src/HOL/Tools/Quickcheck/exhaustive_generators.ML

 Exhaustive generators for various types.
 *)
 
 signature EXHAUSTIVE_GENERATORS =
 sig
-  val compile_generator_expr:
-    Proof.context -> (term * term list) list -> bool -> int list -> (bool * term list) option * Quickcheck.report option
+  val compile_generator_expr: Proof.context -> (term * term list) list -> bool -> int list ->
+    (bool * term list) option * Quickcheck.report option
   val compile_generator_exprs: Proof.context -> term list -> (int -> term list option) list
   val compile_validator_exprs: Proof.context -> term list -> (int -> bool) list
-  val put_counterexample: (unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> (bool * term list) option)
-    -> Proof.context -> Proof.context
-  val put_counterexample_batch: (unit -> (Code_Numeral.natural -> term list option) list)
-    -> Proof.context -> Proof.context
-  val put_validator_batch: (unit -> (Code_Numeral.natural -> bool) list) -> Proof.context -> Proof.context
+  val put_counterexample:
+    (unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> (bool * term list) option) ->
+      Proof.context -> Proof.context
+  val put_counterexample_batch: (unit -> (Code_Numeral.natural -> term list option) list) ->
+    Proof.context -> Proof.context
+  val put_validator_batch: (unit -> (Code_Numeral.natural -> bool) list) ->
+    Proof.context -> Proof.context
   exception Counterexample of term list
   val smart_quantifier : bool Config.T
   val optimise_equality : bool Config.T
   val quickcheck_pretty : bool Config.T
   val setup_exhaustive_datatype_interpretation : theory -> theory
   val setup_bounded_forall_datatype_interpretation : theory -> theory
-  
   val instantiate_full_exhaustive_datatype : Old_Datatype_Aux.config -> Old_Datatype_Aux.descr ->
-    (string * sort) list -> string list -> string -> string list * string list -> typ list * typ list -> theory -> theory
+    (string * sort) list -> string list -> string -> string list * string list ->
+    typ list * typ list -> theory -> theory
   val instantiate_exhaustive_datatype : Old_Datatype_Aux.config -> Old_Datatype_Aux.descr ->
-    (string * sort) list -> string list -> string -> string list * string list -> typ list * typ list -> theory -> theory
-
-end;
+    (string * sort) list -> string list -> string -> string list * string list ->
+    typ list * typ list -> theory -> theory
+end
 
 structure Exhaustive_Generators : EXHAUSTIVE_GENERATORS =
 struct
 
 (* basics *)

 
 val fast = Attrib.setup_config_bool @{binding quickcheck_fast} (K false)
 val bounded_forall = Attrib.setup_config_bool @{binding quickcheck_bounded_forall} (K false)
 val full_support = Attrib.setup_config_bool @{binding quickcheck_full_support} (K true)
 val quickcheck_pretty = Attrib.setup_config_bool @{binding quickcheck_pretty} (K true)
- 
+
 
 (** abstract syntax **)
 
-fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => Code_Evaluation.term"});
+fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit \<Rightarrow> Code_Evaluation.term"})
 
 val size = @{term "i :: natural"}
 val size_pred = @{term "(i :: natural) - 1"}
 val size_ge_zero = @{term "(i :: natural) > 0"}
 
 fun mk_none_continuation (x, y) =
-  let
-    val (T as Type(@{type_name "option"}, _)) = fastype_of x
-  in
-    Const (@{const_name "Quickcheck_Exhaustive.orelse"}, T --> T --> T) $ x $ y
-  end
+  let val (T as Type (@{type_name option}, _)) = fastype_of x
+  in Const (@{const_name Quickcheck_Exhaustive.orelse}, T --> T --> T) $ x $ y end
 
 fun mk_if (b, t, e) =
-  let
-    val T = fastype_of t
-  in Const (@{const_name "HOL.If"}, @{typ bool} --> T --> T --> T) $ b $ t $ e end
+  let val T = fastype_of t
+  in Const (@{const_name If}, @{typ bool} --> T --> T --> T) $ b $ t $ e end
+
 
 (* handling inductive datatypes *)
 
 (** constructing generator instances **)
 
-exception FUNCTION_TYPE;
+exception FUNCTION_TYPE
 
 exception Counterexample of term list
 
-val resultT =  @{typ "(bool * term list) option"};
-
-val exhaustiveN = "exhaustive";
-val full_exhaustiveN = "full_exhaustive";
-val bounded_forallN = "bounded_forall";
-
-fun fast_exhaustiveT T = (T --> @{typ unit})
-  --> @{typ natural} --> @{typ unit}
+val resultT =  @{typ "(bool * term list) option"}
+
+val exhaustiveN = "exhaustive"
+val full_exhaustiveN = "full_exhaustive"
+val bounded_forallN = "bounded_forall"
+
+fun fast_exhaustiveT T = (T --> @{typ unit}) --> @{typ natural} --> @{typ unit}
 
 fun exhaustiveT T = (T --> resultT) --> @{typ natural} --> resultT
 
 fun bounded_forallT T = (T --> @{typ bool}) --> @{typ natural} --> @{typ bool}
 

         { atyp = mk_call, dtyp = mk_aux_call }
       |> (map o apfst) Type
       |> map (fn (T, cs) => map (mk_consexpr T) cs)
       |> map mk_rhs
     val lhss = map2 (fn t => fn T => t $ test_function T $ size) exhaustives Ts
-  in
-    map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss)
-  end
+  in map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss) end
 
 fun gen_mk_call c T =  (T, fn t => c T $ absdummy T t $ size_pred)
 
 fun gen_mk_aux_call functerms fTs (k, _) (tyco, Ts) =
   let
     val T = Type (tyco, Ts)
     val _ = if not (null fTs) then raise FUNCTION_TYPE else ()
-  in
-   (T, fn t => nth functerms k $ absdummy T t $ size_pred)
-  end
+  in (T, fn t => nth functerms k $ absdummy T t $ size_pred) end
 
 fun gen_mk_consexpr test_function simpleT (c, xs) =
   let
     val (Ts, fns) = split_list xs
     val constr = Const (c, Ts ---> simpleT)

 
 fun mk_equations functerms =
   let
     fun test_function T = Free ("f", T --> resultT)
     val mk_call = gen_mk_call (fn T =>
-      Const (@{const_name "Quickcheck_Exhaustive.exhaustive_class.exhaustive"}, exhaustiveT T))
+      Const (@{const_name Quickcheck_Exhaustive.exhaustive_class.exhaustive}, exhaustiveT T))
     val mk_aux_call = gen_mk_aux_call functerms
     val mk_consexpr = gen_mk_consexpr test_function
     fun mk_rhs exprs =
-      mk_if (size_ge_zero, foldr1 mk_none_continuation exprs, Const (@{const_name "None"}, resultT))
-  in
-    mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms)
-  end
+      mk_if (size_ge_zero, foldr1 mk_none_continuation exprs, Const (@{const_name None}, resultT))
+  in mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms) end
 
 fun mk_bounded_forall_equations functerms =
   let
     fun test_function T = Free ("P", T --> @{typ bool})
     val mk_call = gen_mk_call (fn T =>
-      Const (@{const_name "Quickcheck_Exhaustive.bounded_forall_class.bounded_forall"},
+      Const (@{const_name Quickcheck_Exhaustive.bounded_forall_class.bounded_forall},
         bounded_forallT T))
     val mk_aux_call = gen_mk_aux_call functerms
     val mk_consexpr = gen_mk_consexpr test_function
-    fun mk_rhs exprs =
-      mk_if (size_ge_zero, foldr1 HOLogic.mk_conj exprs, @{term "True"})
-  in
-    mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms)
-  end
-  
+    fun mk_rhs exprs = mk_if (size_ge_zero, foldr1 HOLogic.mk_conj exprs, @{term True})
+  in mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms) end
+
 fun mk_full_equations functerms =
   let
     fun test_function T = Free ("f", termifyT T --> resultT)
-    fun case_prod_const T = HOLogic.case_prod_const (T, @{typ "unit => Code_Evaluation.term"}, resultT)
+    fun case_prod_const T =
+      HOLogic.case_prod_const (T, @{typ "unit \<Rightarrow> Code_Evaluation.term"}, resultT)
     fun mk_call T =
       let
         val full_exhaustive =
-          Const (@{const_name "Quickcheck_Exhaustive.full_exhaustive_class.full_exhaustive"},
+          Const (@{const_name Quickcheck_Exhaustive.full_exhaustive_class.full_exhaustive},
             full_exhaustiveT T)
-      in                                   
-        (T, fn t => full_exhaustive $
-          (case_prod_const T $ absdummy T (absdummy @{typ "unit => Code_Evaluation.term"} t)) $ size_pred)
+      in
+        (T,
+          fn t =>
+            full_exhaustive $
+              (case_prod_const T $ absdummy T (absdummy @{typ "unit \<Rightarrow> Code_Evaluation.term"} t)) $
+              size_pred)
       end
     fun mk_aux_call fTs (k, _) (tyco, Ts) =
       let
         val T = Type (tyco, Ts)
         val _ = if not (null fTs) then raise FUNCTION_TYPE else ()
       in
-        (T, fn t => nth functerms k $
-          (case_prod_const T $ absdummy T (absdummy @{typ "unit => Code_Evaluation.term"} t)) $ size_pred)
+        (T,
+          fn t =>
+            nth functerms k $
+              (case_prod_const T $ absdummy T (absdummy @{typ "unit \<Rightarrow> Code_Evaluation.term"} t)) $
+              size_pred)
       end
     fun mk_consexpr simpleT (c, xs) =
       let
         val (Ts, fns) = split_list xs
         val constr = Const (c, Ts ---> simpleT)
         val bounds = map (fn x => Bound (2 * x + 1)) (((length xs) - 1) downto 0)
         val Eval_App =
-          Const (@{const_name Code_Evaluation.App}, HOLogic.termT --> HOLogic.termT --> HOLogic.termT)
+          Const (@{const_name Code_Evaluation.App},
+            HOLogic.termT --> HOLogic.termT --> HOLogic.termT)
         val Eval_Const =
-          Const (@{const_name Code_Evaluation.Const}, HOLogic.literalT --> @{typ typerep} --> HOLogic.termT)
-        val term = fold (fn u => fn t => Eval_App $ t $ (u $ @{term "()"}))
-          bounds (Eval_Const $ HOLogic.mk_literal c $ HOLogic.mk_typerep (Ts ---> simpleT))
-        val start_term = test_function simpleT $ 
-        (HOLogic.pair_const simpleT @{typ "unit => Code_Evaluation.term"}
-          $ (list_comb (constr, bounds)) $ absdummy @{typ unit} term)
+          Const (@{const_name Code_Evaluation.Const},
+            HOLogic.literalT --> @{typ typerep} --> HOLogic.termT)
+        val term =
+          fold (fn u => fn t => Eval_App $ t $ (u $ @{term "()"}))
+            bounds (Eval_Const $ HOLogic.mk_literal c $ HOLogic.mk_typerep (Ts ---> simpleT))
+        val start_term =
+          test_function simpleT $
+            (HOLogic.pair_const simpleT @{typ "unit \<Rightarrow> Code_Evaluation.term"} $
+              (list_comb (constr, bounds)) $ absdummy @{typ unit} term)
       in fold_rev (fn f => fn t => f t) fns start_term end
     fun mk_rhs exprs =
-      mk_if (size_ge_zero, foldr1 mk_none_continuation exprs,
-        Const (@{const_name "None"}, resultT))
-  in
-    mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms)
-  end
-  
+      mk_if (size_ge_zero, foldr1 mk_none_continuation exprs, Const (@{const_name None}, resultT))
+  in mk_equation_terms (mk_call, mk_aux_call, mk_consexpr, mk_rhs, test_function, functerms) end
+
 
 (** instantiating generator classes **)
-  
+
 fun contains_recursive_type_under_function_types xs =
   exists (fn (_, (_, _, cs)) => cs |> exists (snd #> exists (fn dT =>
     (case Old_Datatype_Aux.strip_dtyp dT of (_ :: _, Old_Datatype_Aux.DtRec _) => true | _ => false)))) xs
-    
+
 fun instantiate_datatype (name, constprfx, sort, mk_equations, mk_T, argnames)
     config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
   if not (contains_recursive_type_under_function_types descr) then
     let
       val _ = Old_Datatype_Aux.message config ("Creating " ^ name ^ "...")

   else
     (Old_Datatype_Aux.message config
       ("Creation of " ^ name ^ " failed because the datatype is recursive under a function type");
     thy)
 
-val instantiate_bounded_forall_datatype = instantiate_datatype
- ("bounded universal quantifiers", bounded_forallN, @{sort bounded_forall},
-   mk_bounded_forall_equations, bounded_forallT, ["P", "i"]);
-
-val instantiate_exhaustive_datatype = instantiate_datatype  
-  ("exhaustive generators", exhaustiveN, @{sort exhaustive},
-    mk_equations, exhaustiveT, ["f", "i"])
-
-val instantiate_full_exhaustive_datatype = instantiate_datatype
-  ("full exhaustive generators", full_exhaustiveN, @{sort full_exhaustive},
-    mk_full_equations, full_exhaustiveT, ["f", "i"])
+val instantiate_bounded_forall_datatype =
+  instantiate_datatype
+    ("bounded universal quantifiers", bounded_forallN, @{sort bounded_forall},
+      mk_bounded_forall_equations, bounded_forallT, ["P", "i"])
+
+val instantiate_exhaustive_datatype =
+  instantiate_datatype
+    ("exhaustive generators", exhaustiveN, @{sort exhaustive},
+      mk_equations, exhaustiveT, ["f", "i"])
+
+val instantiate_full_exhaustive_datatype =
+  instantiate_datatype
+    ("full exhaustive generators", full_exhaustiveN, @{sort full_exhaustive},
+      mk_full_equations, full_exhaustiveT, ["f", "i"])
+
 
 (* building and compiling generator expressions *)
 
 fun mk_let_expr (x, t, e) genuine =
+  let val (T1, T2) = (fastype_of x, fastype_of (e genuine))
+  in Const (@{const_name Let}, T1 --> (T1 --> T2) --> T2) $ t $ lambda x (e genuine) end
+
+fun mk_safe_let_expr genuine_only none safe (x, t, e) genuine =
   let
     val (T1, T2) = (fastype_of x, fastype_of (e genuine))
-  in  
-    Const (@{const_name Let}, T1 --> (T1 --> T2) --> T2) $ t $ lambda x (e genuine)
-  end
-
-fun mk_safe_let_expr genuine_only none safe (x, t, e) genuine =
-  let
-    val (T1, T2) = (fastype_of x, fastype_of (e genuine))
-    val if_t = Const (@{const_name "If"}, @{typ bool} --> T2 --> T2 --> T2)
+    val if_t = Const (@{const_name If}, @{typ bool} --> T2 --> T2 --> T2)
   in
-    Const (@{const_name "Quickcheck_Random.catch_match"}, T2 --> T2 --> T2) $ 
+    Const (@{const_name Quickcheck_Random.catch_match}, T2 --> T2 --> T2) $
       (Const (@{const_name Let}, T1 --> (T1 --> T2) --> T2) $ t $ lambda x (e genuine)) $
       (if_t $ genuine_only $ none $ safe false)
   end
 
 fun mk_test_term lookup mk_closure mk_if mk_let none_t return ctxt =
   let
-    val cnstrs = flat (maps
-      (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
-      (Symtab.dest (BNF_LFP_Compat.get_all (Proof_Context.theory_of ctxt)
-         Quickcheck_Common.compat_prefs)))
-    fun is_constrt (Const (s, T), ts) = (case (AList.lookup (op =) cnstrs s, body_type T) of
-        (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname'
-      | _ => false)
+    val cnstrs =
+      flat (maps
+        (map (fn (_, (Tname, _, cs)) => map (apsnd (rpair Tname o length)) cs) o #descr o snd)
+        (Symtab.dest
+          (BNF_LFP_Compat.get_all (Proof_Context.theory_of ctxt) Quickcheck_Common.compat_prefs)))
+    fun is_constrt (Const (s, T), ts) =
+          (case (AList.lookup (op =) cnstrs s, body_type T) of
+            (SOME (i, Tname), Type (Tname', _)) => length ts = i andalso Tname = Tname'
+          | _ => false)
       | is_constrt _ = false
     fun mk_naive_test_term t =
-      fold_rev mk_closure (map lookup (Term.add_free_names t []))
-        (mk_if (t, none_t, return) true)
+      fold_rev mk_closure (map lookup (Term.add_free_names t [])) (mk_if (t, none_t, return) true)
     fun mk_test (vars, check) = fold_rev mk_closure (map lookup vars) check
     fun mk_smart_test_term' concl bound_vars assms genuine =
       let
         fun vars_of t = subtract (op =) bound_vars (Term.add_free_names t [])
         fun mk_equality_term (lhs, f as Free (x, _)) c (assm, assms) =
-          if member (op =) (Term.add_free_names lhs bound_vars) x then
-            c (assm, assms)
-          else
-            (let
-               val rec_call = mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms
-               fun safe genuine =
-                 the_default I (Option.map mk_closure (try lookup x)) (rec_call genuine)
-            in
-              mk_test (remove (op =) x (vars_of assm),
-                mk_let safe f (try lookup x) lhs 
-                  (mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms) genuine)
-            
-            end)
+              if member (op =) (Term.add_free_names lhs bound_vars) x then
+                c (assm, assms)
+              else
+                let
+                   val rec_call = mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms
+                   fun safe genuine =
+                     the_default I (Option.map mk_closure (try lookup x)) (rec_call genuine)
+                in
+                  mk_test (remove (op =) x (vars_of assm),
+                    mk_let safe f (try lookup x) lhs
+                      (mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms) genuine)
+    
+                end
           | mk_equality_term (lhs, t) c (assm, assms) =
-            if is_constrt (strip_comb t) then
-              let
-                val (constr, args) = strip_comb t
-                val T = fastype_of t
-                val vars = map Free (Variable.variant_frees ctxt (concl :: assms)
-                  (map (fn t => ("x", fastype_of t)) args))
-                val varnames = map (fst o dest_Free) vars
-                val dummy_var = Free (singleton
-                  (Variable.variant_frees ctxt (concl :: assms @ vars)) ("dummy", T))
-                val new_assms = map HOLogic.mk_eq (vars ~~ args)
-                val bound_vars' = union (op =) (vars_of lhs) (union (op =) varnames bound_vars)
-                val cont_t = mk_smart_test_term' concl bound_vars' (new_assms @ assms) genuine
-              in
-                mk_test (vars_of lhs,
-                  Case_Translation.make_case ctxt Case_Translation.Quiet Name.context lhs
-                    [(list_comb (constr, vars), cont_t), (dummy_var, none_t)])
-              end
-            else c (assm, assms)
+              if is_constrt (strip_comb t) then
+                let
+                  val (constr, args) = strip_comb t
+                  val T = fastype_of t
+                  val vars =
+                    map Free
+                      (Variable.variant_frees ctxt (concl :: assms)
+                        (map (fn t => ("x", fastype_of t)) args))
+                  val varnames = map (fst o dest_Free) vars
+                  val dummy_var =
+                    Free (singleton
+                      (Variable.variant_frees ctxt (concl :: assms @ vars)) ("dummy", T))
+                  val new_assms = map HOLogic.mk_eq (vars ~~ args)
+                  val bound_vars' = union (op =) (vars_of lhs) (union (op =) varnames bound_vars)
+                  val cont_t = mk_smart_test_term' concl bound_vars' (new_assms @ assms) genuine
+                in
+                  mk_test (vars_of lhs,
+                    Case_Translation.make_case ctxt Case_Translation.Quiet Name.context lhs
+                      [(list_comb (constr, vars), cont_t), (dummy_var, none_t)])
+                end
+              else c (assm, assms)
         fun default (assm, assms) =
-          mk_test (vars_of assm,
-            mk_if (HOLogic.mk_not assm, none_t, 
-            mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms) genuine)
+          mk_test
+            (vars_of assm,
+              mk_if (HOLogic.mk_not assm, none_t,
+                mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms) genuine)
       in
-        case assms of [] => mk_test (vars_of concl, mk_if (concl, none_t, return) genuine)
-          | assm :: assms =>
+        (case assms of
+          [] => mk_test (vars_of concl, mk_if (concl, none_t, return) genuine)
+        | assm :: assms =>
             if Config.get ctxt optimise_equality then
               (case try HOLogic.dest_eq assm of
                 SOME (lhs, rhs) =>
                   mk_equality_term (lhs, rhs) (mk_equality_term (rhs, lhs) default) (assm, assms)
               | NONE => default (assm, assms))
-            else default (assm, assms)
+            else default (assm, assms))
       end
     val mk_smart_test_term =
       Quickcheck_Common.strip_imp #> (fn (assms, concl) => mk_smart_test_term' concl [] assms true)
-  in
-    if Config.get ctxt smart_quantifier then mk_smart_test_term else mk_naive_test_term
-  end
+  in if Config.get ctxt smart_quantifier then mk_smart_test_term else mk_naive_test_term end
 
 fun mk_fast_generator_expr ctxt (t, eval_terms) =
   let
     val ctxt' = Variable.auto_fixes t ctxt
     val names = Term.add_free_names t []
     val frees = map Free (Term.add_frees t [])
     fun lookup v = the (AList.lookup (op =) (names ~~ frees) v)
     val ([depth_name], _) = Variable.variant_fixes ["depth"] ctxt'
     val depth = Free (depth_name, @{typ natural})
-    fun return _ = @{term "throw_Counterexample :: term list => unit"} $
-      (HOLogic.mk_list @{typ "term"}
-        (map (fn t => HOLogic.mk_term_of (fastype_of t) t) (frees @ eval_terms)))
+    fun return _ =
+      @{term "throw_Counterexample :: term list \<Rightarrow> unit"} $
+        (HOLogic.mk_list @{typ term}
+          (map (fn t => HOLogic.mk_term_of (fastype_of t) t) (frees @ eval_terms)))
     fun mk_exhaustive_closure (free as Free (_, T)) t =
-      Const (@{const_name "Quickcheck_Exhaustive.fast_exhaustive_class.fast_exhaustive"},
-        fast_exhaustiveT T)
-        $ lambda free t $ depth
+      Const (@{const_name Quickcheck_Exhaustive.fast_exhaustive_class.fast_exhaustive},
+        fast_exhaustiveT T) $ lambda free t $ depth
     val none_t = @{term "()"}
     fun mk_safe_if (cond, then_t, else_t) genuine = mk_if (cond, then_t, else_t genuine)
     fun mk_let _ def v_opt t e = mk_let_expr (the_default def v_opt, t, e)
-    val mk_test_term = mk_test_term lookup mk_exhaustive_closure mk_safe_if mk_let none_t return ctxt 
+    val mk_test_term =
+      mk_test_term lookup mk_exhaustive_closure mk_safe_if mk_let none_t return ctxt
   in lambda depth (@{term "catch_Counterexample :: unit => term list option"} $ mk_test_term t) end
 
-fun mk_unknown_term T = HOLogic.reflect_term (Const (@{const_name Quickcheck_Exhaustive.unknown}, T))
-
-fun mk_safe_term t = @{term "Quickcheck_Random.catch_match :: term => term => term"}
-      $ (HOLogic.mk_term_of (fastype_of t) t) $ mk_unknown_term (fastype_of t)    
-
-fun mk_return t genuine = @{term "Some :: bool * term list => (bool * term list) option"} $
-  (HOLogic.pair_const @{typ bool} @{typ "term list"} $ Quickcheck_Common.reflect_bool genuine $ t)
+fun mk_unknown_term T =
+  HOLogic.reflect_term (Const (@{const_name Quickcheck_Exhaustive.unknown}, T))
+
+fun mk_safe_term t =
+  @{term "Quickcheck_Random.catch_match :: term \<Rightarrow> term \<Rightarrow> term"} $
+    (HOLogic.mk_term_of (fastype_of t) t) $ mk_unknown_term (fastype_of t)
+
+fun mk_return t genuine =
+  @{term "Some :: bool \<times> term list \<Rightarrow> (bool \<times> term list) option"} $
+    (HOLogic.pair_const @{typ bool} @{typ "term list"} $
+      Quickcheck_Common.reflect_bool genuine $ t)
 
 fun mk_generator_expr ctxt (t, eval_terms) =
   let
     val ctxt' = Variable.auto_fixes t ctxt
     val names = Term.add_free_names t []
     val frees = map Free (Term.add_frees t [])
     fun lookup v = the (AList.lookup (op =) (names ~~ frees) v)
     val ([depth_name, genuine_only_name], _) =
       Variable.variant_fixes ["depth", "genuine_only"] ctxt'
     val depth = Free (depth_name, @{typ natural})
-    val genuine_only = Free (genuine_only_name, @{typ bool}) 
-    val return = mk_return (HOLogic.mk_list @{typ "term"}
+    val genuine_only = Free (genuine_only_name, @{typ bool})
+    val return =
+      mk_return (HOLogic.mk_list @{typ term}
         (map (fn t => HOLogic.mk_term_of (fastype_of t) t) frees @ map mk_safe_term eval_terms))
     fun mk_exhaustive_closure (free as Free (_, T)) t =
-      Const (@{const_name "Quickcheck_Exhaustive.exhaustive_class.exhaustive"}, exhaustiveT T)
-        $ lambda free t $ depth
-    val none_t = Const (@{const_name "None"}, resultT)
+      Const (@{const_name Quickcheck_Exhaustive.exhaustive_class.exhaustive}, exhaustiveT T) $
+        lambda free t $ depth
+    val none_t = Const (@{const_name None}, resultT)
     val mk_if = Quickcheck_Common.mk_safe_if genuine_only none_t
-    fun mk_let safe def v_opt t e = mk_safe_let_expr genuine_only none_t safe (the_default def v_opt, t, e)
+    fun mk_let safe def v_opt t e =
+      mk_safe_let_expr genuine_only none_t safe (the_default def v_opt, t, e)
     val mk_test_term = mk_test_term lookup mk_exhaustive_closure mk_if mk_let none_t return ctxt
   in lambda genuine_only (lambda depth (mk_test_term t)) end
 
 fun mk_full_generator_expr ctxt (t, eval_terms) =
   let

     val frees = map Free (Term.add_frees t [])
     val ([depth_name, genuine_only_name], ctxt'') =
       Variable.variant_fixes ["depth", "genuine_only"] ctxt'
     val (term_names, _) = Variable.variant_fixes (map (prefix "t_") names) ctxt''
     val depth = Free (depth_name, @{typ natural})
-    val genuine_only = Free (genuine_only_name, @{typ bool})    
-    val term_vars = map (fn n => Free (n, @{typ "unit => term"})) term_names
+    val genuine_only = Free (genuine_only_name, @{typ bool})
+    val term_vars = map (fn n => Free (n, @{typ "unit \<Rightarrow> term"})) term_names
     fun lookup v = the (AList.lookup (op =) (names ~~ (frees ~~ term_vars)) v)
-    val return = mk_return (HOLogic.mk_list @{typ term}
+    val return =
+      mk_return
+        (HOLogic.mk_list @{typ term}
           (map (fn v => v $ @{term "()"}) term_vars @ map mk_safe_term eval_terms))
     fun mk_exhaustive_closure (free as Free (_, T), term_var) t =
       if Sign.of_sort thy (T, @{sort check_all}) then
-        Const (@{const_name "Quickcheck_Exhaustive.check_all_class.check_all"}, check_allT T)
-          $ (HOLogic.case_prod_const (T, @{typ "unit => term"}, resultT)
-            $ lambda free (lambda term_var t))
+        Const (@{const_name Quickcheck_Exhaustive.check_all_class.check_all}, check_allT T) $
+          (HOLogic.case_prod_const (T, @{typ "unit \<Rightarrow> term"}, resultT) $
+            lambda free (lambda term_var t))
       else
-        Const (@{const_name "Quickcheck_Exhaustive.full_exhaustive_class.full_exhaustive"}, full_exhaustiveT T)
-          $ (HOLogic.case_prod_const (T, @{typ "unit => term"}, resultT)
-            $ lambda free (lambda term_var t)) $ depth
-    val none_t = Const (@{const_name "None"}, resultT)
+        Const (@{const_name Quickcheck_Exhaustive.full_exhaustive_class.full_exhaustive},
+          full_exhaustiveT T) $
+          (HOLogic.case_prod_const (T, @{typ "unit \<Rightarrow> term"}, resultT) $
+            lambda free (lambda term_var t)) $ depth
+    val none_t = Const (@{const_name None}, resultT)
     val mk_if = Quickcheck_Common.mk_safe_if genuine_only none_t
     fun mk_let safe _ (SOME (v, term_var)) t e =
-        mk_safe_let_expr genuine_only none_t safe (v, t, 
-          e #> subst_free [(term_var, absdummy @{typ unit} (mk_safe_term t))])
+          mk_safe_let_expr genuine_only none_t safe (v, t,
+            e #> subst_free [(term_var, absdummy @{typ unit} (mk_safe_term t))])
       | mk_let safe v NONE t e = mk_safe_let_expr genuine_only none_t safe (v, t, e)
     val mk_test_term = mk_test_term lookup mk_exhaustive_closure mk_if mk_let none_t return ctxt
   in lambda genuine_only (lambda depth (mk_test_term t)) end
 
 fun mk_parametric_generator_expr mk_generator_expr =
-  Quickcheck_Common.gen_mk_parametric_generator_expr 
+  Quickcheck_Common.gen_mk_parametric_generator_expr
     ((mk_generator_expr,
-      absdummy @{typ bool} (absdummy @{typ natural} (Const (@{const_name "None"}, resultT)))),
+      absdummy @{typ bool} (absdummy @{typ natural} (Const (@{const_name None}, resultT)))),
       @{typ bool} --> @{typ natural} --> resultT)
 
 fun mk_validator_expr ctxt t =
   let
     fun bounded_forallT T = (T --> @{typ bool}) --> @{typ natural} --> @{typ bool}

     val frees = map Free (Term.add_frees t [])
     fun lookup v = the (AList.lookup (op =) (names ~~ frees) v)
     val ([depth_name], _) = Variable.variant_fixes ["depth"] ctxt'
     val depth = Free (depth_name, @{typ natural})
     fun mk_bounded_forall (Free (s, T)) t =
-      Const (@{const_name "Quickcheck_Exhaustive.bounded_forall_class.bounded_forall"}, bounded_forallT T)
-        $ lambda (Free (s, T)) t $ depth
+      Const (@{const_name Quickcheck_Exhaustive.bounded_forall_class.bounded_forall},
+        bounded_forallT T) $ lambda (Free (s, T)) t $ depth
     fun mk_safe_if (cond, then_t, else_t) genuine = mk_if (cond, then_t, else_t genuine)
     fun mk_let _ def v_opt t e = mk_let_expr (the_default def v_opt, t, e)
     val mk_test_term =
       mk_test_term lookup mk_bounded_forall mk_safe_if mk_let @{term True} (K @{term False}) ctxt
   in lambda depth (mk_test_term t) end
 
-
-fun mk_bounded_forall_generator_expr ctxt (t, eval_terms) = 
+fun mk_bounded_forall_generator_expr ctxt (t, eval_terms) =
   let
     val frees = Term.add_free_names t []
-    val dummy_term = @{term "Code_Evaluation.Const (STR ''Pure.dummy_pattern'')
-      (Typerep.Typerep (STR ''dummy'') [])"}
-    val return = @{term "Some :: term list => term list option"} $
-      (HOLogic.mk_list @{typ "term"}
-        (replicate (length frees + length eval_terms) dummy_term))
+    val dummy_term =
+      @{term "Code_Evaluation.Const (STR ''Pure.dummy_pattern'') (Typerep.Typerep (STR ''dummy'') [])"}
+    val return =
+      @{term "Some :: term list => term list option"} $
+        (HOLogic.mk_list @{typ term} (replicate (length frees + length eval_terms) dummy_term))
     val wrap = absdummy @{typ bool}
-      (@{term "If :: bool => term list option => term list option => term list option"} $
+      (@{term "If :: bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option"} $
         Bound 0 $ @{term "None :: term list option"} $ return)
   in HOLogic.mk_comp (wrap, mk_validator_expr ctxt t) end
-  
+
 
 (** generator compiliation **)
 
 structure Data = Proof_Data
 (
   type T =
-    (unit -> Code_Numeral.natural -> bool ->
-      Code_Numeral.natural -> (bool * term list) option) *
+    (unit -> Code_Numeral.natural -> bool -> Code_Numeral.natural -> (bool * term list) option) *
     (unit -> (Code_Numeral.natural -> term list option) list) *
-    (unit -> (Code_Numeral.natural -> bool) list);
+    (unit -> (Code_Numeral.natural -> bool) list)
   val empty: T =
    (fn () => raise Fail "counterexample",
     fn () => raise Fail "counterexample_batch",
-    fn () => raise Fail "validator_batch");
-  fun init _ = empty;
-);
-
-val get_counterexample = #1 o Data.get;
-val get_counterexample_batch = #2 o Data.get;
-val get_validator_batch = #3 o Data.get;
-
-val put_counterexample = Data.map o @{apply 3(1)} o K;
-val put_counterexample_batch = Data.map o @{apply 3(2)} o K;
-val put_validator_batch = Data.map o @{apply 3(3)} o K;
-
-val target = "Quickcheck";
+    fn () => raise Fail "validator_batch")
+  fun init _ = empty
+)
+
+val get_counterexample = #1 o Data.get
+val get_counterexample_batch = #2 o Data.get
+val get_validator_batch = #3 o Data.get
+
+val put_counterexample = Data.map o @{apply 3(1)} o K
+val put_counterexample_batch = Data.map o @{apply 3(2)} o K
+val put_validator_batch = Data.map o @{apply 3(3)} o K
+
+val target = "Quickcheck"
 
 fun compile_generator_expr_raw ctxt ts =
   let
-    val mk_generator_expr = 
+    val mk_generator_expr =
       if Config.get ctxt fast then mk_fast_generator_expr
       else if Config.get ctxt bounded_forall then mk_bounded_forall_generator_expr
       else if Config.get ctxt full_support then mk_full_generator_expr else mk_generator_expr
-    val t' = mk_parametric_generator_expr mk_generator_expr ctxt ts;
-    val compile = Code_Runtime.dynamic_value_strict
-      (get_counterexample, put_counterexample, "Exhaustive_Generators.put_counterexample")
-      ctxt (SOME target) (fn proc => fn g =>
-        fn card => fn genuine_only => fn size => g card genuine_only size
+    val t' = mk_parametric_generator_expr mk_generator_expr ctxt ts
+    val compile =
+      Code_Runtime.dynamic_value_strict
+        (get_counterexample, put_counterexample, "Exhaustive_Generators.put_counterexample")
+        ctxt (SOME target)
+        (fn proc => fn g => fn card => fn genuine_only => fn size =>
+          g card genuine_only size
           |> (Option.map o apsnd o map) proc) t' []
   in
-    fn genuine_only => fn [card, size] => rpair NONE (compile card genuine_only size |> 
-      (if Config.get ctxt quickcheck_pretty then
-        Option.map (apsnd (map Quickcheck_Common.post_process_term)) else I))
-  end;
+    fn genuine_only => fn [card, size] =>
+      rpair NONE (compile card genuine_only size
+      |> (if Config.get ctxt quickcheck_pretty then
+          Option.map (apsnd (map Quickcheck_Common.post_process_term)) else I))
+  end
 
 fun compile_generator_expr ctxt ts =
-  let
-    val compiled = compile_generator_expr_raw ctxt ts;
-  in fn genuine_only => fn [card, size] =>
-    compiled genuine_only [Code_Numeral.natural_of_integer card, Code_Numeral.natural_of_integer size]
-  end;
+  let val compiled = compile_generator_expr_raw ctxt ts in
+    fn genuine_only => fn [card, size] =>
+      compiled genuine_only
+        [Code_Numeral.natural_of_integer card, Code_Numeral.natural_of_integer size]
+  end
 
 fun compile_generator_exprs_raw ctxt ts =
   let
-    val ts' = map (fn t => mk_generator_expr ctxt (t, [])) ts;
-    val compiles = Code_Runtime.dynamic_value_strict
-      (get_counterexample_batch, put_counterexample_batch,
-        "Exhaustive_Generators.put_counterexample_batch")
-      ctxt (SOME target) (fn proc => map (fn g => g #> (Option.map o map) proc))
-      (HOLogic.mk_list @{typ "natural => term list option"} ts') []
+    val ts' = map (fn t => mk_generator_expr ctxt (t, [])) ts
+    val compiles =
+      Code_Runtime.dynamic_value_strict
+        (get_counterexample_batch, put_counterexample_batch,
+          "Exhaustive_Generators.put_counterexample_batch")
+        ctxt (SOME target) (fn proc => map (fn g => g #> (Option.map o map) proc))
+        (HOLogic.mk_list @{typ "natural => term list option"} ts') []
   in
-    map (fn compile => fn size => compile size
-      |> (Option.map o map) Quickcheck_Common.post_process_term) compiles
-  end;
+    map (fn compile => fn size =>
+      compile size |> (Option.map o map) Quickcheck_Common.post_process_term) compiles
+  end
 
 fun compile_generator_exprs ctxt ts =
   compile_generator_exprs_raw ctxt ts
-  |> map (fn f => fn size => f (Code_Numeral.natural_of_integer size));
+  |> map (fn f => fn size => f (Code_Numeral.natural_of_integer size))
 
 fun compile_validator_exprs_raw ctxt ts =
-  let
-    val ts' = map (mk_validator_expr ctxt) ts
-  in
+  let val ts' = map (mk_validator_expr ctxt) ts in
     Code_Runtime.dynamic_value_strict
       (get_validator_batch, put_validator_batch, "Exhaustive_Generators.put_validator_batch")
-      ctxt (SOME target) (K I) (HOLogic.mk_list @{typ "natural => bool"} ts') []
-  end;
+      ctxt (SOME target) (K I) (HOLogic.mk_list @{typ "natural \<Rightarrow> bool"} ts') []
+  end
 
 fun compile_validator_exprs ctxt ts =
   compile_validator_exprs_raw ctxt ts
-  |> map (fn f => fn size => f (Code_Numeral.natural_of_integer size));
+  |> map (fn f => fn size => f (Code_Numeral.natural_of_integer size))
 
 fun size_matters_for thy Ts = not (forall (fn T => Sign.of_sort thy (T,  @{sort check_all})) Ts)
 
 val test_goals =
-  Quickcheck_Common.generator_test_goal_terms ("exhaustive", (size_matters_for, compile_generator_expr));
-  
+  Quickcheck_Common.generator_test_goal_terms
+    ("exhaustive", (size_matters_for, compile_generator_expr))
+
+
 (* setup *)
 
 val setup_exhaustive_datatype_interpretation =
   Quickcheck_Common.datatype_interpretation @{plugin quickcheck_exhaustive}
     (@{sort exhaustive}, instantiate_exhaustive_datatype)

     (Quickcheck_Common.ensure_sort
        (((@{sort type}, @{sort type}), @{sort bounded_forall}),
        (fn thy => BNF_LFP_Compat.the_descr thy Quickcheck_Common.compat_prefs,
         instantiate_bounded_forall_datatype)))
 
-val active = Attrib.setup_config_bool @{binding quickcheck_exhaustive_active} (K true);
+val active = Attrib.setup_config_bool @{binding quickcheck_exhaustive_active} (K true)
 
 val _ =
   Theory.setup
    (Quickcheck_Common.datatype_interpretation @{plugin quickcheck_full_exhaustive}
       (@{sort full_exhaustive}, instantiate_full_exhaustive_datatype)
     #> Context.theory_map (Quickcheck.add_tester ("exhaustive", (active, test_goals)))
     #> Context.theory_map (Quickcheck.add_batch_generator ("exhaustive", compile_generator_exprs))
-    #> Context.theory_map (Quickcheck.add_batch_validator ("exhaustive", compile_validator_exprs)));
-
-end;
+    #> Context.theory_map (Quickcheck.add_batch_validator ("exhaustive", compile_validator_exprs)))
+
+end