src/HOL/Tools/Quickcheck/exhaustive_generators.ML
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Fri, 01 Apr 2011 13:49:38 +0200
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adding an exhaustive validator for quickcheck's batch validating; moving strip_imp; minimal setup for bounded_forall
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(*  Title:      HOL/Tools/Quickcheck/exhaustive_generators.ML
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    Author:     Lukas Bulwahn, TU Muenchen
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Exhaustive generators for various types.
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*)
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signature EXHAUSTIVE_GENERATORS =
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sig
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  val compile_generator_expr:
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    Proof.context -> (term * term list) list -> int list -> term list option * Quickcheck.report option
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  val compile_generator_exprs: Proof.context -> term list -> (int -> term list option) list
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  val compile_validator_exprs: Proof.context -> term list -> (int -> bool) list
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  val put_counterexample: (unit -> int -> int -> term list option)
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    -> Proof.context -> Proof.context
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  val put_counterexample_batch: (unit -> (int -> term list option) list)
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    -> Proof.context -> Proof.context
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  val put_validator_batch: (unit -> (int -> bool) list) -> Proof.context -> Proof.context
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  val smart_quantifier : bool Config.T
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  val quickcheck_pretty : bool Config.T
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  val setup: theory -> theory
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end;
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structure Exhaustive_Generators : EXHAUSTIVE_GENERATORS =
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struct
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(* static options *)
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val define_foundationally = false
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(* dynamic options *)
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val (smart_quantifier, setup_smart_quantifier) =
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  Attrib.config_bool "quickcheck_smart_quantifier" (K true)
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val (quickcheck_pretty, setup_quickcheck_pretty) =
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  Attrib.config_bool "quickcheck_pretty" (K true)
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(** general term functions **)
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fun mk_measure f =
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  let
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    val Type ("fun", [T, @{typ nat}]) = fastype_of f 
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  in
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    Const (@{const_name Wellfounded.measure},
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      (T --> @{typ nat}) --> HOLogic.mk_prodT (T, T) --> @{typ bool})
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    $ f
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  end
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fun mk_sumcases rT f (Type (@{type_name Sum_Type.sum}, [TL, TR])) =
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  let
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    val lt = mk_sumcases rT f TL
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    val rt = mk_sumcases rT f TR
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  in
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    SumTree.mk_sumcase TL TR rT lt rt
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  end
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  | mk_sumcases _ f T = f T
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fun mk_undefined T = Const(@{const_name undefined}, T)
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(** abstract syntax **)
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fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => Code_Evaluation.term"});
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val size = @{term "i :: code_numeral"}
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val size_pred = @{term "(i :: code_numeral) - 1"}
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val size_ge_zero = @{term "(i :: code_numeral) > 0"}
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fun test_function T = Free ("f", termifyT T --> @{typ "term list option"})
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fun mk_none_continuation (x, y) =
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  let
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    val (T as Type(@{type_name "option"}, [T'])) = fastype_of x
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  in
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    Const (@{const_name "Quickcheck_Exhaustive.orelse"}, T --> T --> T)
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      $ x $ y
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  end
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(** datatypes **)
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(* constructing exhaustive generator instances on datatypes *)
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exception FUNCTION_TYPE;
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val exhaustiveN = "exhaustive";
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fun exhaustiveT T = (termifyT T --> @{typ "Code_Evaluation.term list option"})
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  --> @{typ code_numeral} --> @{typ "Code_Evaluation.term list option"}
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fun check_allT T = (termifyT T --> @{typ "Code_Evaluation.term list option"})
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  --> @{typ "Code_Evaluation.term list option"}
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fun mk_equations descr vs tycos exhaustives (Ts, Us) =
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  let
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    fun mk_call T =
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      let
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        val exhaustive = Const (@{const_name "Quickcheck_Exhaustive.exhaustive_class.exhaustive"}, exhaustiveT T)
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      in
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        (T, (fn t => exhaustive $
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          (HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"})
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          $ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, t))) $ size_pred))
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      end
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    fun mk_aux_call fTs (k, _) (tyco, Ts) =
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      let
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        val T = Type (tyco, Ts)
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        val _ = if not (null fTs) then raise FUNCTION_TYPE else ()
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      in
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       (T, (fn t => nth exhaustives k $
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          (HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"})
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            $ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, t))) $ size_pred))
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      end
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    fun mk_consexpr simpleT (c, xs) =
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      let
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        val (Ts, fns) = split_list xs
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        val constr = Const (c, Ts ---> simpleT)
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        val bounds = map (fn x => Bound (2 * x + 1)) (((length xs) - 1) downto 0)
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        val term_bounds = map (fn x => Bound (2 * x)) (((length xs) - 1) downto 0)
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        val Eval_App = Const ("Code_Evaluation.App", HOLogic.termT --> HOLogic.termT --> HOLogic.termT)
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        val Eval_Const = Const ("Code_Evaluation.Const", HOLogic.literalT --> @{typ typerep} --> HOLogic.termT)
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        val term = fold (fn u => fn t => Eval_App $ t $ (u $ @{term "()"}))
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          bounds (Eval_Const $ HOLogic.mk_literal c $ HOLogic.mk_typerep (Ts ---> simpleT))
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        val start_term = test_function simpleT $ 
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        (HOLogic.pair_const simpleT @{typ "unit => Code_Evaluation.term"}
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          $ (list_comb (constr, bounds)) $ absdummy (@{typ unit}, term))
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      in fold_rev (fn f => fn t => f t) fns start_term end
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    fun mk_rhs exprs =
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        @{term "If :: bool => term list option => term list option => term list option"}
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            $ size_ge_zero $ (foldr1 mk_none_continuation exprs) $ @{term "None :: term list option"}
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    val rhss =
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      Datatype_Aux.interpret_construction descr vs
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        { atyp = mk_call, dtyp = mk_aux_call }
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      |> (map o apfst) Type
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      |> map (fn (T, cs) => map (mk_consexpr T) cs)
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      |> map mk_rhs
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    val lhss = map2 (fn t => fn T => t $ test_function T $ size) exhaustives (Ts @ Us);
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    val eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss)
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  in
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    eqs
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  end
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(* foundational definition with the function package *)
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val less_int_pred = @{lemma "i > 0 ==> Code_Numeral.nat_of ((i :: code_numeral) - 1) < Code_Numeral.nat_of i" by auto}
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fun mk_single_measure T = HOLogic.mk_comp (@{term "Code_Numeral.nat_of"},
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    Const (@{const_name "Product_Type.snd"}, T --> @{typ "code_numeral"}))
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fun mk_termination_measure T =
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  let
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    val T' = fst (HOLogic.dest_prodT (HOLogic.dest_setT T))
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  in
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    mk_measure (mk_sumcases @{typ nat} mk_single_measure T')
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  end
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fun termination_tac ctxt = 
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  Function_Relation.relation_tac ctxt mk_termination_measure 1
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  THEN rtac @{thm wf_measure} 1
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  THEN (REPEAT_DETERM (Simplifier.asm_full_simp_tac 
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    (HOL_basic_ss addsimps [@{thm in_measure}, @{thm o_def}, @{thm snd_conv},
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     @{thm nat_mono_iff}, less_int_pred] @ @{thms sum.cases}) 1))
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fun pat_completeness_auto ctxt =
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  Pat_Completeness.pat_completeness_tac ctxt 1
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  THEN auto_tac (clasimpset_of ctxt)    
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(* creating the instances *)
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fun instantiate_exhaustive_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
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  let
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    val _ = Datatype_Aux.message config "Creating exhaustive generators ...";
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    val exhaustivesN = map (prefix (exhaustiveN ^ "_")) (names @ auxnames);
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  in
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    thy
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    |> Class.instantiation (tycos, vs, @{sort exhaustive})
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    |> (if define_foundationally then
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      let
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        val exhaustives = map2 (fn name => fn T => Free (name, exhaustiveT T)) exhaustivesN (Ts @ Us)
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        val eqs = mk_equations descr vs tycos exhaustives (Ts, Us)
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      in
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        Function.add_function
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          (map (fn (name, T) =>
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              Syntax.no_syn (Binding.conceal (Binding.name name), SOME (exhaustiveT T)))
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                (exhaustivesN ~~ (Ts @ Us)))
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            (map (pair (apfst Binding.conceal Attrib.empty_binding)) eqs)
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          Function_Common.default_config pat_completeness_auto
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        #> snd
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        #> Local_Theory.restore
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        #> (fn lthy => Function.prove_termination NONE (termination_tac lthy) lthy)
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        #> snd
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      end
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    else
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      fold_map (fn (name, T) => Local_Theory.define
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          ((Binding.conceal (Binding.name name), NoSyn),
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            (apfst Binding.conceal Attrib.empty_binding, mk_undefined (exhaustiveT T)))
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        #> apfst fst) (exhaustivesN ~~ (Ts @ Us))
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      #> (fn (exhaustives, lthy) =>
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        let
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          val eqs_t = mk_equations descr vs tycos exhaustives (Ts, Us)
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          val eqs = map (fn eq => Goal.prove lthy ["f", "i"] [] eq
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            (fn _ => Skip_Proof.cheat_tac (ProofContext.theory_of lthy))) eqs_t
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        in
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          fold (fn (name, eq) => Local_Theory.note
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          ((Binding.conceal (Binding.qualify true prfx
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             (Binding.qualify true name (Binding.name "simps"))),
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             Code.add_default_eqn_attrib :: map (Attrib.internal o K)
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               [Simplifier.simp_add, Nitpick_Simps.add]), [eq]) #> snd) (exhaustivesN ~~ eqs) lthy
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        end))
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    |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
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  end handle FUNCTION_TYPE =>
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    (Datatype_Aux.message config
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      "Creation of exhaustive generators failed because the datatype contains a function type";
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    thy)
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(** building and compiling generator expressions **)
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fun mk_generator_expr ctxt (t, eval_terms) =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val ctxt' = Variable.auto_fixes t ctxt
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    val names = Term.add_free_names t []
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    val frees = map Free (Term.add_frees t [])
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    val ([depth_name], ctxt'') = Variable.variant_fixes ["depth"] ctxt'
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    val (term_names, ctxt''') = Variable.variant_fixes (map (prefix "t_") names) ctxt''
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    val depth = Free (depth_name, @{typ code_numeral})
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    val term_vars = map (fn n => Free (n, @{typ "unit => term"})) term_names
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    val terms = HOLogic.mk_list @{typ term} (map (fn v => v $ @{term "()"}) term_vars)
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    val appendC = @{term "List.append :: term list => term list => term list"}  
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    val return = @{term "Some :: term list => term list option"} $ (appendC $ terms $
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      (HOLogic.mk_list @{typ "term"} (map (fn t => HOLogic.mk_term_of (fastype_of t) t) eval_terms)))
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    fun mk_exhaustive_closure (free as Free (_, T), term_var) t =
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      if Sign.of_sort thy (T, @{sort enum}) then
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        Const (@{const_name "Quickcheck_Exhaustive.check_all_class.check_all"}, check_allT T)
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          $ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"}) 
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            $ lambda free (lambda term_var t))
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      else
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        Const (@{const_name "Quickcheck_Exhaustive.exhaustive_class.exhaustive"}, exhaustiveT T)
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          $ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"})
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            $ lambda free (lambda term_var t)) $ depth
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    val none_t = @{term "None :: term list option"}
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    fun mk_safe_if (cond, then_t, else_t) =
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      @{term "Quickcheck_Exhaustive.catch_match :: term list option => term list option => term list option"} $
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        (@{term "If :: bool => term list option => term list option => term list option"}
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        $ cond $ then_t $ else_t) $ none_t;
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    fun lookup v = the (AList.lookup (op =) (names ~~ (frees ~~ term_vars)) v)
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    fun mk_naive_test_term t =
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      fold_rev mk_exhaustive_closure (frees ~~ term_vars) (mk_safe_if (t, none_t, return)) 
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    fun mk_smart_test_term' concl bound_vars assms =
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      let
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        fun vars_of t = subtract (op =) bound_vars (Term.add_free_names t [])
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        val (vars, check) =
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          case assms of [] => (vars_of concl, (concl, none_t, return))
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            | assm :: assms => (vars_of assm, (assm,
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                mk_smart_test_term' concl (union (op =) (vars_of assm) bound_vars) assms, none_t))
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      in
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        fold_rev mk_exhaustive_closure (map lookup vars) (mk_safe_if check)
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      end
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    fun mk_smart_test_term t =
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      let
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        val (assms, concl) = Quickcheck_Common.strip_imp t
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      in
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        mk_smart_test_term' concl [] assms
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      end
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    val mk_test_term =
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      if Config.get ctxt smart_quantifier then mk_smart_test_term else mk_naive_test_term 
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  in lambda depth (mk_test_term t) end
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val mk_parametric_generator_expr =
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  Quickcheck_Common.gen_mk_parametric_generator_expr 
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    ((mk_generator_expr, absdummy (@{typ "code_numeral"}, @{term "None :: term list option"})),
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      @{typ "code_numeral => term list option"})
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fun mk_validator_expr ctxt t =
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  let
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    fun bounded_forallT T = (T --> @{typ bool}) --> @{typ code_numeral} --> @{typ bool}
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    val thy = ProofContext.theory_of ctxt
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    val ctxt' = Variable.auto_fixes t ctxt
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    val ([depth_name], ctxt'') = Variable.variant_fixes ["depth"] ctxt'
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    val depth = Free (depth_name, @{typ code_numeral})
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    fun mk_bounded_forall (s, T) t =
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      Const (@{const_name "Quickcheck_Exhaustive.bounded_forall_class.bounded_forall"}, bounded_forallT T)
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        $ lambda (Free (s, T)) t $ depth
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    fun mk_implies (cond, then_t) =
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      @{term "If :: bool => bool => bool => bool"} $ cond $ then_t $ @{term False}
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    fun mk_naive_test_term t = fold_rev mk_bounded_forall (Term.add_frees t []) t 
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    fun mk_smart_test_term' concl bound_frees assms =
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      let
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        fun vars_of t = subtract (op =) bound_frees (Term.add_frees t [])
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        val (vars, check) =
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          case assms of [] => (vars_of concl, concl)
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            | assm :: assms => (vars_of assm, mk_implies (assm,
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                mk_smart_test_term' concl (union (op =) (vars_of assm) bound_frees) assms))
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      in
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        fold_rev mk_bounded_forall vars check
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      end
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    fun mk_smart_test_term t =
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      let
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        val (assms, concl) = Quickcheck_Common.strip_imp t
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      in
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        mk_smart_test_term' concl [] assms
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      end
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    val mk_test_term =
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      if Config.get ctxt smart_quantifier then mk_smart_test_term else mk_naive_test_term 
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  in lambda depth (mk_test_term t) end
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(** generator compiliation **)
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structure Counterexample = Proof_Data
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(
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  type T = unit -> int -> int -> term list option
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  (* FIXME avoid user error with non-user text *)
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  fun init _ () = error "Counterexample"
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);
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val put_counterexample = Counterexample.put;
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structure Counterexample_Batch = Proof_Data
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(
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  type T = unit -> (int -> term list option) list
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  (* FIXME avoid user error with non-user text *)
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  fun init _ () = error "Counterexample"
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);
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val put_counterexample_batch = Counterexample_Batch.put;
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structure Validator_Batch = Proof_Data
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(
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  type T = unit -> (int -> bool) list
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  (* FIXME avoid user error with non-user text *)
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  fun init _ () = error "Counterexample"
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);
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val put_validator_batch = Validator_Batch.put;
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val target = "Quickcheck";
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fun compile_generator_expr ctxt ts =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val t' = mk_parametric_generator_expr ctxt ts;
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    val compile = Code_Runtime.dynamic_value_strict
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      (Counterexample.get, put_counterexample, "Exhaustive_Generators.put_counterexample")
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      thy (SOME target) (fn proc => fn g =>
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        fn card => fn size => g card size |> (Option.map o map) proc) t' []
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  in
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    fn [card, size] => rpair NONE (compile card size |> 
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      (if Config.get ctxt quickcheck_pretty then
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        Option.map (map Quickcheck_Common.post_process_term) else I))
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  end;
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fun compile_generator_exprs ctxt ts =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val ts' = map (fn t => mk_generator_expr ctxt (t, [])) ts;
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    val compiles = Code_Runtime.dynamic_value_strict
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      (Counterexample_Batch.get, put_counterexample_batch,
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        "Exhaustive_Generators.put_counterexample_batch")
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      thy (SOME target) (fn proc => map (fn g => g #> (Option.map o map) proc))
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      (HOLogic.mk_list @{typ "code_numeral => term list option"} ts') []
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  in
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    map (fn compile => fn size => compile size
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      |> Option.map (map Quickcheck_Common.post_process_term)) compiles
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  end;
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fun compile_validator_exprs ctxt ts =
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  let
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    val thy = ProofContext.theory_of ctxt
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    val ts' = map (mk_validator_expr ctxt) ts;
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  in
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    Code_Runtime.dynamic_value_strict
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      (Validator_Batch.get, put_validator_batch, "Exhaustive_Generators.put_validator_batch")
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      thy (SOME target) (K I) (HOLogic.mk_list @{typ "code_numeral => bool"} ts') []
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  end;
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(** setup **)
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val setup =
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  Datatype.interpretation
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    (Quickcheck_Common.ensure_sort_datatype (@{sort exhaustive}, instantiate_exhaustive_datatype))
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  #> setup_smart_quantifier
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  #> setup_quickcheck_pretty
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  #> Context.theory_map (Quickcheck.add_generator ("exhaustive", compile_generator_expr))
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  #> Context.theory_map (Quickcheck.add_batch_generator ("exhaustive", compile_generator_exprs))
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  #> Context.theory_map (Quickcheck.add_batch_validator ("exhaustive", compile_validator_exprs));
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end;