using more conventional names for monad plus operations

--- a/src/HOL/Library/Predicate_Compile_Alternative_Defs.thy	Fri Nov 11 10:40:36 2011 +0100
+++ b/src/HOL/Library/Predicate_Compile_Alternative_Defs.thy	Fri Nov 11 12:10:49 2011 +0100
@@ -100,12 +100,12 @@
   val minus_nat = Core_Data.functional_compilation @{const_name "minus"} iio
   fun subtract_nat compfuns (_ : typ) =
     let
-      val T = Predicate_Compile_Aux.mk_predT compfuns @{typ nat}
+      val T = Predicate_Compile_Aux.mk_monadT compfuns @{typ nat}
     in
       absdummy @{typ nat} (absdummy @{typ nat}
         (Const (@{const_name "If"}, @{typ bool} --> T --> T --> T) $
           (@{term "op > :: nat => nat => bool"} $ Bound 1 $ Bound 0) $
-          Predicate_Compile_Aux.mk_bot compfuns @{typ nat} $
+          Predicate_Compile_Aux.mk_empty compfuns @{typ nat} $
           Predicate_Compile_Aux.mk_single compfuns
           (@{term "op - :: nat => nat => nat"} $ Bound 0 $ Bound 1)))
     end
@@ -118,7 +118,7 @@
   fun enumerate_nats compfuns  (_ : typ) =
     let
       val (single_const, _) = strip_comb (Predicate_Compile_Aux.mk_single compfuns @{term "0 :: nat"})
-      val T = Predicate_Compile_Aux.mk_predT compfuns @{typ nat}
+      val T = Predicate_Compile_Aux.mk_monadT compfuns @{typ nat}
     in
       absdummy @{typ nat} (absdummy @{typ nat}
         (Const (@{const_name If}, @{typ bool} --> T --> T --> T) $

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML	Fri Nov 11 10:40:36 2011 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_aux.ML	Fri Nov 11 12:10:49 2011 +0100
@@ -66,23 +66,23 @@
   val find_split_thm : theory -> term -> thm option
   (* datastructures and setup for generic compilation *)
   datatype compilation_funs = CompilationFuns of {
-    mk_predT : typ -> typ,
-    dest_predT : typ -> typ,
-    mk_bot : typ -> term,
+    mk_monadT : typ -> typ,
+    dest_monadT : typ -> typ,
+    mk_empty : typ -> term,
     mk_single : term -> term,
     mk_bind : term * term -> term,
-    mk_sup : term * term -> term,
+    mk_plus : term * term -> term,
     mk_if : term -> term,
     mk_iterate_upto : typ -> term * term * term -> term,
     mk_not : term -> term,
     mk_map : typ -> typ -> term -> term -> term
   };
-  val mk_predT : compilation_funs -> typ -> typ
-  val dest_predT : compilation_funs -> typ -> typ
-  val mk_bot : compilation_funs -> typ -> term
+  val mk_monadT : compilation_funs -> typ -> typ
+  val dest_monadT : compilation_funs -> typ -> typ
+  val mk_empty : compilation_funs -> typ -> term
   val mk_single : compilation_funs -> term -> term
   val mk_bind : compilation_funs -> term * term -> term
-  val mk_sup : compilation_funs -> term * term -> term
+  val mk_plus : compilation_funs -> term * term -> term
   val mk_if : compilation_funs -> term -> term
   val mk_iterate_upto : compilation_funs -> typ -> term * term * term -> term
   val mk_not : compilation_funs -> term -> term
@@ -699,24 +699,24 @@
 (* datastructures and setup for generic compilation *)
 
 datatype compilation_funs = CompilationFuns of {
-  mk_predT : typ -> typ,
-  dest_predT : typ -> typ,
-  mk_bot : typ -> term,
+  mk_monadT : typ -> typ,
+  dest_monadT : typ -> typ,
+  mk_empty : typ -> term,
   mk_single : term -> term,
   mk_bind : term * term -> term,
-  mk_sup : term * term -> term,
+  mk_plus : term * term -> term,
   mk_if : term -> term,
   mk_iterate_upto : typ -> term * term * term -> term,
   mk_not : term -> term,
   mk_map : typ -> typ -> term -> term -> term
 };
 
-fun mk_predT (CompilationFuns funs) = #mk_predT funs
-fun dest_predT (CompilationFuns funs) = #dest_predT funs
-fun mk_bot (CompilationFuns funs) = #mk_bot funs
+fun mk_monadT (CompilationFuns funs) = #mk_monadT funs
+fun dest_monadT (CompilationFuns funs) = #dest_monadT funs
+fun mk_empty (CompilationFuns funs) = #mk_empty funs
 fun mk_single (CompilationFuns funs) = #mk_single funs
 fun mk_bind (CompilationFuns funs) = #mk_bind funs
-fun mk_sup (CompilationFuns funs) = #mk_sup funs
+fun mk_plus (CompilationFuns funs) = #mk_plus funs
 fun mk_if (CompilationFuns funs) = #mk_if funs
 fun mk_iterate_upto (CompilationFuns funs) = #mk_iterate_upto funs
 fun mk_not (CompilationFuns funs) = #mk_not funs
@@ -729,7 +729,7 @@
     val Ts = binder_types T
     val (inTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode Ts
   in
-    inTs ---> (mk_predT compfuns (HOLogic.mk_tupleT outTs))
+    inTs ---> (mk_monadT compfuns (HOLogic.mk_tupleT outTs))
   end;
 
 (* Different options for compiler *)

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_compilations.ML	Fri Nov 11 10:40:36 2011 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_compilations.ML	Fri Nov 11 12:10:49 2011 +0100
@@ -7,16 +7,16 @@
 structure Predicate_Comp_Funs =
 struct
 
-fun mk_predT T = Type (@{type_name Predicate.pred}, [T])
+fun mk_monadT T = Type (@{type_name Predicate.pred}, [T])
 
-fun dest_predT (Type (@{type_name Predicate.pred}, [T])) = T
-  | dest_predT T = raise TYPE ("dest_predT", [T], []);
+fun dest_monadT (Type (@{type_name Predicate.pred}, [T])) = T
+  | dest_monadT T = raise TYPE ("dest_monadT", [T], []);
 
-fun mk_bot T = Const (@{const_name Orderings.bot}, mk_predT T);
+fun mk_empty T = Const (@{const_name Orderings.bot}, mk_monadT T);
 
 fun mk_single t =
   let val T = fastype_of t
-  in Const(@{const_name Predicate.single}, T --> mk_predT T) $ t end;
+  in Const(@{const_name Predicate.single}, T --> mk_monadT T) $ t end;
 
 fun mk_bind (x, f) =
   let val T as Type ("fun", [_, U]) = fastype_of f
@@ -24,42 +24,42 @@
     Const (@{const_name Predicate.bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name sup};
+val mk_plus = HOLogic.mk_binop @{const_name sup};
 
 fun mk_if cond = Const (@{const_name Predicate.if_pred},
-  HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;
+  HOLogic.boolT --> mk_monadT HOLogic.unitT) $ cond;
 
 fun mk_iterate_upto T (f, from, to) =
   list_comb (Const (@{const_name Code_Numeral.iterate_upto},
-      [@{typ code_numeral} --> T, @{typ code_numeral}, @{typ code_numeral}] ---> mk_predT T),
+      [@{typ code_numeral} --> T, @{typ code_numeral}, @{typ code_numeral}] ---> mk_monadT T),
     [f, from, to])
 
 fun mk_not t =
   let
-    val T = mk_predT HOLogic.unitT
+    val T = mk_monadT HOLogic.unitT
   in Const (@{const_name Predicate.not_pred}, T --> T) $ t end
 
 fun mk_Enum f =
   let val T as Type ("fun", [T', _]) = fastype_of f
   in
-    Const (@{const_name Predicate.Pred}, T --> mk_predT T') $ f    
+    Const (@{const_name Predicate.Pred}, T --> mk_monadT T') $ f    
   end;
 
 fun mk_Eval (f, x) =
   let
-    val T = dest_predT (fastype_of f)
+    val T = dest_monadT (fastype_of f)
   in
-    Const (@{const_name Predicate.eval}, mk_predT T --> T --> HOLogic.boolT) $ f $ x
+    Const (@{const_name Predicate.eval}, mk_monadT 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;
+  (T1 --> T2) --> mk_monadT T1 --> mk_monadT T2) $ tf $ tp;
 
 val compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,
-    mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_monadT, dest_monadT = dest_monadT, mk_empty = mk_empty,
+    mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map};
 
 end;
@@ -67,16 +67,16 @@
 structure CPS_Comp_Funs =
 struct
 
-fun mk_predT T = (T --> @{typ "Code_Evaluation.term list option"}) --> @{typ "Code_Evaluation.term list option"}
+fun mk_monadT T = (T --> @{typ "Code_Evaluation.term list option"}) --> @{typ "Code_Evaluation.term list option"}
 
-fun dest_predT (Type ("fun", [Type ("fun", [T, @{typ "term list option"}]), @{typ "term list option"}])) = T
-  | dest_predT T = raise TYPE ("dest_predT", [T], []);
+fun dest_monadT (Type ("fun", [Type ("fun", [T, @{typ "term list option"}]), @{typ "term list option"}])) = T
+  | dest_monadT T = raise TYPE ("dest_monadT", [T], []);
 
-fun mk_bot T = Const (@{const_name Quickcheck_Exhaustive.cps_empty}, mk_predT T);
+fun mk_empty T = Const (@{const_name Quickcheck_Exhaustive.cps_empty}, mk_monadT T);
 
 fun mk_single t =
   let val T = fastype_of t
-  in Const(@{const_name Quickcheck_Exhaustive.cps_single}, T --> mk_predT T) $ t end;
+  in Const(@{const_name Quickcheck_Exhaustive.cps_single}, T --> mk_monadT T) $ t end;
 
 fun mk_bind (x, f) =
   let val T as Type ("fun", [_, U]) = fastype_of f
@@ -84,16 +84,16 @@
     Const (@{const_name Quickcheck_Exhaustive.cps_bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name Quickcheck_Exhaustive.cps_plus};
+val mk_plus = HOLogic.mk_binop @{const_name Quickcheck_Exhaustive.cps_plus};
 
 fun mk_if cond = Const (@{const_name Quickcheck_Exhaustive.cps_if},
-  HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;
+  HOLogic.boolT --> mk_monadT HOLogic.unitT) $ cond;
 
 fun mk_iterate_upto T (f, from, to) = error "not implemented yet"
 
 fun mk_not t =
   let
-    val T = mk_predT HOLogic.unitT
+    val T = mk_monadT HOLogic.unitT
   in Const (@{const_name Quickcheck_Exhaustive.cps_not}, T --> T) $ t end
 
 fun mk_Enum f = error "not implemented"
@@ -105,8 +105,8 @@
 fun mk_map T1 T2 tf tp = error "not implemented"
 
 val compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,
-    mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_monadT, dest_monadT = dest_monadT, mk_empty = mk_empty,
+    mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map};
 
 end;
@@ -114,16 +114,16 @@
 structure Pos_Bounded_CPS_Comp_Funs =
 struct
 
-fun mk_predT T = (T --> @{typ "Code_Evaluation.term list option"}) --> @{typ "code_numeral => Code_Evaluation.term list option"}
+fun mk_monadT T = (T --> @{typ "Code_Evaluation.term list option"}) --> @{typ "code_numeral => Code_Evaluation.term list option"}
 
-fun dest_predT (Type ("fun", [Type ("fun", [T, @{typ "term list option"}]), @{typ "code_numeral => term list option"}])) = T
-  | dest_predT T = raise TYPE ("dest_predT", [T], []);
+fun dest_monadT (Type ("fun", [Type ("fun", [T, @{typ "term list option"}]), @{typ "code_numeral => term list option"}])) = T
+  | dest_monadT T = raise TYPE ("dest_monadT", [T], []);
 
-fun mk_bot T = Const (@{const_name Quickcheck_Exhaustive.pos_bound_cps_empty}, mk_predT T);
+fun mk_empty T = Const (@{const_name Quickcheck_Exhaustive.pos_bound_cps_empty}, mk_monadT T);
 
 fun mk_single t =
   let val T = fastype_of t
-  in Const(@{const_name Quickcheck_Exhaustive.pos_bound_cps_single}, T --> mk_predT T) $ t end;
+  in Const(@{const_name Quickcheck_Exhaustive.pos_bound_cps_single}, T --> mk_monadT T) $ t end;
 
 fun mk_bind (x, f) =
   let val T as Type ("fun", [_, U]) = fastype_of f
@@ -131,10 +131,10 @@
     Const (@{const_name Quickcheck_Exhaustive.pos_bound_cps_bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name Quickcheck_Exhaustive.pos_bound_cps_plus};
+val mk_plus = HOLogic.mk_binop @{const_name Quickcheck_Exhaustive.pos_bound_cps_plus};
 
 fun mk_if cond = Const (@{const_name Quickcheck_Exhaustive.pos_bound_cps_if},
-  HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;
+  HOLogic.boolT --> mk_monadT HOLogic.unitT) $ cond;
 
 fun mk_iterate_upto T (f, from, to) = error "not implemented yet"
 
@@ -143,7 +143,7 @@
     val nT = @{typ "(unit Quickcheck_Exhaustive.unknown =>
       Code_Evaluation.term list Quickcheck_Exhaustive.three_valued) => code_numeral =>
       Code_Evaluation.term list Quickcheck_Exhaustive.three_valued"}
-    val T = mk_predT HOLogic.unitT
+    val T = mk_monadT HOLogic.unitT
   in Const (@{const_name Quickcheck_Exhaustive.pos_bound_cps_not}, nT --> T) $ t end
 
 fun mk_Enum f = error "not implemented"
@@ -155,8 +155,8 @@
 fun mk_map T1 T2 tf tp = error "not implemented"
 
 val compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,
-    mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_monadT, dest_monadT = dest_monadT, mk_empty = mk_empty,
+    mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map};
 
 end;
@@ -164,21 +164,21 @@
 structure Neg_Bounded_CPS_Comp_Funs =
 struct
 
-fun mk_predT T =
+fun mk_monadT T =
   (Type (@{type_name "Quickcheck_Exhaustive.unknown"}, [T])
     --> @{typ "Code_Evaluation.term list Quickcheck_Exhaustive.three_valued"})
     --> @{typ "code_numeral => Code_Evaluation.term list Quickcheck_Exhaustive.three_valued"}
 
-fun dest_predT (Type ("fun", [Type ("fun", [Type (@{type_name "Quickcheck_Exhaustive.unknown"}, [T]),
+fun dest_monadT (Type ("fun", [Type ("fun", [Type (@{type_name "Quickcheck_Exhaustive.unknown"}, [T]),
     @{typ "term list Quickcheck_Exhaustive.three_valued"}]),
     @{typ "code_numeral => term list Quickcheck_Exhaustive.three_valued"}])) = T
-  | dest_predT T = raise TYPE ("dest_predT", [T], []);
+  | dest_monadT T = raise TYPE ("dest_monadT", [T], []);
 
-fun mk_bot T = Const (@{const_name Quickcheck_Exhaustive.neg_bound_cps_empty}, mk_predT T);
+fun mk_empty T = Const (@{const_name Quickcheck_Exhaustive.neg_bound_cps_empty}, mk_monadT T);
 
 fun mk_single t =
   let val T = fastype_of t
-  in Const(@{const_name Quickcheck_Exhaustive.neg_bound_cps_single}, T --> mk_predT T) $ t end;
+  in Const(@{const_name Quickcheck_Exhaustive.neg_bound_cps_single}, T --> mk_monadT T) $ t end;
 
 fun mk_bind (x, f) =
   let val T as Type ("fun", [_, U]) = fastype_of f
@@ -186,16 +186,16 @@
     Const (@{const_name Quickcheck_Exhaustive.neg_bound_cps_bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name Quickcheck_Exhaustive.neg_bound_cps_plus};
+val mk_plus = HOLogic.mk_binop @{const_name Quickcheck_Exhaustive.neg_bound_cps_plus};
 
 fun mk_if cond = Const (@{const_name Quickcheck_Exhaustive.neg_bound_cps_if},
-  HOLogic.boolT --> mk_predT HOLogic.unitT) $ cond;
+  HOLogic.boolT --> mk_monadT HOLogic.unitT) $ cond;
 
 fun mk_iterate_upto T (f, from, to) = error "not implemented"
 
 fun mk_not t =
   let
-    val T = mk_predT HOLogic.unitT
+    val T = mk_monadT HOLogic.unitT
     val pT = @{typ "(unit => Code_Evaluation.term list option) => code_numeral => Code_Evaluation.term list option"}
   in Const (@{const_name Quickcheck_Exhaustive.neg_bound_cps_not}, pT --> T) $ t end
 
@@ -208,8 +208,8 @@
 fun mk_map T1 T2 tf tp = error "not implemented"
 
 val compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_predT, dest_predT = dest_predT, mk_bot = mk_bot,
-    mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_monadT, dest_monadT = dest_monadT, mk_empty = mk_empty,
+    mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map};
 
 end;
@@ -219,13 +219,13 @@
 struct
 
 fun mk_randompredT T =
-  @{typ Random.seed} --> HOLogic.mk_prodT (Predicate_Comp_Funs.mk_predT T, @{typ Random.seed})
+  @{typ Random.seed} --> HOLogic.mk_prodT (Predicate_Comp_Funs.mk_monadT T, @{typ Random.seed})
 
 fun dest_randompredT (Type ("fun", [@{typ Random.seed}, Type (@{type_name Product_Type.prod},
   [Type (@{type_name "Predicate.pred"}, [T]), @{typ Random.seed}])])) = T
   | dest_randompredT T = raise TYPE ("dest_randompredT", [T], []);
 
-fun mk_bot T = Const(@{const_name Quickcheck.empty}, mk_randompredT T)
+fun mk_empty T = Const(@{const_name Quickcheck.empty}, mk_randompredT T)
 
 fun mk_single t =
   let               
@@ -241,7 +241,7 @@
     Const (@{const_name Quickcheck.bind}, fastype_of x --> T --> U) $ x $ f
   end
 
-val mk_sup = HOLogic.mk_binop @{const_name Quickcheck.union}
+val mk_plus = HOLogic.mk_binop @{const_name Quickcheck.union}
 
 fun mk_if cond = Const (@{const_name Quickcheck.if_randompred},
   HOLogic.boolT --> mk_randompredT HOLogic.unitT) $ cond;
@@ -260,8 +260,8 @@
   (T1 --> T2) --> mk_randompredT T1 --> mk_randompredT T2) $ tf $ tp
 
 val compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_randompredT, dest_predT = dest_randompredT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_randompredT, dest_monadT = dest_randompredT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map};
 
 end;
@@ -276,7 +276,7 @@
   Type (@{type_name Option.option}, [Type (@{type_name Lazy_Sequence.lazy_sequence}, [T])])])])) = T
   | dest_dseqT T = raise TYPE ("dest_dseqT", [T], []);
 
-fun mk_bot T = Const (@{const_name DSequence.empty}, mk_dseqT T);
+fun mk_empty T = Const (@{const_name DSequence.empty}, mk_dseqT T);
 
 fun mk_single t =
   let val T = fastype_of t
@@ -288,7 +288,7 @@
     Const (@{const_name DSequence.bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name DSequence.union};
+val mk_plus = HOLogic.mk_binop @{const_name DSequence.union};
 
 fun mk_if cond = Const (@{const_name DSequence.if_seq},
   HOLogic.boolT --> mk_dseqT HOLogic.unitT) $ cond;
@@ -302,8 +302,8 @@
   (T1 --> T2) --> mk_dseqT T1 --> mk_dseqT T2) $ tf $ tp
 
 val compfuns = Predicate_Compile_Aux.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_monadT = mk_dseqT, dest_monadT = dest_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 end;
@@ -318,7 +318,7 @@
     Type (@{type_name Lazy_Sequence.lazy_sequence}, [T])])) = T
   | dest_pos_dseqT T = raise TYPE ("dest_pos_dseqT", [T], []);
 
-fun mk_bot T = Const (@{const_name New_DSequence.pos_empty}, mk_pos_dseqT T);
+fun mk_empty T = Const (@{const_name New_DSequence.pos_empty}, mk_pos_dseqT T);
 
 fun mk_single t =
   let
@@ -339,7 +339,7 @@
     Const (@{const_name New_DSequence.pos_decr_bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name New_DSequence.pos_union};
+val mk_plus = HOLogic.mk_binop @{const_name New_DSequence.pos_union};
 
 fun mk_if cond = Const (@{const_name New_DSequence.pos_if_seq},
   HOLogic.boolT --> mk_pos_dseqT HOLogic.unitT) $ cond;
@@ -358,13 +358,13 @@
   (T1 --> T2) --> mk_pos_dseqT T1 --> mk_pos_dseqT T2) $ tf $ tp
 
 val depth_limited_compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_pos_dseqT, dest_predT = dest_pos_dseqT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_decr_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_pos_dseqT, dest_monadT = dest_pos_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_decr_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 val depth_unlimited_compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_pos_dseqT, dest_predT = dest_pos_dseqT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_pos_dseqT, dest_monadT = dest_pos_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 end;
@@ -379,7 +379,7 @@
     Type (@{type_name Lazy_Sequence.lazy_sequence}, [Type (@{type_name Option.option}, [T])])])) = T
   | dest_neg_dseqT T = raise TYPE ("dest_neg_dseqT", [T], []);
 
-fun mk_bot T = Const (@{const_name New_DSequence.neg_empty}, mk_neg_dseqT T);
+fun mk_empty T = Const (@{const_name New_DSequence.neg_empty}, mk_neg_dseqT T);
 
 fun mk_single t =
   let
@@ -400,7 +400,7 @@
     Const (@{const_name New_DSequence.neg_decr_bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name New_DSequence.neg_union};
+val mk_plus = HOLogic.mk_binop @{const_name New_DSequence.neg_union};
 
 fun mk_if cond = Const (@{const_name New_DSequence.neg_if_seq},
   HOLogic.boolT --> mk_neg_dseqT HOLogic.unitT) $ cond;
@@ -419,13 +419,13 @@
   (T1 --> T2) --> mk_neg_dseqT T1 --> mk_neg_dseqT T2) $ tf $ tp
 
 val depth_limited_compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_neg_dseqT, dest_predT = dest_neg_dseqT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_decr_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_neg_dseqT, dest_monadT = dest_neg_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_decr_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 val depth_unlimited_compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_neg_dseqT, dest_predT = dest_neg_dseqT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_neg_dseqT, dest_monadT = dest_neg_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 end;
@@ -442,7 +442,7 @@
     Type (@{type_name Lazy_Sequence.lazy_sequence}, [T])])])])])) = T
   | dest_pos_random_dseqT T = raise TYPE ("dest_random_dseqT", [T], []);
 
-fun mk_bot T = Const (@{const_name New_Random_Sequence.pos_empty}, mk_pos_random_dseqT T);
+fun mk_empty T = Const (@{const_name New_Random_Sequence.pos_empty}, mk_pos_random_dseqT T);
 
 fun mk_single t =
   let
@@ -463,7 +463,7 @@
     Const (@{const_name New_Random_Sequence.pos_decr_bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name New_Random_Sequence.pos_union};
+val mk_plus = HOLogic.mk_binop @{const_name New_Random_Sequence.pos_union};
 
 fun mk_if cond = Const (@{const_name New_Random_Sequence.pos_if_random_dseq},
   HOLogic.boolT --> mk_pos_random_dseqT HOLogic.unitT) $ cond;
@@ -487,13 +487,13 @@
   (T1 --> T2) --> mk_pos_random_dseqT T1 --> mk_pos_random_dseqT T2) $ tf $ tp
 
 val depth_limited_compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_pos_random_dseqT, dest_predT = dest_pos_random_dseqT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_decr_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_pos_random_dseqT, dest_monadT = dest_pos_random_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_decr_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 val depth_unlimited_compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_pos_random_dseqT, dest_predT = dest_pos_random_dseqT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_pos_random_dseqT, dest_monadT = dest_pos_random_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 end;
 
@@ -511,7 +511,7 @@
         [Type (@{type_name Option.option}, [T])])])])])])) = T
   | dest_neg_random_dseqT T = raise TYPE ("dest_random_dseqT", [T], []);
 
-fun mk_bot T = Const (@{const_name New_Random_Sequence.neg_empty}, mk_neg_random_dseqT T);
+fun mk_empty T = Const (@{const_name New_Random_Sequence.neg_empty}, mk_neg_random_dseqT T);
 
 fun mk_single t =
   let
@@ -532,7 +532,7 @@
     Const (@{const_name New_Random_Sequence.neg_decr_bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name New_Random_Sequence.neg_union};
+val mk_plus = HOLogic.mk_binop @{const_name New_Random_Sequence.neg_union};
 
 fun mk_if cond = Const (@{const_name New_Random_Sequence.neg_if_random_dseq},
   HOLogic.boolT --> mk_neg_random_dseqT HOLogic.unitT) $ cond;
@@ -554,13 +554,13 @@
   (T1 --> T2) --> mk_neg_random_dseqT T1 --> mk_neg_random_dseqT T2) $ tf $ tp
 
 val depth_limited_compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_neg_random_dseqT, dest_predT = dest_neg_random_dseqT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_decr_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_neg_random_dseqT, dest_monadT = dest_neg_random_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_decr_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 val depth_unlimited_compfuns = Predicate_Compile_Aux.CompilationFuns
-    {mk_predT = mk_neg_random_dseqT, dest_predT = dest_neg_random_dseqT,
-    mk_bot = mk_bot, mk_single = mk_single, mk_bind = mk_bind, mk_sup = mk_sup, mk_if = mk_if,
+    {mk_monadT = mk_neg_random_dseqT, dest_monadT = dest_neg_random_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 end;
@@ -577,7 +577,7 @@
   Type (@{type_name Product_Type.prod}, [T, @{typ Random.seed}])])])])) = DSequence_CompFuns.dest_dseqT T
   | dest_random_dseqT T = raise TYPE ("dest_random_dseqT", [T], []);
 
-fun mk_bot T = Const (@{const_name Random_Sequence.empty}, mk_random_dseqT T);
+fun mk_empty T = Const (@{const_name Random_Sequence.empty}, mk_random_dseqT T);
 
 fun mk_single t =
   let
@@ -591,7 +591,7 @@
     Const (@{const_name Random_Sequence.bind}, fastype_of x --> T --> U) $ x $ f
   end;
 
-val mk_sup = HOLogic.mk_binop @{const_name Random_Sequence.union};
+val mk_plus = HOLogic.mk_binop @{const_name Random_Sequence.union};
 
 fun mk_if cond = Const (@{const_name Random_Sequence.if_random_dseq},
   HOLogic.boolT --> mk_random_dseqT HOLogic.unitT) $ cond;
@@ -607,8 +607,8 @@
   (T1 --> T2) --> mk_random_dseqT T1 --> mk_random_dseqT T2) $ tf $ tp
 
 val compfuns = Predicate_Compile_Aux.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_monadT = mk_random_dseqT, dest_monadT = dest_random_dseqT,
+    mk_empty = mk_empty, mk_single = mk_single, mk_bind = mk_bind, mk_plus = mk_plus, mk_if = mk_if,
     mk_iterate_upto = mk_iterate_upto, mk_not = mk_not, mk_map = mk_map}
 
 end;

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML	Fri Nov 11 10:40:36 2011 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_core.ML	Fri Nov 11 12:10:49 2011 +0100
@@ -312,11 +312,11 @@
     let
       val [depth] = additional_arguments
       val (_, Ts) = split_modeT mode (binder_types T)
-      val T' = mk_predT compfuns (HOLogic.mk_tupleT Ts)
+      val T' = mk_monadT compfuns (HOLogic.mk_tupleT Ts)
       val if_const = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
     in
       if_const $ HOLogic.mk_eq (depth, @{term "0 :: code_numeral"})
-        $ mk_bot compfuns (dest_predT compfuns T')
+        $ mk_empty compfuns (dest_monadT compfuns T')
         $ compilation
     end,
   transform_additional_arguments =
@@ -337,7 +337,7 @@
   mk_random = (fn T => fn additional_arguments =>
   list_comb (Const(@{const_name Quickcheck.iter},
   [@{typ code_numeral}, @{typ code_numeral}, @{typ Random.seed}] ---> 
-    Predicate_Comp_Funs.mk_predT T), additional_arguments)),
+    Predicate_Comp_Funs.mk_monadT T), additional_arguments)),
   modify_funT = (fn T =>
     let
       val (Ts, U) = strip_type T
@@ -363,7 +363,7 @@
   mk_random = (fn T => fn additional_arguments =>
   list_comb (Const(@{const_name Quickcheck.iter},
   [@{typ code_numeral}, @{typ code_numeral}, @{typ Random.seed}] ---> 
-    Predicate_Comp_Funs.mk_predT T), tl additional_arguments)),
+    Predicate_Comp_Funs.mk_monadT T), tl additional_arguments)),
   modify_funT = (fn T =>
     let
       val (Ts, U) = strip_type T
@@ -383,11 +383,11 @@
       val depth = hd (additional_arguments)
       val (_, Ts) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE))
         mode (binder_types T)
-      val T' = mk_predT compfuns (HOLogic.mk_tupleT Ts)
+      val T' = mk_monadT compfuns (HOLogic.mk_tupleT Ts)
       val if_const = Const (@{const_name "If"}, @{typ bool} --> T' --> T' --> T')
     in
       if_const $ HOLogic.mk_eq (depth, @{term "0 :: code_numeral"})
-        $ mk_bot compfuns (dest_predT compfuns T')
+        $ mk_empty compfuns (dest_monadT compfuns T')
         $ compilation
     end,
   transform_additional_arguments =
@@ -658,7 +658,7 @@
     val name' = singleton (Name.variant_list (name :: names)) "y";
     val T = HOLogic.mk_tupleT (map fastype_of out_ts);
     val U = fastype_of success_t;
-    val U' = dest_predT compfuns U;
+    val U' = dest_monadT compfuns U;
     val v = Free (name, T);
     val v' = Free (name', T);
   in
@@ -667,8 +667,8 @@
         if null eqs'' then success_t
         else Const (@{const_name HOL.If}, HOLogic.boolT --> U --> U --> U) $
           foldr1 HOLogic.mk_conj eqs'' $ success_t $
-            mk_bot compfuns U'),
-       (v', mk_bot compfuns U')])
+            mk_empty compfuns U'),
+       (v', mk_empty compfuns U')])
   end;
 
 fun string_of_tderiv ctxt (t, deriv) = 
@@ -928,7 +928,7 @@
               compile_clause compilation_modifiers ctxt all_vs param_modes additional_arguments
                 inp (in_ts', out_ts') moded_ps'
             end
-        in SOME (foldr1 (mk_sup compfuns) (map compile_clause' moded_clauses)) end
+        in SOME (foldr1 (mk_plus compfuns) (map compile_clause' moded_clauses)) end
     | compile_switch_tree all_vs ctxt_eqs (Node ((position, switched_clauses), left_clauses)) =
       let
         val (i, is) = argument_position_of mode position
@@ -943,18 +943,18 @@
             val args = map2 (curry Free) argnames Ts
             val pattern = list_comb (Const (c, T), args)
             val ctxt_eqs' = (inp_var, pattern) :: ctxt_eqs
-            val compilation = the_default (mk_bot compfuns (HOLogic.mk_tupleT outTs))
+            val compilation = the_default (mk_empty compfuns (HOLogic.mk_tupleT outTs))
               (compile_switch_tree (argnames @ x :: all_vs) ctxt_eqs' switched)
         in
           (pattern, compilation)
         end
         val switch = Datatype.make_case ctxt Datatype_Case.Quiet [] inp_var
           ((map compile_single_case switched_clauses) @
-            [(xt, mk_bot compfuns (HOLogic.mk_tupleT outTs))])
+            [(xt, mk_empty compfuns (HOLogic.mk_tupleT outTs))])
       in
         case compile_switch_tree all_vs ctxt_eqs left_clauses of
           NONE => SOME switch
-        | SOME left_comp => SOME (mk_sup compfuns (switch, left_comp))
+        | SOME left_comp => SOME (mk_plus compfuns (switch, left_comp))
       end
   in
     compile_switch_tree all_vs [] switch_tree
@@ -978,11 +978,11 @@
       (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)
+      is_some (try (dest_monadT compfuns) T) orelse is_param_type T'
+      | is_param_type T = is_some (try (dest_monadT compfuns) T)
     val (inpTs, outTs) = split_map_modeT (fn m => fn T => (SOME (funT_of compfuns m T), NONE)) mode
       (binder_types T)
-    val predT = mk_predT compfuns (HOLogic.mk_tupleT outTs)
+    val predT = mk_monadT 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) =>
@@ -998,7 +998,7 @@
     val param_modes = param_vs ~~ ho_arg_modes_of mode
     val compilation =
       if detect_switches options then
-        the_default (mk_bot compfuns (HOLogic.mk_tupleT outTs))
+        the_default (mk_empty compfuns (HOLogic.mk_tupleT outTs))
           (compile_switch compilation_modifiers ctxt all_vs param_modes additional_arguments mode
             in_ts' outTs (mk_switch_tree ctxt mode moded_cls))
       else
@@ -1010,9 +1010,9 @@
         in
           Comp_Mod.wrap_compilation compilation_modifiers compfuns s T mode additional_arguments
             (if null cl_ts then
-              mk_bot compfuns (HOLogic.mk_tupleT outTs)
+              mk_empty compfuns (HOLogic.mk_tupleT outTs)
             else
-              foldr1 (mk_sup compfuns) cl_ts)
+              foldr1 (mk_plus compfuns) cl_ts)
         end
     val fun_const =
       Const (function_name_of (Comp_Mod.compilation compilation_modifiers)
@@ -1341,7 +1341,7 @@
               (map (fn i => "x" ^ string_of_int i) (1 upto length Ts))
             val args = map2 (curry Free) arg_names Ts
             val predfun = Const (function_name_of Pred ctxt predname full_mode,
-              Ts ---> Predicate_Comp_Funs.mk_predT @{typ unit})
+              Ts ---> Predicate_Comp_Funs.mk_monadT @{typ unit})
             val rhs = @{term Predicate.holds} $ (list_comb (predfun, args))
             val eq_term = HOLogic.mk_Trueprop
               (HOLogic.mk_eq (list_comb (Const (predname, T), args), rhs))
@@ -1833,7 +1833,7 @@
         val (_, outargs) = split_mode (head_mode_of deriv) all_args
         val t_pred = compile_expr comp_modifiers ctxt
           (body, deriv) [] additional_arguments;
-        val T_pred = dest_predT compfuns (fastype_of t_pred)
+        val T_pred = dest_monadT compfuns (fastype_of t_pred)
         val arrange = HOLogic.tupled_lambda (HOLogic.mk_tuple outargs) output
       in
         if null outargs then t_pred else mk_map compfuns T_pred T_compr arrange t_pred
@@ -1876,7 +1876,7 @@
       | New_Pos_Random_DSeq => []
       | Pos_Generator_DSeq => []
     val t = analyze_compr ctxt (comp_modifiers, additional_arguments) param_user_modes options t_compr;
-    val T = dest_predT compfuns (fastype_of t);
+    val T = dest_monadT compfuns (fastype_of t);
     val t' =
       if stats andalso compilation = New_Pos_Random_DSeq then
         mk_map compfuns T (HOLogic.mk_prodT (HOLogic.termT, @{typ code_numeral}))

--- a/src/HOL/Tools/Predicate_Compile/predicate_compile_quickcheck.ML	Fri Nov 11 10:40:36 2011 +0100
+++ b/src/HOL/Tools/Predicate_Compile/predicate_compile_quickcheck.ML	Fri Nov 11 12:10:49 2011 +0100
@@ -186,23 +186,23 @@
   set_no_higher_order_predicate (!no_higher_order_predicate)
     (if !debug then debug_options else options)
 
-val mk_predT = Predicate_Compile_Aux.mk_predT Predicate_Comp_Funs.compfuns
+val mk_predT = Predicate_Compile_Aux.mk_monadT Predicate_Comp_Funs.compfuns
 val mk_return' = Predicate_Compile_Aux.mk_single Predicate_Comp_Funs.compfuns
 val mk_bind' = Predicate_Compile_Aux.mk_bind Predicate_Comp_Funs.compfuns
 
-val mk_randompredT = Predicate_Compile_Aux.mk_predT RandomPredCompFuns.compfuns
+val mk_randompredT = Predicate_Compile_Aux.mk_monadT RandomPredCompFuns.compfuns
 val mk_return = Predicate_Compile_Aux.mk_single RandomPredCompFuns.compfuns
 val mk_bind = Predicate_Compile_Aux.mk_bind RandomPredCompFuns.compfuns
 
 val mk_new_randompredT =
-  Predicate_Compile_Aux.mk_predT New_Pos_Random_Sequence_CompFuns.depth_unlimited_compfuns
+  Predicate_Compile_Aux.mk_monadT New_Pos_Random_Sequence_CompFuns.depth_unlimited_compfuns
 val mk_new_return =
   Predicate_Compile_Aux.mk_single New_Pos_Random_Sequence_CompFuns.depth_unlimited_compfuns
 val mk_new_bind =
   Predicate_Compile_Aux.mk_bind New_Pos_Random_Sequence_CompFuns.depth_unlimited_compfuns
 
 val mk_new_dseqT =
-  Predicate_Compile_Aux.mk_predT New_Pos_DSequence_CompFuns.depth_unlimited_compfuns
+  Predicate_Compile_Aux.mk_monadT New_Pos_DSequence_CompFuns.depth_unlimited_compfuns
 val mk_gen_return =
   Predicate_Compile_Aux.mk_single New_Pos_DSequence_CompFuns.depth_unlimited_compfuns
 val mk_gen_bind =
@@ -210,7 +210,7 @@
   
 
 val mk_cpsT =
-  Predicate_Compile_Aux.mk_predT Pos_Bounded_CPS_Comp_Funs.compfuns
+  Predicate_Compile_Aux.mk_monadT Pos_Bounded_CPS_Comp_Funs.compfuns
 val mk_cps_return =
   Predicate_Compile_Aux.mk_single Pos_Bounded_CPS_Comp_Funs.compfuns
 val mk_cps_bind =