src/HOL/Quickcheck_Exhaustive.thy
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(* Author: Lukas Bulwahn, TU Muenchen *)
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header {* A simple counterexample generator performing exhaustive testing *}
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theory Quickcheck_Exhaustive
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imports Quickcheck
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keywords "quickcheck_generator" :: thy_decl
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begin
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subsection {* basic operations for exhaustive generators *}
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definition orelse :: "'a option => 'a option => 'a option" (infixr "orelse" 55)
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where
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  [code_unfold]: "x orelse y = (case x of Some x' => Some x' | None => y)"
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subsection {* exhaustive generator type classes *}
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class exhaustive = term_of +
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  fixes exhaustive :: "('a \<Rightarrow> (bool * term list) option) \<Rightarrow> code_numeral \<Rightarrow> (bool * term list) option"
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class full_exhaustive = term_of +
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  fixes full_exhaustive :: "('a * (unit => term) \<Rightarrow> (bool * term list) option) \<Rightarrow> code_numeral \<Rightarrow> (bool * term list) option"
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instantiation code_numeral :: full_exhaustive
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begin
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function full_exhaustive_code_numeral' :: "(code_numeral * (unit => term) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
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  where "full_exhaustive_code_numeral' f d i =
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    (if d < i then None
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    else (f (i, %_. Code_Evaluation.term_of i)) orelse (full_exhaustive_code_numeral' f d (i + 1)))"
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by pat_completeness auto
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termination
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  by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
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definition "full_exhaustive f d = full_exhaustive_code_numeral' f d 0"
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instance ..
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end
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instantiation code_numeral :: exhaustive
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begin
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function exhaustive_code_numeral' :: "(code_numeral => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
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  where "exhaustive_code_numeral' f d i =
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    (if d < i then None
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    else (f i orelse exhaustive_code_numeral' f d (i + 1)))"
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by pat_completeness auto
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termination
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  by (relation "measure (%(_, d, i). Code_Numeral.nat_of (d + 1 - i))") auto
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definition "exhaustive f d = exhaustive_code_numeral' f d 0"
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instance ..
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end
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instantiation nat :: exhaustive
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begin
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definition "exhaustive f d = exhaustive (%x. f (Code_Numeral.nat_of x)) d"
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instance ..
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end
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instantiation nat :: full_exhaustive
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begin
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definition "full_exhaustive f d = full_exhaustive (%(x, xt). f (Code_Numeral.nat_of x, %_. Code_Evaluation.term_of (Code_Numeral.nat_of x))) d"
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instance ..
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end
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instantiation int :: exhaustive
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begin
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function exhaustive' :: "(int => (bool * term list) option) => int => int => (bool * term list) option"
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  where "exhaustive' f d i = (if d < i then None else (f i orelse exhaustive' f d (i + 1)))"
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by pat_completeness auto
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termination 
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  by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
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definition "exhaustive f d = exhaustive' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
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instance ..
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end
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instantiation int :: full_exhaustive
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begin
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function full_exhaustive' :: "(int * (unit => term) => (bool * term list) option) => int => int => (bool * term list) option"
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  where "full_exhaustive' f d i = (if d < i then None else (case f (i, %_. Code_Evaluation.term_of i) of Some t => Some t | None => full_exhaustive' f d (i + 1)))"
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by pat_completeness auto
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termination 
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  by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
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definition "full_exhaustive f d = full_exhaustive' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
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instance ..
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end
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instantiation prod :: (exhaustive, exhaustive) exhaustive
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begin
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definition
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  "exhaustive f d = exhaustive (%x. exhaustive (%y. f ((x, y))) d) d"
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instance ..
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end
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definition (in term_syntax) [code_unfold]: "valtermify_pair x y = Code_Evaluation.valtermify (Pair :: 'a :: typerep => 'b :: typerep => 'a * 'b) {\<cdot>} x {\<cdot>} y"
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instantiation prod :: (full_exhaustive, full_exhaustive) full_exhaustive
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begin
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definition
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  "full_exhaustive f d = full_exhaustive (%x. full_exhaustive (%y. f (valtermify_pair x y)) d) d"
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instance ..
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end
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instantiation set :: (exhaustive) exhaustive
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begin
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fun exhaustive_set
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where
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  "exhaustive_set f i = (if i = 0 then None else (f {} orelse exhaustive_set (%A. f A orelse exhaustive (%x. if x \<in> A then None else f (insert x A)) (i - 1)) (i - 1)))"
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instance ..
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end
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instantiation set :: (full_exhaustive) full_exhaustive
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begin
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fun full_exhaustive_set 
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where
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  "full_exhaustive_set f i = (if i = 0 then None else (f valterm_emptyset orelse full_exhaustive_set (%A. f A orelse Quickcheck_Exhaustive.full_exhaustive (%x. if fst x \<in> fst A then None else f (valtermify_insert x A)) (i - 1)) (i - 1)))"
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instance ..
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end
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instantiation "fun" :: ("{equal, exhaustive}", exhaustive) exhaustive
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begin
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fun exhaustive_fun' :: "(('a => 'b) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
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where
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  "exhaustive_fun' f i d = (exhaustive (%b. f (%_. b)) d)
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   orelse (if i > 1 then
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     exhaustive_fun' (%g. exhaustive (%a. exhaustive (%b.
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       f (g(a := b))) d) d) (i - 1) d else None)"
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definition exhaustive_fun :: "(('a => 'b) => (bool * term list) option) => code_numeral => (bool * term list) option"
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where
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  "exhaustive_fun f d = exhaustive_fun' f d d" 
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instance ..
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end
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definition [code_unfold]: "valtermify_absdummy = (%(v, t). (%_::'a. v, %u::unit. Code_Evaluation.Abs (STR ''x'') (Typerep.typerep TYPE('a::typerep)) (t ())))"
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definition (in term_syntax) [code_unfold]: "valtermify_fun_upd g a b = Code_Evaluation.valtermify (fun_upd :: ('a :: typerep => 'b :: typerep) => 'a => 'b => 'a => 'b) {\<cdot>} g {\<cdot>} a {\<cdot>} b"
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instantiation "fun" :: ("{equal, full_exhaustive}", full_exhaustive) full_exhaustive
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begin
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fun full_exhaustive_fun' :: "(('a => 'b) * (unit => term) => (bool * term list) option) => code_numeral => code_numeral => (bool * term list) option"
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where
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  "full_exhaustive_fun' f i d = (full_exhaustive (%v. f (valtermify_absdummy v)) d)
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   orelse (if i > 1 then
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     full_exhaustive_fun' (%g. full_exhaustive (%a. full_exhaustive (%b.
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       f (valtermify_fun_upd g a b)) d) d) (i - 1) d else None)"
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definition full_exhaustive_fun :: "(('a => 'b) * (unit => term) => (bool * term list) option) => code_numeral => (bool * term list) option"
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where
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  "full_exhaustive_fun f d = full_exhaustive_fun' f d d" 
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instance ..
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end
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subsubsection {* A smarter enumeration scheme for functions over finite datatypes *}
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class check_all = enum + term_of +
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  fixes check_all :: "('a * (unit \<Rightarrow> term) \<Rightarrow> (bool * term list) option) \<Rightarrow> (bool * term list) option"
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  fixes enum_term_of :: "'a itself \<Rightarrow> unit \<Rightarrow> term list"
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fun check_all_n_lists :: "(('a :: check_all) list * (unit \<Rightarrow> term list) \<Rightarrow> (bool * term list) option) \<Rightarrow> code_numeral \<Rightarrow> (bool * term list) option"
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where
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  "check_all_n_lists f n =
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     (if n = 0 then f ([], (%_. [])) else check_all (%(x, xt). check_all_n_lists (%(xs, xst). f ((x # xs), (%_. (xt () # xst ())))) (n - 1)))"
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definition (in term_syntax) [code_unfold]: "termify_fun_upd g a b = (Code_Evaluation.termify (fun_upd :: ('a :: typerep => 'b :: typerep) => 'a => 'b => 'a => 'b) <\<cdot>> g <\<cdot>> a <\<cdot>> b)"
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definition mk_map_term :: " (unit \<Rightarrow> typerep) \<Rightarrow> (unit \<Rightarrow> typerep) \<Rightarrow> (unit \<Rightarrow> term list) \<Rightarrow> (unit \<Rightarrow> term list) \<Rightarrow> unit \<Rightarrow> term"
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where
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  "mk_map_term T1 T2 domm rng =
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     (%_. let T1 = T1 ();
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              T2 = T2 ();
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              update_term = (%g (a, b).
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                Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App
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                 (Code_Evaluation.Const (STR ''Fun.fun_upd'')
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                   (Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2],
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                      Typerep.Typerep (STR ''fun'') [T1,
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                        Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]]))
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                        g) a) b)
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          in
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             List.foldl update_term (Code_Evaluation.Abs (STR ''x'') T1 (Code_Evaluation.Const (STR ''HOL.undefined'') T2)) (zip (domm ()) (rng ())))"
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instantiation "fun" :: ("{equal, check_all}", check_all) check_all
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begin
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definition
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  "check_all f =
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    (let
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      mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) (enum_term_of (TYPE('a)));
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      enum = (Enum.enum :: 'a list)
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    in check_all_n_lists (\<lambda>(ys, yst). f (the o map_of (zip enum ys), mk_term yst)) (Code_Numeral.of_nat (length enum)))"
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definition enum_term_of_fun :: "('a => 'b) itself => unit => term list"
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where
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  "enum_term_of_fun = (%_ _. let
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    enum_term_of_a = enum_term_of (TYPE('a));
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    mk_term = mk_map_term (%_. Typerep.typerep (TYPE('a))) (%_. Typerep.typerep (TYPE('b))) enum_term_of_a
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  in map (%ys. mk_term (%_. ys) ()) (Enum.n_lists (length (enum_term_of_a ())) (enum_term_of (TYPE('b)) ())))"
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instance ..
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end
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fun (in term_syntax) check_all_subsets :: "(('a :: typerep) set * (unit => term) => (bool * term list) option) => ('a * (unit => term)) list => (bool * term list) option"
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where
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  "check_all_subsets f [] = f valterm_emptyset"
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| "check_all_subsets f (x # xs) = check_all_subsets (%s. case f s of Some ts => Some ts | None => f (valtermify_insert x s)) xs"
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definition (in term_syntax) [code_unfold]: "term_emptyset = Code_Evaluation.termify ({} :: ('a :: typerep) set)"
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definition (in term_syntax) [code_unfold]: "termify_insert x s = Code_Evaluation.termify (insert :: ('a::typerep) => 'a set => 'a set)  <\<cdot>> x <\<cdot>> s"
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definition (in term_syntax) setify :: "('a::typerep) itself => term list => term"
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where
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  "setify T ts = foldr (termify_insert T) ts (term_emptyset T)" 
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instantiation set :: (check_all) check_all
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begin
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definition
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  "check_all_set f =
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     check_all_subsets f (zip (Enum.enum :: 'a list) (map (%a. %u :: unit. a) (Quickcheck_Exhaustive.enum_term_of (TYPE ('a)) ())))"
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definition enum_term_of_set :: "'a set itself => unit => term list"
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where
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  "enum_term_of_set _ _ = map (setify (TYPE('a))) (sublists (Quickcheck_Exhaustive.enum_term_of (TYPE('a)) ()))"
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instance ..
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end
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instantiation unit :: check_all
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begin
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definition
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  "check_all f = f (Code_Evaluation.valtermify ())"
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definition enum_term_of_unit :: "unit itself => unit => term list"
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where
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  "enum_term_of_unit = (%_ _. [Code_Evaluation.term_of ()])"
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instance ..
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end
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instantiation bool :: check_all
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begin
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definition
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  "check_all f = (case f (Code_Evaluation.valtermify False) of Some x' \<Rightarrow> Some x' | None \<Rightarrow> f (Code_Evaluation.valtermify True))"
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definition enum_term_of_bool :: "bool itself => unit => term list"
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where
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  "enum_term_of_bool = (%_ _. map Code_Evaluation.term_of (Enum.enum :: bool list))"
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instance ..
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end
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definition (in term_syntax) [code_unfold]: "termify_pair x y = Code_Evaluation.termify (Pair :: 'a :: typerep => 'b :: typerep => 'a * 'b) <\<cdot>> x <\<cdot>> y"
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instantiation prod :: (check_all, check_all) check_all
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begin
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definition
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  "check_all f = check_all (%x. check_all (%y. f (valtermify_pair x y)))"
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definition enum_term_of_prod :: "('a * 'b) itself => unit => term list"
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where
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  "enum_term_of_prod = (%_ _. map (%(x, y). termify_pair TYPE('a) TYPE('b) x y)
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     (Enum.product (enum_term_of (TYPE('a)) ()) (enum_term_of (TYPE('b)) ())))"
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instance ..
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end
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definition (in term_syntax) [code_unfold]: "valtermify_Inl x = Code_Evaluation.valtermify (Inl :: 'a :: typerep => 'a + 'b :: typerep) {\<cdot>} x"
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definition (in term_syntax) [code_unfold]: "valtermify_Inr x = Code_Evaluation.valtermify (Inr :: 'b :: typerep => 'a ::typerep + 'b) {\<cdot>} x"
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instantiation sum :: (check_all, check_all) check_all
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begin
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definition
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  "check_all f = check_all (%a. f (valtermify_Inl a)) orelse check_all (%b. f (valtermify_Inr b))"
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definition enum_term_of_sum :: "('a + 'b) itself => unit => term list"
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where
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  "enum_term_of_sum = (%_ _.
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     let
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       T1 = (Typerep.typerep (TYPE('a)));
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       T2 = (Typerep.typerep (TYPE('b)))
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     in
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       map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'') 
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             (Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
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             (enum_term_of (TYPE('a)) ()) @
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       map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'') 
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             (Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]])))
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             (enum_term_of (TYPE('b)) ()))"
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instance ..
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end
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instantiation nibble :: check_all
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begin
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definition
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  "check_all f =
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    f (Code_Evaluation.valtermify Nibble0) orelse
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    f (Code_Evaluation.valtermify Nibble1) orelse
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    f (Code_Evaluation.valtermify Nibble2) orelse
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    f (Code_Evaluation.valtermify Nibble3) orelse
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    f (Code_Evaluation.valtermify Nibble4) orelse
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    f (Code_Evaluation.valtermify Nibble5) orelse
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    f (Code_Evaluation.valtermify Nibble6) orelse
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    f (Code_Evaluation.valtermify Nibble7) orelse
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    f (Code_Evaluation.valtermify Nibble8) orelse
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    f (Code_Evaluation.valtermify Nibble9) orelse
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    f (Code_Evaluation.valtermify NibbleA) orelse
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    f (Code_Evaluation.valtermify NibbleB) orelse
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    f (Code_Evaluation.valtermify NibbleC) orelse
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    f (Code_Evaluation.valtermify NibbleD) orelse
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    f (Code_Evaluation.valtermify NibbleE) orelse
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    f (Code_Evaluation.valtermify NibbleF)"
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definition enum_term_of_nibble :: "nibble itself => unit => term list"
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where
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  "enum_term_of_nibble = (%_ _. map Code_Evaluation.term_of (Enum.enum :: nibble list))"
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instance ..
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end
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instantiation char :: check_all
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begin
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   377
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definition
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  "check_all f = check_all (%(x, t1). check_all (%(y, t2). f (Char x y, %_. Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.term_of Char) (t1 ())) (t2 ()))))"
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definition enum_term_of_char :: "char itself => unit => term list"
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where
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  "enum_term_of_char = (%_ _. map Code_Evaluation.term_of (Enum.enum :: char list))"
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instance ..
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end
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   388
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   389
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instantiation option :: (check_all) check_all
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begin
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   392
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   393
definition
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  "check_all f = f (Code_Evaluation.valtermify (None :: 'a option)) orelse check_all (%(x, t). f (Some x, %_. Code_Evaluation.App
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    (Code_Evaluation.Const (STR ''Option.option.Some'')
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      (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a),  Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]])) (t ())))"
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   397
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definition enum_term_of_option :: "'a option itself => unit => term list"
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where
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  "enum_term_of_option = (% _ _. (Code_Evaluation.term_of (None :: 'a option)) # (map (Code_Evaluation.App (Code_Evaluation.Const (STR ''Option.option.Some'')
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      (Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a),  Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]]))) (enum_term_of (TYPE('a)) ())))"
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   402
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instance ..
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   404
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end
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   406
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   407
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instantiation Enum.finite_1 :: check_all
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begin
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   410
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   411
definition
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  "check_all f = f (Code_Evaluation.valtermify Enum.finite_1.a\<^isub>1)"
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   413
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   414
definition enum_term_of_finite_1 :: "Enum.finite_1 itself => unit => term list"
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where
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  "enum_term_of_finite_1 = (%_ _. [Code_Evaluation.term_of Enum.finite_1.a\<^isub>1])"
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   417
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instance ..
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   419
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end
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   421
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instantiation Enum.finite_2 :: check_all
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   423
begin
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   424
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   425
definition
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  "check_all f = (f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>1)
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    orelse f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>2))"
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   428
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   429
definition enum_term_of_finite_2 :: "Enum.finite_2 itself => unit => term list"
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   430
where
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   431
  "enum_term_of_finite_2 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_2 list))"
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   432
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instance ..
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   434
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   435
end
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   436
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   437
instantiation Enum.finite_3 :: check_all
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   438
begin
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   439
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   440
definition
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   441
  "check_all f = (f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>1)
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    orelse f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>2)
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   443
    orelse f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>3))"
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   444
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   445
definition enum_term_of_finite_3 :: "Enum.finite_3 itself => unit => term list"
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   446
where
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  "enum_term_of_finite_3 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_3 list))"
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   448
41085
a549ff1d4070 adding a smarter enumeration scheme for finite functions
bulwahn
parents: 40915
diff changeset
   449
instance ..
a549ff1d4070 adding a smarter enumeration scheme for finite functions
bulwahn
parents: 40915
diff changeset
   450
a549ff1d4070 adding a smarter enumeration scheme for finite functions
bulwahn
parents: 40915
diff changeset
   451
end
a549ff1d4070 adding a smarter enumeration scheme for finite functions
bulwahn
parents: 40915
diff changeset
   452
46417
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   453
instantiation Enum.finite_4 :: check_all
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   454
begin
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   455
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   456
definition
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   457
  "check_all f = (f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>1)
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   458
    orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>2)
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   459
    orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>3)
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   460
    orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>4))"
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   461
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   462
definition enum_term_of_finite_4 :: "Enum.finite_4 itself => unit => term list"
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   463
where
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   464
  "enum_term_of_finite_4 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_4 list))"
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   465
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   466
instance ..
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   467
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   468
end
1a68fcb80b62 beautifying definitions of check_all and adding instance for finite_4
bulwahn
parents: 46311
diff changeset
   469
42195
1e7b62c93f5d adding an exhaustive validator for quickcheck's batch validating; moving strip_imp; minimal setup for bounded_forall
bulwahn
parents: 42117
diff changeset
   470
subsection {* Bounded universal quantifiers *}
41085
a549ff1d4070 adding a smarter enumeration scheme for finite functions
bulwahn
parents: 40915
diff changeset
   471
42195
1e7b62c93f5d adding an exhaustive validator for quickcheck's batch validating; moving strip_imp; minimal setup for bounded_forall
bulwahn
parents: 42117
diff changeset
   472
class bounded_forall =
1e7b62c93f5d adding an exhaustive validator for quickcheck's batch validating; moving strip_imp; minimal setup for bounded_forall
bulwahn
parents: 42117
diff changeset
   473
  fixes bounded_forall :: "('a \<Rightarrow> bool) \<Rightarrow> code_numeral \<Rightarrow> bool"
1e7b62c93f5d adding an exhaustive validator for quickcheck's batch validating; moving strip_imp; minimal setup for bounded_forall
bulwahn
parents: 42117
diff changeset
   474
42305
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   475
subsection {* Fast exhaustive combinators *}
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   476
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   477
class fast_exhaustive = term_of +
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   478
  fixes fast_exhaustive :: "('a \<Rightarrow> unit) \<Rightarrow> code_numeral \<Rightarrow> unit"
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   479
45818
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   480
axiomatization throw_Counterexample :: "term list => unit"
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   481
axiomatization catch_Counterexample :: "unit => term list option"
42305
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   482
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   483
code_const throw_Counterexample
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   484
  (Quickcheck "raise (Exhaustive'_Generators.Counterexample _)")
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   485
code_const catch_Counterexample
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   486
  (Quickcheck "(((_); NONE) handle Exhaustive'_Generators.Counterexample ts => SOME ts)")
494c31fdec95 theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents: 42304
diff changeset
   487
45450
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   488
subsection {* Continuation passing style functions as plus monad *}
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   489
  
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   490
type_synonym 'a cps = "('a => term list option) => term list option"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   491
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   492
definition cps_empty :: "'a cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   493
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   494
  "cps_empty = (%cont. None)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   495
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   496
definition cps_single :: "'a => 'a cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   497
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   498
  "cps_single v = (%cont. cont v)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   499
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   500
definition cps_bind :: "'a cps => ('a => 'b cps) => 'b cps" 
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   501
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   502
  "cps_bind m f = (%cont. m (%a. (f a) cont))"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   503
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   504
definition cps_plus :: "'a cps => 'a cps => 'a cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   505
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   506
  "cps_plus a b = (%c. case a c of None => b c | Some x => Some x)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   507
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   508
definition cps_if :: "bool => unit cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   509
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   510
  "cps_if b = (if b then cps_single () else cps_empty)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   511
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   512
definition cps_not :: "unit cps => unit cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   513
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   514
  "cps_not n = (%c. case n (%u. Some []) of None => c () | Some _ => None)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   515
45750
17100f4ce0b5 adding genuine flag to predicate_compile_quickcheck and prolog_quickcheck (cf. 5e46c225370e);
bulwahn
parents: 45733
diff changeset
   516
type_synonym 'a pos_bound_cps = "('a => (bool * term list) option) => code_numeral => (bool * term list) option"
45450
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   517
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   518
definition pos_bound_cps_empty :: "'a pos_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   519
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   520
  "pos_bound_cps_empty = (%cont i. None)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   521
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   522
definition pos_bound_cps_single :: "'a => 'a pos_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   523
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   524
  "pos_bound_cps_single v = (%cont i. cont v)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   525
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   526
definition pos_bound_cps_bind :: "'a pos_bound_cps => ('a => 'b pos_bound_cps) => 'b pos_bound_cps" 
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   527
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   528
  "pos_bound_cps_bind m f = (%cont i. if i = 0 then None else (m (%a. (f a) cont i) (i - 1)))"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   529
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   530
definition pos_bound_cps_plus :: "'a pos_bound_cps => 'a pos_bound_cps => 'a pos_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   531
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   532
  "pos_bound_cps_plus a b = (%c i. case a c i of None => b c i | Some x => Some x)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   533
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   534
definition pos_bound_cps_if :: "bool => unit pos_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   535
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   536
  "pos_bound_cps_if b = (if b then pos_bound_cps_single () else pos_bound_cps_empty)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   537
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   538
datatype 'a unknown = Unknown | Known 'a
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   539
datatype 'a three_valued = Unknown_value | Value 'a | No_value
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   540
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   541
type_synonym 'a neg_bound_cps = "('a unknown => term list three_valued) => code_numeral => term list three_valued"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   542
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   543
definition neg_bound_cps_empty :: "'a neg_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   544
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   545
  "neg_bound_cps_empty = (%cont i. No_value)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   546
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   547
definition neg_bound_cps_single :: "'a => 'a neg_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   548
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   549
  "neg_bound_cps_single v = (%cont i. cont (Known v))"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   550
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   551
definition neg_bound_cps_bind :: "'a neg_bound_cps => ('a => 'b neg_bound_cps) => 'b neg_bound_cps" 
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   552
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   553
  "neg_bound_cps_bind m f = (%cont i. if i = 0 then cont Unknown else m (%a. case a of Unknown => cont Unknown | Known a' => f a' cont i) (i - 1))"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   554
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   555
definition neg_bound_cps_plus :: "'a neg_bound_cps => 'a neg_bound_cps => 'a neg_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   556
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   557
  "neg_bound_cps_plus a b = (%c i. case a c i of No_value => b c i | Value x => Value x | Unknown_value => (case b c i of No_value => Unknown_value | Value x => Value x | Unknown_value => Unknown_value))"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   558
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   559
definition neg_bound_cps_if :: "bool => unit neg_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   560
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   561
  "neg_bound_cps_if b = (if b then neg_bound_cps_single () else neg_bound_cps_empty)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   562
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   563
definition neg_bound_cps_not :: "unit pos_bound_cps => unit neg_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   564
where
45750
17100f4ce0b5 adding genuine flag to predicate_compile_quickcheck and prolog_quickcheck (cf. 5e46c225370e);
bulwahn
parents: 45733
diff changeset
   565
  "neg_bound_cps_not n = (%c i. case n (%u. Some (True, [])) i of None => c (Known ()) | Some _ => No_value)"
45450
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   566
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   567
definition pos_bound_cps_not :: "unit neg_bound_cps => unit pos_bound_cps"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   568
where
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   569
  "pos_bound_cps_not n = (%c i. case n (%u. Value []) i of No_value => c () | Value _ => None | Unknown_value => None)"
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   570
45925
cd4243c025bb quickcheck generators for abstract types; tuned
bulwahn
parents: 45818
diff changeset
   571
subsection {* Defining generators for any first-order data type *}
40420
552563ea3304 adding code and theory for smallvalue generators, but do not setup the interpretation yet
bulwahn
parents:
diff changeset
   572
45697
3b7c35a08723 more stable introduction of the internally used unknown term
bulwahn
parents: 45684
diff changeset
   573
axiomatization unknown :: 'a
3b7c35a08723 more stable introduction of the internally used unknown term
bulwahn
parents: 45684
diff changeset
   574
3b7c35a08723 more stable introduction of the internally used unknown term
bulwahn
parents: 45684
diff changeset
   575
notation (output) unknown  ("?")
45684
3d6ee9c7d7ef adding a exception-safe term reification step in quickcheck; adding examples
bulwahn
parents: 45450
diff changeset
   576
 
48891
c0eafbd55de3 prefer ML_file over old uses;
wenzelm
parents: 47203
diff changeset
   577
ML_file "Tools/Quickcheck/exhaustive_generators.ML"
40420
552563ea3304 adding code and theory for smallvalue generators, but do not setup the interpretation yet
bulwahn
parents:
diff changeset
   578
41918
d2ab869f8b0b replacing naming of small by exhaustive
bulwahn
parents: 41916
diff changeset
   579
setup {* Exhaustive_Generators.setup *}
40420
552563ea3304 adding code and theory for smallvalue generators, but do not setup the interpretation yet
bulwahn
parents:
diff changeset
   580
43882
05d5696f177f renaming quickcheck_tester to quickcheck_batch_tester; tuned
bulwahn
parents: 42310
diff changeset
   581
declare [[quickcheck_batch_tester = exhaustive]]
40915
a4c956d1f91f declaring quickcheck testers as default after their setup
bulwahn
parents: 40914
diff changeset
   582
45925
cd4243c025bb quickcheck generators for abstract types; tuned
bulwahn
parents: 45818
diff changeset
   583
subsection {* Defining generators for abstract types *}
cd4243c025bb quickcheck generators for abstract types; tuned
bulwahn
parents: 45818
diff changeset
   584
48891
c0eafbd55de3 prefer ML_file over old uses;
wenzelm
parents: 47203
diff changeset
   585
ML_file "Tools/Quickcheck/abstract_generators.ML"
45925
cd4243c025bb quickcheck generators for abstract types; tuned
bulwahn
parents: 45818
diff changeset
   586
47203
ac625d8346b2 hiding fact not so aggressively
bulwahn
parents: 46950
diff changeset
   587
hide_fact (open) orelse_def
41105
a76ee71c3313 adding check_all instances for a few more finite types in smallcheck
bulwahn
parents: 41104
diff changeset
   588
no_notation orelse (infixr "orelse" 55)
45818
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   589
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   590
hide_fact
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   591
  exhaustive'_def
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   592
  exhaustive_code_numeral'_def
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   593
46307
ec8f975c059b shortened definitions by adding some termify constants
bulwahn
parents: 46305
diff changeset
   594
hide_const valtermify_absdummy valtermify_fun_upd valterm_emptyset valtermify_insert valtermify_pair
ec8f975c059b shortened definitions by adding some termify constants
bulwahn
parents: 46305
diff changeset
   595
  valtermify_Inl valtermify_Inr
ec8f975c059b shortened definitions by adding some termify constants
bulwahn
parents: 46305
diff changeset
   596
  termify_fun_upd term_emptyset termify_insert termify_pair setify
46305
8ea02e499d53 adding check_all instance for sets; tuned
bulwahn
parents: 46193
diff changeset
   597
45818
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   598
hide_const (open)
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   599
  exhaustive full_exhaustive exhaustive' exhaustive_code_numeral' full_exhaustive_code_numeral'
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   600
  throw_Counterexample catch_Counterexample
53a697f5454a hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents: 45750
diff changeset
   601
  check_all enum_term_of
46305
8ea02e499d53 adding check_all instance for sets; tuned
bulwahn
parents: 46193
diff changeset
   602
  orelse unknown mk_map_term check_all_n_lists check_all_subsets
40420
552563ea3304 adding code and theory for smallvalue generators, but do not setup the interpretation yet
bulwahn
parents:
diff changeset
   603
45450
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   604
hide_type (open) cps pos_bound_cps neg_bound_cps unknown three_valued
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   605
hide_const (open) cps_empty cps_single cps_bind cps_plus cps_if cps_not
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   606
  pos_bound_cps_empty pos_bound_cps_single pos_bound_cps_bind pos_bound_cps_plus pos_bound_cps_if pos_bound_cps_not
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   607
  neg_bound_cps_empty neg_bound_cps_single neg_bound_cps_bind neg_bound_cps_plus neg_bound_cps_if neg_bound_cps_not
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   608
  Unknown Known Unknown_value Value No_value
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   609
dc2236b19a3d adding CPS compilation to predicate compiler;
bulwahn
parents: 43882
diff changeset
   610
end