odd'.depth_limited_equation
-values [depth_limit = 2] "{x. odd' 7}"
-values [depth_limit = 9] "{x. odd' 7}"
+values [expected "{}" dseq 2] "{x. odd' 7}"
+values [expected "{()}" dseq 9] "{x. odd' 7}"
+values [expected "{}" dseq 2] "{x. odd' 8}"
+values [expected "{}" dseq 10] "{x. odd' 8}"
+
 
 inductive is_even :: "nat \<Rightarrow> bool"
 where
@@ -280,22 +346,28 @@
   | "append xs ys zs \<Longrightarrow> append (x # xs) ys (x # zs)"
 
 code_pred (modes: i => i => o => bool as "concat", o => o => i => bool as "slice", o => i => i => bool as prefix,
-  i => o => i => bool as suffix) append .
-code_pred [depth_limited] append .
-code_pred [random] append .
-code_pred [annotated] append .
+  i => o => i => bool as suffix, i => i => i => bool) append .
+code_pred [dseq] append .
+code_pred [random_dseq] append .
 
 thm append.equation
-thm append.depth_limited_equation
-thm append.random_equation
-thm append.annotated_equation
+thm append.dseq_equation
+thm append.random_dseq_equation
 
 values "{(ys, xs). append xs ys [0, Suc 0, 2]}"
 values "{zs. append [0, Suc 0, 2] [17, 8] zs}"
 values "{ys. append [0, Suc 0, 2] ys [0, Suc 0, 2, 17, 0, 5]}"
 
-values [depth_limit = 3] "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}"
-values [random] 1 "{(ys, zs). append [1::nat, 2] ys zs}"
+values [expected "{}" dseq 0] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}"
+values [expected "{(([]::nat list), [Suc 0, 2, 3, 4, (5::nat)])}" dseq 1] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}"
+values [dseq 4] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}"
+values [dseq 6] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}"
+values [random_dseq 1, 1, 4] 10 "{(xs, ys). append xs ys [1, 2, 3, 4, (5::nat)]}"
+values [random_dseq 1, 1, 1] 10 "{(xs, ys, zs::int list). append xs ys zs}"
+values [random_dseq 1, 1, 3] 10 "{(xs, ys, zs::int list). append xs ys zs}"
+values [random_dseq 3, 1, 3] 10 "{(xs, ys, zs::int list). append xs ys zs}"
+values [random_dseq 1, 3, 3] 10 "{(xs, ys, zs::int list). append xs ys zs}"
+values [random_dseq 1, 1, 4] 10 "{(xs, ys, zs::int list). append xs ys zs}"
 
 value [code] "Predicate.the (concat [0::int, 1, 2] [3, 4, 5])"
 value [code] "Predicate.the (slice ([]::int list))"
@@ -320,11 +392,11 @@
   from append2(1) show thesis
   proof
     fix xs
-    assume "a1 = []" "a2 = xs" "a3 = xs"
+    assume "xa = []" "xb = xs" "xc = xs"
     from this append2(2) show thesis by simp
   next
     fix xs ys zs x
-    assume "a1 = x # xs" "a2 = ys" "a3 = x # zs" "append2 xs ys zs"
+    assume "xa = x # xs" "xb = ys" "xc = x # zs" "append2 xs ys zs"
     from this append2(3) show thesis by fastsimp
   qed
 qed
@@ -336,11 +408,10 @@
 
 code_pred (expected_modes: i * i * o => bool, o * o * i => bool, o * i * i => bool,
   i * o * i => bool, i * i * i => bool) tupled_append .
-code_pred [random] tupled_append .
+code_pred [random_dseq] tupled_append .
 thm tupled_append.equation
 
-(*TODO: values with tupled modes*)
-(*values "{xs. tupled_append ([1,2,3], [4,5], xs)}"*)
+values "{xs. tupled_append ([(1::nat), 2, 3], [4, 5], xs)}"
 
 inductive tupled_append'
 where
@@ -358,7 +429,7 @@
 | "ys = fst yszs ==> x # zs = snd yszs ==> tupled_append'' (xs, ys, zs) \<Longrightarrow> tupled_append'' (x # xs, yszs)"
 
 code_pred (expected_modes: i * i * o => bool, o * o * i => bool, o * i * i => bool,
-  i * o * i => bool, i * i * i => bool) [inductify] tupled_append'' .
+  i * o * i => bool, i * i * i => bool) tupled_append'' .
 thm tupled_append''.equation
 
 inductive tupled_append''' :: "'a list \<times> 'a list \<times> 'a list \<Rightarrow> bool"
@@ -367,7 +438,7 @@
 | "yszs = (ys, zs) ==> tupled_append''' (xs, yszs) \<Longrightarrow> tupled_append''' (x # xs, ys, x # zs)"
 
 code_pred (expected_modes: i * i * o => bool, o * o * i => bool, o * i * i => bool,
-  i * o * i => bool, i * i * i => bool) [inductify] tupled_append''' .
+  i * o * i => bool, i * i * i => bool) tupled_append''' .
 thm tupled_append'''.equation
 
 subsection {* map_ofP predicate *}
@@ -390,39 +461,46 @@
 | "\<not> P x ==> filter1 P xs ys ==> filter1 P (x#xs) ys"
 
 code_pred (expected_modes: (i => bool) => i => o => bool, (i => bool) => i => i => bool) filter1 .
-code_pred [depth_limited] filter1 .
-code_pred [random] filter1 .
+code_pred [dseq] filter1 .
+code_pred [random_dseq] filter1 .
 
 thm filter1.equation
 
+values [expected "{[0::nat, 2, 4]}"] "{xs. filter1 even [0, 1, 2, 3, 4] xs}"
+values [expected "{}" dseq 9] "{xs. filter1 even [0, 1, 2, 3, 4] xs}"
+values [expected "{[0::nat, 2, 4]}" dseq 10] "{xs. filter1 even [0, 1, 2, 3, 4] xs}"
+
 inductive filter2
 where
   "filter2 P [] []"
 | "P x ==> filter2 P xs ys ==> filter2 P (x#xs) (x#ys)"
 | "\<not> P x ==> filter2 P xs ys ==> filter2 P (x#xs) ys"
 
-code_pred (expected_modes: i => i => i => bool, i => i => o => bool) filter2 .
-code_pred [depth_limited] filter2 .
-code_pred [random] filter2 .
+code_pred (expected_modes: (i => bool) => i => i => bool, (i => bool) => i => o => bool) filter2 .
+code_pred [dseq] filter2 .
+code_pred [random_dseq] filter2 .
+
 thm filter2.equation
-thm filter2.random_equation
+thm filter2.random_dseq_equation
 
+(*
 inductive filter3
 for P
 where
   "List.filter P xs = ys ==> filter3 P xs ys"
 
-code_pred (expected_modes: (o => bool) => i => o => bool, (o => bool) => i => i => bool , (i => bool) => i => o => bool, (i => bool) => i => i => bool) filter3 .
-code_pred [depth_limited] filter3 .
-thm filter3.depth_limited_equation
+code_pred (expected_modes: (o => bool) => i => o => bool, (o => bool) => i => i => bool , (i => bool) => i => o => bool, (i => bool) => i => i => bool) [skip_proof] filter3 .
 
+code_pred [dseq] filter3 .
+thm filter3.dseq_equation
+*)
 inductive filter4
 where
   "List.filter P xs = ys ==> filter4 P xs ys"
 
-code_pred (expected_modes: i => i => o => bool, i => i => i => bool) filter4 .
-code_pred [depth_limited] filter4 .
-code_pred [random] filter4 .
+(*code_pred (expected_modes: i => i => o => bool, i => i => i => bool) filter4 .*)
+(*code_pred [depth_limited] filter4 .*)
+(*code_pred [random] filter4 .*)
 
 subsection {* reverse predicate *}
 
@@ -452,9 +530,10 @@
   | "\<not> f x \<Longrightarrow> partition f xs ys zs \<Longrightarrow> partition f (x # xs) ys (x # zs)"
 
 code_pred (expected_modes: (i => bool) => i => o => o => bool, (i => bool) => o => i => i => bool,
-  (i => bool) => i => i => o => bool, (i => bool) => i => o => i => bool, (i => bool) => i => i => i => bool) partition .
-code_pred [depth_limited] partition .
-code_pred [random] partition .
+  (i => bool) => i => i => o => bool, (i => bool) => i => o => i => bool, (i => bool) => i => i => i => bool)
+  partition .
+code_pred [dseq] partition .
+code_pred [random_dseq] partition .
 
 values 10 "{(ys, zs). partition is_even
   [0, Suc 0, 2, 3, 4, 5, 6, 7] ys zs}"
@@ -489,19 +568,44 @@
   from this converse_tranclpE[OF this(1)] show thesis by metis
 qed
 
-code_pred [depth_limited] tranclp .
-code_pred [random] tranclp .
+
+code_pred [dseq] tranclp .
+code_pred [random_dseq] tranclp .
 thm tranclp.equation
-thm tranclp.random_equation
+thm tranclp.random_dseq_equation
+
+inductive rtrancl' :: "'a => 'a => ('a => 'a => bool) => bool" 
+where
+  "rtrancl' x x r"
+| "r x y ==> rtrancl' y z r ==> rtrancl' x z r"
+
+code_pred [random_dseq] rtrancl' .
+
+thm rtrancl'.random_dseq_equation
+
+inductive rtrancl'' :: "('a * 'a * ('a \<Rightarrow> 'a \<Rightarrow> bool)) \<Rightarrow> bool"  
+where
+  "rtrancl'' (x, x, r)"
+| "r x y \<Longrightarrow> rtrancl'' (y, z, r) \<Longrightarrow> rtrancl'' (x, z, r)"
+
+code_pred rtrancl'' .
+
+inductive rtrancl''' :: "('a * ('a * 'a) * ('a * 'a => bool)) => bool" 
+where
+  "rtrancl''' (x, (x, x), r)"
+| "r (x, y) ==> rtrancl''' (y, (z, z), r) ==> rtrancl''' (x, (z, z), r)"
+
+code_pred rtrancl''' .
+
 
 inductive succ :: "nat \<Rightarrow> nat \<Rightarrow> bool" where
     "succ 0 1"
   | "succ m n \<Longrightarrow> succ (Suc m) (Suc n)"
 
-code_pred succ .
-code_pred [random] succ .
+code_pred (modes: i => i => bool, i => o => bool, o => i => bool, o => o => bool) succ .
+code_pred [random_dseq] succ .
 thm succ.equation
-thm succ.random_equation
+thm succ.random_dseq_equation
 
 values 10 "{(m, n). succ n m}"
 values "{m. succ 0 m}"
@@ -531,10 +635,55 @@
 code_pred (expected_modes: i => i => bool) not_reachable_in_example_graph .
 
 thm not_reachable_in_example_graph.equation
-
+thm tranclp.equation
 value "not_reachable_in_example_graph 0 3"
 value "not_reachable_in_example_graph 4 8"
 value "not_reachable_in_example_graph 5 6"
+text {* rtrancl compilation is strange! *}
+(*
+value "not_reachable_in_example_graph 0 4"
+value "not_reachable_in_example_graph 1 6"
+value "not_reachable_in_example_graph 8 4"*)
+
+code_pred [dseq] not_reachable_in_example_graph .
+
+values [dseq 6] "{x. tranclp example_graph 0 3}"
+
+values [dseq 0] "{x. not_reachable_in_example_graph 0 3}"
+values [dseq 0] "{x. not_reachable_in_example_graph 0 4}"
+values [dseq 20] "{x. not_reachable_in_example_graph 0 4}"
+values [dseq 6] "{x. not_reachable_in_example_graph 0 3}"
+values [dseq 3] "{x. not_reachable_in_example_graph 4 2}"
+values [dseq 6] "{x. not_reachable_in_example_graph 4 2}"
+
+
+inductive not_reachable_in_example_graph' :: "int => int => bool"
+where "\<not> (rtranclp example_graph x y) ==> not_reachable_in_example_graph' x y"
+
+code_pred not_reachable_in_example_graph' .
+
+value "not_reachable_in_example_graph' 0 3"
+(* value "not_reachable_in_example_graph' 0 5" would not terminate *)
+
+
+(*values [depth_limited 0] "{x. not_reachable_in_example_graph' 0 3}"*)
+(*values [depth_limited 3] "{x. not_reachable_in_example_graph' 0 3}"*) (* fails with undefined *)
+(*values [depth_limited 5] "{x. not_reachable_in_example_graph' 0 3}"*)
+(*values [depth_limited 1] "{x. not_reachable_in_example_graph' 0 4}"*)
+(*values [depth_limit = 4] "{x. not_reachable_in_example_graph' 0 4}"*) (* fails with undefined *)
+(*values [depth_limit = 20] "{x. not_reachable_in_example_graph' 0 4}"*) (* fails with undefined *)
+
+code_pred [dseq] not_reachable_in_example_graph' .
+
+(*thm not_reachable_in_example_graph'.dseq_equation*)
+
+(*values [dseq 0] "{x. not_reachable_in_example_graph' 0 3}"*)
+(*values [depth_limited 3] "{x. not_reachable_in_example_graph' 0 3}"*) (* fails with undefined *)
+(*values [depth_limited 5] "{x. not_reachable_in_example_graph' 0 3}"
+values [depth_limited 1] "{x. not_reachable_in_example_graph' 0 4}"*)
+(*values [depth_limit = 4] "{x. not_reachable_in_example_graph' 0 4}"*) (* fails with undefined *)
+(*values [depth_limit = 20] "{x. not_reachable_in_example_graph' 0 4}"*) (* fails with undefined *)
+
 
 subsection {* IMP *}
 
@@ -564,6 +713,7 @@
  (While (%s. s!0 > 0) (Seq (Ass 0 (%s. s!0 - 1)) (Ass 1 (%s. s!1 + 1))))
  [3,5] t}"
 
+
 inductive tupled_exec :: "(com \<times> state \<times> state) \<Rightarrow> bool" where
 "tupled_exec (Skip, s, s)" |
 "tupled_exec (Ass x e, s, s[x := e(s)])" |
@@ -575,6 +725,8 @@
 
 code_pred tupled_exec .
 
+values "{s. tupled_exec (While (%s. s!0 > 0) (Seq (Ass 0 (%s. s!0 - 1)) (Ass 1 (%s. s!1 + 1))), [3, 5], s)}"
+
 subsection {* CCS *}
 
 text{* This example formalizes finite CCS processes without communication or
@@ -633,13 +785,16 @@
 where "Min s r x \<equiv> s x \<and> (\<forall>y. r x y \<longrightarrow> x = y)"
 
 code_pred [inductify] Min .
+thm Min.equation
 
 subsection {* Lexicographic order *}
 
+declare lexord_def[code_pred_def]
 code_pred [inductify] lexord .
-code_pred [inductify, random] lexord .
+code_pred [random_dseq inductify] lexord .
+
 thm lexord.equation
-thm lexord.random_equation
+thm lexord.random_dseq_equation
 
 inductive less_than_nat :: "nat * nat => bool"
 where
@@ -648,38 +803,100 @@
  
 code_pred less_than_nat .
 
-code_pred [depth_limited] less_than_nat .
-code_pred [random] less_than_nat .
+code_pred [dseq] less_than_nat .
+code_pred [random_dseq] less_than_nat .
 
 inductive test_lexord :: "nat list * nat list => bool"
 where
   "lexord less_than_nat (xs, ys) ==> test_lexord (xs, ys)"
 
-code_pred [random] test_lexord .
-code_pred [depth_limited] test_lexord .
-thm test_lexord.depth_limited_equation
-thm test_lexord.random_equation
+code_pred test_lexord .
+code_pred [dseq] test_lexord .
+code_pred [random_dseq] test_lexord .
+thm test_lexord.dseq_equation
+thm test_lexord.random_dseq_equation
 
 values "{x. test_lexord ([1, 2, 3], [1, 2, 5])}"
-values [depth_limit = 5] "{x. test_lexord ([1, 2, 3], [1, 2, 5])}"
+(*values [depth_limited 5] "{x. test_lexord ([1, 2, 3], [1, 2, 5])}"*)
 
+declare list.size(3,4)[code_pred_def]
 lemmas [code_pred_def] = lexn_conv lex_conv lenlex_conv
-
+(*
 code_pred [inductify] lexn .
 thm lexn.equation
+*)
+(*
+code_pred [random_dseq inductify] lexn .
+thm lexn.random_dseq_equation
 
-code_pred [random] lexn .
+values [random_dseq 4, 4, 6] 100 "{(n, xs, ys::int list). lexn (%(x, y). x <= y) n (xs, ys)}"
+*)
+inductive has_length
+where
+  "has_length [] 0"
+| "has_length xs i ==> has_length (x # xs) (Suc i)" 
+
+lemma has_length:
+  "has_length xs n = (length xs = n)"
+proof (rule iffI)
+  assume "has_length xs n"
+  from this show "length xs = n"
+    by (rule has_length.induct) auto
+next
+  assume "length xs = n"
+  from this show "has_length xs n"
+    by (induct xs arbitrary: n) (auto intro: has_length.intros)
+qed
 
-thm lexn.random_equation
+lemma lexn_intros [code_pred_intro]:
+  "has_length xs i ==> has_length ys i ==> r (x, y) ==> lexn r (Suc i) (x # xs, y # ys)"
+  "lexn r i (xs, ys) ==> lexn r (Suc i) (x # xs, x # ys)"
+proof -
+  assume "has_length xs i" "has_length ys i" "r (x, y)"
+  from this has_length show "lexn r (Suc i) (x # xs, y # ys)"
+    unfolding lexn_conv Collect_def mem_def
+    by fastsimp
+next
+  assume "lexn r i (xs, ys)"
+  thm lexn_conv
+  from this show "lexn r (Suc i) (x#xs, x#ys)"
+    unfolding Collect_def mem_def lexn_conv
+    apply auto
+    apply (rule_tac x="x # xys" in exI)
+    by auto
+qed
+
+code_pred [random_dseq inductify] lexn
+proof -
+  fix n xs ys
+  assume 1: "lexn r n (xs, ys)"
+  assume 2: "\<And>i x xs' y ys'. r = r ==> n = Suc i ==> (xs, ys) = (x # xs', y # ys') ==> has_length xs' i ==> has_length ys' i ==> r (x, y) ==> thesis"
+  assume 3: "\<And>i x xs' ys'. r = r ==> n = Suc i ==> (xs, ys) = (x # xs', x # ys') ==> lexn r i (xs', ys') ==> thesis"
+  from 1 2 3 show thesis   
+    unfolding lexn_conv Collect_def mem_def
+    apply (auto simp add: has_length)
+    apply (case_tac xys)
+    apply auto
+    apply fastsimp
+    apply fastsimp done
+qed
+
+
+values [random_dseq 1, 2, 5] 10 "{(n, xs, ys::int list). lexn (%(x, y). x <= y) n (xs, ys)}"
+
 
 code_pred [inductify] lenlex .
 thm lenlex.equation
 
-code_pred [inductify, random] lenlex .
-thm lenlex.random_equation
+code_pred [random_dseq inductify] lenlex .
+thm lenlex.random_dseq_equation
 
+values [random_dseq 4, 2, 4] 100 "{(xs, ys::int list). lenlex (%(x, y). x <= y) (xs, ys)}"
+thm lists.intros
+(*
 code_pred [inductify] lists .
-thm lists.equation
+*)
+(*thm lists.equation*)
 
 subsection {* AVL Tree *}
 
@@ -693,12 +910,14 @@
   "avl ET = True"
   "avl (MKT x l r h) = ((height l = height r \<or> height l = 1 + height r \<or> height r = 1+height l) \<and> 
   h = max (height l) (height r) + 1 \<and> avl l \<and> avl r)"
-
+(*
 code_pred [inductify] avl .
-thm avl.equation
+thm avl.equation*)
 
-code_pred [random] avl .
-thm avl.random_equation
+code_pred [random_dseq inductify] avl .
+thm avl.random_dseq_equation
+
+values [random_dseq 2, 1, 7] 5 "{t:: int tree. avl t}"
 
 fun set_of
 where
@@ -714,30 +933,57 @@
 code_pred (expected_modes: i => o => bool, i => i => bool) [inductify] set_of .
 thm set_of.equation
 
-code_pred [inductify] is_ord .
+code_pred (expected_modes: i => bool) [inductify] is_ord .
 thm is_ord_aux.equation
 thm is_ord.equation
 
 
 subsection {* Definitions about Relations *}
+term "converse"
+code_pred (modes:
+  (i * i => bool) => i * i => bool,
+  (i * o => bool) => o * i => bool,
+  (i * o => bool) => i * i => bool,
+  (o * i => bool) => i * o => bool,
+  (o * i => bool) => i * i => bool,
+  (o * o => bool) => o * o => bool,
+  (o * o => bool) => i * o => bool,
+  (o * o => bool) => o * i => bool,
+  (o * o => bool) => i * i => bool) [inductify] converse .
 
-code_pred [inductify] converse .
 thm converse.equation
 code_pred [inductify] rel_comp .
 thm rel_comp.equation
 code_pred [inductify] Image .
 thm Image.equation
-code_pred (expected_modes: (o => bool) => o => bool, (o => bool) => i * o => bool,
-  (o => bool) => o * i => bool, (o => bool) => i => bool) [inductify] Id_on .
+declare singleton_iff[code_pred_inline]
+declare Id_on_def[unfolded Bex_def UNION_def singleton_iff, code_pred_def]
+
+code_pred (expected_modes:
+  (o => bool) => o => bool,
+  (o => bool) => i * o => bool,
+  (o => bool) => o * i => bool,
+  (o => bool) => i => bool,
+  (i => bool) => i * o => bool,
+  (i => bool) => o * i => bool,
+  (i => bool) => i => bool) [inductify] Id_on .
 thm Id_on.equation
-code_pred [inductify] Domain .
+thm Domain_def
+code_pred (modes:
+  (o * o => bool) => o => bool,
+  (o * o => bool) => i => bool,
+  (i * o => bool) => i => bool) [inductify] Domain .
 thm Domain.equation
-code_pred [inductify] Range .
+code_pred (modes:
+  (o * o => bool) => o => bool,
+  (o * o => bool) => i => bool,
+  (o * i => bool) => i => bool) [inductify] Range .
 thm Range.equation
 code_pred [inductify] Field .
 thm Field.equation
+(*thm refl_on_def
 code_pred [inductify] refl_on .
-thm refl_on.equation
+thm refl_on.equation*)
 code_pred [inductify] total_on .
 thm total_on.equation
 code_pred [inductify] antisym .
@@ -751,11 +997,11 @@
 
 subsection {* Inverting list functions *}
 
-code_pred [inductify] length .
-code_pred [inductify, random] length .
+(*code_pred [inductify] length .
+code_pred [random inductify] length .
 thm size_listP.equation
 thm size_listP.random_equation
-
+*)
 (*values [random] 1 "{xs. size_listP (xs::nat list) (5::nat)}"*)
 
 code_pred (expected_modes: i => o => bool, o => i => bool, i => i => bool) [inductify] List.concat .
@@ -764,19 +1010,19 @@
 values "{ys. concatP [[1, 2], [3, (4::int)]] ys}"
 values "{ys. concatP [[1, 2], [3]] [1, 2, (3::nat)]}"
 
-code_pred [inductify, depth_limited] List.concat .
-thm concatP.depth_limited_equation
+code_pred [dseq inductify] List.concat .
+thm concatP.dseq_equation
 
-values [depth_limit = 3] 3
+values [dseq 3] 3
   "{xs. concatP xs ([0] :: nat list)}"
 
-values [depth_limit = 5] 3
+values [dseq 5] 3
   "{xs. concatP xs ([1] :: int list)}"
 
-values [depth_limit = 5] 3
+values [dseq 5] 3
   "{xs. concatP xs ([1] :: nat list)}"
 
-values [depth_limit = 5] 3
+values [dseq 5] 3
   "{xs. concatP xs [(1::int), 2]}"
 
 code_pred (expected_modes: i => o => bool, i => i => bool) [inductify] hd .
@@ -803,11 +1049,11 @@
 code_pred [inductify] zip .
 thm zipP.equation
 
-(*code_pred [inductify] upt .*)
+code_pred [inductify] upt .
 code_pred [inductify] remdups .
 thm remdupsP.equation
-code_pred [inductify, depth_limited] remdups .
-values [depth_limit = 4] 5 "{xs. remdupsP xs [1, (2::int)]}"
+code_pred [dseq inductify] remdups .
+values [dseq 4] 5 "{xs. remdupsP xs [1, (2::int)]}"
 
 code_pred [inductify] remove1 .
 thm remove1P.equation
@@ -815,13 +1061,12 @@
 
 code_pred [inductify] removeAll .
 thm removeAllP.equation
-code_pred [inductify, depth_limited] removeAll .
+code_pred [dseq inductify] removeAll .
 
-values [depth_limit = 4] 10 "{xs. removeAllP 1 xs [(2::nat)]}"
+values [dseq 4] 10 "{xs. removeAllP 1 xs [(2::nat)]}"
 
 code_pred [inductify] distinct .
 thm distinct.equation
-
 code_pred [inductify] replicate .
 thm replicateP.equation
 values 5 "{(n, xs). replicateP n (0::int) xs}"
@@ -837,7 +1082,7 @@
 code_pred [inductify] foldr .
 code_pred [inductify] foldl .
 code_pred [inductify] filter .
-code_pred [inductify, random] filter .
+code_pred [random_dseq inductify] filter .
 
 subsection {* Context Free Grammar *}
 
@@ -852,11 +1097,11 @@
 | "\<lbrakk>v \<in> B\<^isub>1; v \<in> B\<^isub>1\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>1"
 
 code_pred [inductify] S\<^isub>1p .
-code_pred [inductify, random] S\<^isub>1p .
+code_pred [random_dseq inductify] S\<^isub>1p .
 thm S\<^isub>1p.equation
-thm S\<^isub>1p.random_equation
+thm S\<^isub>1p.random_dseq_equation
 
-values [random] 5 "{x. S\<^isub>1p x}"
+values [random_dseq 5, 5, 5] 5 "{x. S\<^isub>1p x}"
 
 inductive_set S\<^isub>2 and A\<^isub>2 and B\<^isub>2 where
   "[] \<in> S\<^isub>2"
@@ -866,12 +1111,12 @@
 | "w \<in> S\<^isub>2 \<Longrightarrow> b # w \<in> B\<^isub>2"
 | "\<lbrakk>v \<in> B\<^isub>2; v \<in> B\<^isub>2\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>2"
 
-code_pred [inductify, random] S\<^isub>2 .
-thm S\<^isub>2.random_equation
-thm A\<^isub>2.random_equation
-thm B\<^isub>2.random_equation
+code_pred [random_dseq inductify] S\<^isub>2p .
+thm S\<^isub>2p.random_dseq_equation
+thm A\<^isub>2p.random_dseq_equation
+thm B\<^isub>2p.random_dseq_equation
 
-values [random] 10 "{x. S\<^isub>2 x}"
+values [random_dseq 5, 5, 5] 10 "{x. S\<^isub>2p x}"
 
 inductive_set S\<^isub>3 and A\<^isub>3 and B\<^isub>3 where
   "[] \<in> S\<^isub>3"
@@ -881,10 +1126,10 @@
 | "w \<in> S\<^isub>3 \<Longrightarrow> b # w \<in> B\<^isub>3"
 | "\<lbrakk>v \<in> B\<^isub>3; w \<in> B\<^isub>3\<rbrakk> \<Longrightarrow> a # v @ w \<in> B\<^isub>3"
 
-code_pred [inductify] S\<^isub>3 .
-thm S\<^isub>3.equation
+code_pred [inductify] S\<^isub>3p .
+thm S\<^isub>3p.equation
 
-values 10 "{x. S\<^isub>3 x}"
+values 10 "{x. S\<^isub>3p x}"
 
 inductive_set S\<^isub>4 and A\<^isub>4 and B\<^isub>4 where
   "[] \<in> S\<^isub>4"
@@ -950,7 +1195,7 @@
 code_pred (expected_modes: i => i => o => bool, i => i => i => bool) typing .
 thm typing.equation
 
-code_pred (modes: i => o => bool as reduce') beta .
+code_pred (modes: i => i => bool,  i => o => bool as reduce') beta .
 thm beta.equation
 
 values "{x. App (Abs (Atom 0) (Var 0)) (Var 1) \<rightarrow>\<^sub>\<beta> x}"
@@ -959,18 +1204,19 @@
 
 value "reduce (App (Abs (Atom 0) (Var 0)) (Var 1))"
 
-code_pred [random] typing .
+code_pred [dseq] typing .
+code_pred [random_dseq] typing .
 
-values [random] 1 "{(\<Gamma>, t, T). \<Gamma> \<turnstile> t : T}"
+values [random_dseq 1,1,5] 10 "{(\<Gamma>, t, T). \<Gamma> \<turnstile> t : T}"
 
 subsection {* A minimal example of yet another semantics *}
 
 text {* thanks to Elke Salecker *}
 
 types
-vname = nat
-vvalue = int
-var_assign = "vname \<Rightarrow> vvalue"  --"variable assignment"
+  vname = nat
+  vvalue = int
+  var_assign = "vname \<Rightarrow> vvalue"  --"variable assignment"
 
 datatype ir_expr = 
   IrConst vvalue
@@ -981,10 +1227,10 @@
   IntVal  vvalue
 
 record  configuration =
-Env :: var_assign
+  Env :: var_assign
 
 inductive eval_var ::
-"ir_expr \<Rightarrow> configuration \<Rightarrow> val \<Rightarrow> bool"
+  "ir_expr \<Rightarrow> configuration \<Rightarrow> val \<Rightarrow> bool"
 where
   irconst: "eval_var (IrConst i) conf (IntVal i)"
 | objaddr: "\<lbrakk> Env conf n = i \<rbrakk> \<Longrightarrow> eval_var (ObjAddr n) conf (IntVal i)"

--- a/src/Pure/Isar/spec_rules.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/Pure/Isar/spec_rules.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -12,6 +12,8 @@
   type spec = rough_classification * (term list * thm list)
   val get: Proof.context -> spec list
   val get_global: theory -> spec list
+  val retrieve: Proof.context -> term -> spec list
+  val retrieve_global: theory -> term -> spec list
   val add: rough_classification -> term list * thm list -> local_theory -> local_theory
   val add_global: rough_classification -> term list * thm list -> theory -> theory
 end;
@@ -41,6 +43,9 @@
 val get = Item_Net.content o Rules.get o Context.Proof;
 val get_global = Item_Net.content o Rules.get o Context.Theory;
 
+val retrieve = Item_Net.retrieve o Rules.get o Context.Proof;
+val retrieve_global = Item_Net.retrieve o Rules.get o Context.Theory;
+
 fun add class (ts, ths) lthy =
   let
     val cts = map (Thm.cterm_of (ProofContext.theory_of lthy)) ts;

--- a/src/Tools/quickcheck.ML	Wed Jan 20 11:54:19 2010 +0100
+++ b/src/Tools/quickcheck.ML	Wed Jan 20 14:05:17 2010 +0100
@@ -7,6 +7,7 @@
 signature QUICKCHECK =
 sig
   val auto: bool Unsynchronized.ref
+  val timing : bool Unsynchronized.ref
   val test_term: Proof.context -> bool -> string option -> int -> int -> term ->
     (string * term) list option
   val add_generator: string * (Proof.context -> term -> int -> term list option) -> theory -> theory
@@ -21,6 +22,8 @@
 
 val auto = Unsynchronized.ref false;
 
+val timing = Unsynchronized.ref false;
+
 val _ =
   ProofGeneralPgip.add_preference Preferences.category_tracing
   (setmp_CRITICAL auto true (fn () =>
@@ -97,9 +100,10 @@
 fun test_term ctxt quiet generator_name size i t =
   let
     val (names, t') = prep_test_term t;
-    val testers = case generator_name
-     of NONE => if quiet then mk_testers ctxt t' else mk_testers_strict ctxt t'
-      | SOME name => [mk_tester_select name ctxt t'];
+    val testers = (*cond_timeit (!timing) "quickcheck compilation"
+      (fn () => *)(case generator_name
+       of NONE => if quiet then mk_testers ctxt t' else mk_testers_strict ctxt t'
+        | SOME name => [mk_tester_select name ctxt t']);
     fun iterate f 0 = NONE
       | iterate f j = case f () handle Match => (if quiet then ()
              else warning "Exception Match raised during quickcheck"; NONE)
@@ -113,9 +117,11 @@
       else (if quiet then () else priority ("Test data size: " ^ string_of_int k);
         case with_testers k testers
          of NONE => with_size (k + 1) | SOME q => SOME q);
-  in case with_size 1
-   of NONE => NONE
-    | SOME ts => SOME (names ~~ ts)
+  in
+    cond_timeit (!timing) "quickcheck execution"
+    (fn () => case with_size 1
+      of NONE => NONE
+      | SOME ts => SOME (names ~~ ts))
   end;
 
 fun monomorphic_term thy insts default_T =