author  wenzelm 
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permissions  rwrr 
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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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uses 
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("Tools/Quickcheck/exhaustive_generators.ML") 

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("Tools/Quickcheck/abstract_generators.ML") 

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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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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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"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 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" 
247 
where 

248 
"check_all_subsets f [] = f valterm_emptyset" 

249 
 "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" 

250 

251 

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definition (in term_syntax) [code_unfold]: "term_emptyset = Code_Evaluation.termify ({} :: ('a :: typerep) set)" 

253 
definition (in term_syntax) [code_unfold]: "termify_insert x s = Code_Evaluation.termify (insert :: ('a::typerep) => 'a set => 'a set) <\<cdot>> x <\<cdot>> s" 

254 

255 
definition (in term_syntax) setify :: "('a::typerep) itself => term list => term" 

256 
where 

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"setify T ts = foldr (termify_insert T) ts (term_emptyset T)" 

258 

259 
instantiation set :: (check_all) check_all 

260 
begin 

261 

262 
definition 

263 
"check_all_set f = 

264 
check_all_subsets f (zip (Enum.enum :: 'a list) (map (%a. %u :: unit. a) (Quickcheck_Exhaustive.enum_term_of (TYPE ('a)) ())))" 

265 

266 
definition enum_term_of_set :: "'a set itself => unit => term list" 

267 
where 

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"enum_term_of_set _ _ = map (setify (TYPE('a))) (sublists (Quickcheck_Exhaustive.enum_term_of (TYPE('a)) ()))" 

269 

270 
instance .. 

271 

272 
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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325 

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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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328 

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definition enum_term_of_sum :: "('a + 'b) itself => unit => term list" 
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330 
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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335 
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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341 
(enum_term_of (TYPE('b)) ()))" 
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342 

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343 
instance .. 
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344 

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end 
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346 

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instantiation nibble :: check_all 
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begin 
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349 

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350 
definition 
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"check_all f = 
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f (Code_Evaluation.valtermify Nibble0) orelse 
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353 
f (Code_Evaluation.valtermify Nibble1) orelse 
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f (Code_Evaluation.valtermify Nibble2) orelse 
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355 
f (Code_Evaluation.valtermify Nibble3) orelse 
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356 
f (Code_Evaluation.valtermify Nibble4) orelse 
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357 
f (Code_Evaluation.valtermify Nibble5) orelse 
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358 
f (Code_Evaluation.valtermify Nibble6) orelse 
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359 
f (Code_Evaluation.valtermify Nibble7) orelse 
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360 
f (Code_Evaluation.valtermify Nibble8) orelse 
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361 
f (Code_Evaluation.valtermify Nibble9) orelse 
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362 
f (Code_Evaluation.valtermify NibbleA) orelse 
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363 
f (Code_Evaluation.valtermify NibbleB) orelse 
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364 
f (Code_Evaluation.valtermify NibbleC) orelse 
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365 
f (Code_Evaluation.valtermify NibbleD) orelse 
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366 
f (Code_Evaluation.valtermify NibbleE) orelse 
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367 
f (Code_Evaluation.valtermify NibbleF)" 
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368 

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369 
definition enum_term_of_nibble :: "nibble itself => unit => term list" 
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370 
where 
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"enum_term_of_nibble = (%_ _. map Code_Evaluation.term_of (Enum.enum :: nibble list))" 
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372 

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373 
instance .. 
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374 

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375 
end 
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376 

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377 

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378 
instantiation char :: check_all 
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379 
begin 
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380 

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381 
definition 
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382 
"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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383 

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384 
definition enum_term_of_char :: "char itself => unit => term list" 
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385 
where 
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386 
"enum_term_of_char = (%_ _. map Code_Evaluation.term_of (Enum.enum :: char list))" 
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387 

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388 
instance .. 
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389 

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390 
end 
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391 

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392 

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393 
instantiation option :: (check_all) check_all 
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394 
begin 
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395 

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396 
definition 
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397 
"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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398 
(Code_Evaluation.Const (STR ''Option.option.Some'') 
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399 
(Typerep.Typerep (STR ''fun'') [Typerep.typerep TYPE('a), Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]])) (t ())))" 
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400 

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401 
definition enum_term_of_option :: "'a option itself => unit => term list" 
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402 
where 
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403 
"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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404 
(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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405 

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406 
instance .. 
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407 

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408 
end 
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409 

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410 

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411 
instantiation Enum.finite_1 :: check_all 
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412 
begin 
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413 

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414 
definition 
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415 
"check_all f = f (Code_Evaluation.valtermify Enum.finite_1.a\<^isub>1)" 
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416 

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417 
definition enum_term_of_finite_1 :: "Enum.finite_1 itself => unit => term list" 
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418 
where 
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419 
"enum_term_of_finite_1 = (%_ _. [Code_Evaluation.term_of Enum.finite_1.a\<^isub>1])" 
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420 

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421 
instance .. 
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422 

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423 
end 
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424 

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425 
instantiation Enum.finite_2 :: check_all 
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426 
begin 
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427 

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428 
definition 
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429 
"check_all f = (f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>1) 
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430 
orelse f (Code_Evaluation.valtermify Enum.finite_2.a\<^isub>2))" 
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431 

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432 
definition enum_term_of_finite_2 :: "Enum.finite_2 itself => unit => term list" 
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433 
where 
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434 
"enum_term_of_finite_2 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_2 list))" 
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435 

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436 
instance .. 
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437 

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438 
end 
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439 

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440 
instantiation Enum.finite_3 :: check_all 
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441 
begin 
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442 

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443 
definition 
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444 
"check_all f = (f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>1) 
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445 
orelse f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>2) 
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446 
orelse f (Code_Evaluation.valtermify Enum.finite_3.a\<^isub>3))" 
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447 

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448 
definition enum_term_of_finite_3 :: "Enum.finite_3 itself => unit => term list" 
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449 
where 
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450 
"enum_term_of_finite_3 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_3 list))" 
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451 

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452 
instance .. 
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453 

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454 
end 
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455 

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456 
instantiation Enum.finite_4 :: check_all 
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457 
begin 
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458 

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459 
definition 
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460 
"check_all f = (f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>1) 
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461 
orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>2) 
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462 
orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>3) 
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463 
orelse f (Code_Evaluation.valtermify Enum.finite_4.a\<^isub>4))" 
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464 

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465 
definition enum_term_of_finite_4 :: "Enum.finite_4 itself => unit => term list" 
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466 
where 
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467 
"enum_term_of_finite_4 = (%_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_4 list))" 
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468 

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469 
instance .. 
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470 

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471 
end 
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472 

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473 
subsection {* Bounded universal quantifiers *} 
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474 

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475 
class bounded_forall = 
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476 
fixes bounded_forall :: "('a \<Rightarrow> bool) \<Rightarrow> code_numeral \<Rightarrow> bool" 
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477 

42305
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478 
subsection {* Fast exhaustive combinators *} 
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479 

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480 
class fast_exhaustive = term_of + 
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481 
fixes fast_exhaustive :: "('a \<Rightarrow> unit) \<Rightarrow> code_numeral \<Rightarrow> unit" 
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482 

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483 
axiomatization throw_Counterexample :: "term list => unit" 
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484 
axiomatization catch_Counterexample :: "unit => term list option" 
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485 

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486 
code_const throw_Counterexample 
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487 
(Quickcheck "raise (Exhaustive'_Generators.Counterexample _)") 
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488 
code_const catch_Counterexample 
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489 
(Quickcheck "(((_); NONE) handle Exhaustive'_Generators.Counterexample ts => SOME ts)") 
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490 

45450  491 
subsection {* Continuation passing style functions as plus monad *} 
492 

493 
type_synonym 'a cps = "('a => term list option) => term list option" 

494 

495 
definition cps_empty :: "'a cps" 

496 
where 

497 
"cps_empty = (%cont. None)" 

498 

499 
definition cps_single :: "'a => 'a cps" 

500 
where 

501 
"cps_single v = (%cont. cont v)" 

502 

503 
definition cps_bind :: "'a cps => ('a => 'b cps) => 'b cps" 

504 
where 

505 
"cps_bind m f = (%cont. m (%a. (f a) cont))" 

506 

507 
definition cps_plus :: "'a cps => 'a cps => 'a cps" 

508 
where 

509 
"cps_plus a b = (%c. case a c of None => b c  Some x => Some x)" 

510 

511 
definition cps_if :: "bool => unit cps" 

512 
where 

513 
"cps_if b = (if b then cps_single () else cps_empty)" 

514 

515 
definition cps_not :: "unit cps => unit cps" 

516 
where 

517 
"cps_not n = (%c. case n (%u. Some []) of None => c ()  Some _ => None)" 

518 

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519 
type_synonym 'a pos_bound_cps = "('a => (bool * term list) option) => code_numeral => (bool * term list) option" 
45450  520 

521 
definition pos_bound_cps_empty :: "'a pos_bound_cps" 

522 
where 

523 
"pos_bound_cps_empty = (%cont i. None)" 

524 

525 
definition pos_bound_cps_single :: "'a => 'a pos_bound_cps" 

526 
where 

527 
"pos_bound_cps_single v = (%cont i. cont v)" 

528 

529 
definition pos_bound_cps_bind :: "'a pos_bound_cps => ('a => 'b pos_bound_cps) => 'b pos_bound_cps" 

530 
where 

531 
"pos_bound_cps_bind m f = (%cont i. if i = 0 then None else (m (%a. (f a) cont i) (i  1)))" 

532 

533 
definition pos_bound_cps_plus :: "'a pos_bound_cps => 'a pos_bound_cps => 'a pos_bound_cps" 

534 
where 

535 
"pos_bound_cps_plus a b = (%c i. case a c i of None => b c i  Some x => Some x)" 

536 

537 
definition pos_bound_cps_if :: "bool => unit pos_bound_cps" 

538 
where 

539 
"pos_bound_cps_if b = (if b then pos_bound_cps_single () else pos_bound_cps_empty)" 

540 

541 
datatype 'a unknown = Unknown  Known 'a 

542 
datatype 'a three_valued = Unknown_value  Value 'a  No_value 

543 

544 
type_synonym 'a neg_bound_cps = "('a unknown => term list three_valued) => code_numeral => term list three_valued" 

545 

546 
definition neg_bound_cps_empty :: "'a neg_bound_cps" 

547 
where 

548 
"neg_bound_cps_empty = (%cont i. No_value)" 

549 

550 
definition neg_bound_cps_single :: "'a => 'a neg_bound_cps" 

551 
where 

552 
"neg_bound_cps_single v = (%cont i. cont (Known v))" 

553 

554 
definition neg_bound_cps_bind :: "'a neg_bound_cps => ('a => 'b neg_bound_cps) => 'b neg_bound_cps" 

555 
where 

556 
"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))" 

557 

558 
definition neg_bound_cps_plus :: "'a neg_bound_cps => 'a neg_bound_cps => 'a neg_bound_cps" 

559 
where 

560 
"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))" 

561 

562 
definition neg_bound_cps_if :: "bool => unit neg_bound_cps" 

563 
where 

564 
"neg_bound_cps_if b = (if b then neg_bound_cps_single () else neg_bound_cps_empty)" 

565 

566 
definition neg_bound_cps_not :: "unit pos_bound_cps => unit neg_bound_cps" 

567 
where 

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568 
"neg_bound_cps_not n = (%c i. case n (%u. Some (True, [])) i of None => c (Known ())  Some _ => No_value)" 
45450  569 

570 
definition pos_bound_cps_not :: "unit neg_bound_cps => unit pos_bound_cps" 

571 
where 

572 
"pos_bound_cps_not n = (%c i. case n (%u. Value []) i of No_value => c ()  Value _ => None  Unknown_value => None)" 

573 

45925  574 
subsection {* Defining generators for any firstorder data type *} 
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575 

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576 
axiomatization unknown :: 'a 
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577 

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578 
notation (output) unknown ("?") 
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579 

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580 
use "Tools/Quickcheck/exhaustive_generators.ML" 
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581 

41918  582 
setup {* Exhaustive_Generators.setup *} 
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583 

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584 
declare [[quickcheck_batch_tester = exhaustive]] 
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585 

45925  586 
subsection {* Defining generators for abstract types *} 
587 

588 
use "Tools/Quickcheck/abstract_generators.ML" 

589 

47203  590 
hide_fact (open) orelse_def 
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591 
no_notation orelse (infixr "orelse" 55) 
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592 

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593 
hide_fact 
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594 
exhaustive'_def 
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595 
exhaustive_code_numeral'_def 
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596 

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597 
hide_const valtermify_absdummy valtermify_fun_upd valterm_emptyset valtermify_insert valtermify_pair 
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598 
valtermify_Inl valtermify_Inr 
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599 
termify_fun_upd term_emptyset termify_insert termify_pair setify 
46305  600 

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601 
hide_const (open) 
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602 
exhaustive full_exhaustive exhaustive' exhaustive_code_numeral' full_exhaustive_code_numeral' 
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603 
throw_Counterexample catch_Counterexample 
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604 
check_all enum_term_of 
46305  605 
orelse unknown mk_map_term check_all_n_lists check_all_subsets 
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606 

45450  607 
hide_type (open) cps pos_bound_cps neg_bound_cps unknown three_valued 
608 
hide_const (open) cps_empty cps_single cps_bind cps_plus cps_if cps_not 

609 
pos_bound_cps_empty pos_bound_cps_single pos_bound_cps_bind pos_bound_cps_plus pos_bound_cps_if pos_bound_cps_not 

610 
neg_bound_cps_empty neg_bound_cps_single neg_bound_cps_bind neg_bound_cps_plus neg_bound_cps_if neg_bound_cps_not 

611 
Unknown Known Unknown_value Value No_value 

612 

613 
end 