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(* Title: HOL/Quickcheck_Exhaustive.thy 
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Author: Lukas Bulwahn, TU Muenchen 

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*) 

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section \<open>A simple counterexample generator performing exhaustive testing\<close> 
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theory Quickcheck_Exhaustive 
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imports Quickcheck_Random 
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keywords "quickcheck_generator" :: thy_decl 
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begin 
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subsection \<open>Basic operations for exhaustive generators\<close> 
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definition orelse :: "'a option \<Rightarrow> 'a option \<Rightarrow> 'a option" (infixr "orelse" 55) 
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where [code_unfold]: "x orelse y = (case x of Some x' \<Rightarrow> Some x'  None \<Rightarrow> y)" 

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subsection \<open>Exhaustive generator type classes\<close> 

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class exhaustive = term_of + 
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fixes exhaustive :: "('a \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> natural \<Rightarrow> (bool \<times> term list) option" 
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class full_exhaustive = term_of + 
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fixes full_exhaustive :: 
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"('a \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> natural \<Rightarrow> (bool \<times> term list) option" 

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instantiation natural :: full_exhaustive 
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begin 
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function full_exhaustive_natural' :: 
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"(natural \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> 

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natural \<Rightarrow> natural \<Rightarrow> (bool \<times> term list) option" 

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where "full_exhaustive_natural' f d i = 
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(if d < i then None 
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else (f (i, \<lambda>_. Code_Evaluation.term_of i)) orelse (full_exhaustive_natural' f d (i + 1)))" 
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by pat_completeness auto 
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termination 

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by (relation "measure (\<lambda>(_, d, i). nat_of_natural (d + 1  i))") (auto simp add: less_natural_def) 
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definition "full_exhaustive f d = full_exhaustive_natural' f d 0" 
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instance .. 
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end 
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instantiation natural :: exhaustive 
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begin 
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function exhaustive_natural' :: 
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"(natural \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> natural \<Rightarrow> natural \<Rightarrow> (bool \<times> term list) option" 

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where "exhaustive_natural' f d i = 
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(if d < i then None 
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else (f i orelse exhaustive_natural' f d (i + 1)))" 
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by pat_completeness auto 
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termination 
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by (relation "measure (\<lambda>(_, d, i). nat_of_natural (d + 1  i))") (auto simp add: less_natural_def) 
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definition "exhaustive f d = exhaustive_natural' f d 0" 
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instance .. 
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end 
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instantiation integer :: exhaustive 
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begin 
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function exhaustive_integer' :: 
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"(integer \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> integer \<Rightarrow> integer \<Rightarrow> (bool \<times> term list) option" 

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where "exhaustive_integer' f d i = 

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(if d < i then None else (f i orelse exhaustive_integer' f d (i + 1)))" 

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by pat_completeness auto 
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termination 
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by (relation "measure (\<lambda>(_, d, i). nat_of_integer (d + 1  i))") 

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(auto simp add: less_integer_def nat_of_integer_def) 
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definition "exhaustive f d = exhaustive_integer' f (integer_of_natural d) ( (integer_of_natural d))" 
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instance .. 
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end 
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instantiation integer :: full_exhaustive 
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begin 
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function full_exhaustive_integer' :: 
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"(integer \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> 

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integer \<Rightarrow> integer \<Rightarrow> (bool \<times> term list) option" 

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where "full_exhaustive_integer' f d i = 

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(if d < i then None 

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else 

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(case f (i, \<lambda>_. Code_Evaluation.term_of i) of 

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Some t \<Rightarrow> Some t 

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 None \<Rightarrow> full_exhaustive_integer' f d (i + 1)))" 

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by pat_completeness auto 
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termination 
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by (relation "measure (\<lambda>(_, d, i). nat_of_integer (d + 1  i))") 

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(auto simp add: less_integer_def nat_of_integer_def) 
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definition "full_exhaustive f d = 
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full_exhaustive_integer' f (integer_of_natural d) ( (integer_of_natural d))" 

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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 (\<lambda>x. f (nat_of_natural 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 = 
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full_exhaustive (\<lambda>(x, xt). f (nat_of_natural x, \<lambda>_. Code_Evaluation.term_of (nat_of_natural 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' :: 
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"(int \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> int \<Rightarrow> int \<Rightarrow> (bool \<times> term list) option" 

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where "exhaustive_int' f d i = 

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(if d < i then None else (f i orelse exhaustive_int' f d (i + 1)))" 

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by pat_completeness auto 
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termination 
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by (relation "measure (\<lambda>(_, d, i). nat (d + 1  i))") auto 

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definition "exhaustive f d = 
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exhaustive_int' f (int_of_integer (integer_of_natural d)) 

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( (int_of_integer (integer_of_natural 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' :: 
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"(int \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> 

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int \<Rightarrow> int \<Rightarrow> (bool \<times> term list) option" 

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where "full_exhaustive_int' f d i = 

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(if d < i then None 

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else 

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(case f (i, \<lambda>_. Code_Evaluation.term_of i) of 

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Some t \<Rightarrow> Some t 

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 None \<Rightarrow> full_exhaustive_int' f d (i + 1)))" 

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by pat_completeness auto 
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termination 
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by (relation "measure (\<lambda>(_, d, i). nat (d + 1  i))") auto 

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definition "full_exhaustive f d = 
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full_exhaustive_int' f (int_of_integer (integer_of_natural d)) 

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( (int_of_integer (integer_of_natural 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 "exhaustive f d = exhaustive (\<lambda>x. exhaustive (\<lambda>y. f ((x, y))) d) d" 
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instance .. 
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end 
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definition (in term_syntax) 
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[code_unfold]: "valtermify_pair x y = 

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Code_Evaluation.valtermify (Pair :: 'a::typerep \<Rightarrow> 'b::typerep \<Rightarrow> 'a \<times> '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 "full_exhaustive f d = 
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full_exhaustive (\<lambda>x. full_exhaustive (\<lambda>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 
62979  202 
"exhaustive_set f i = 
203 
(if i = 0 then None 

204 
else 

205 
f {} orelse 

206 
exhaustive_set 

207 
(\<lambda>A. f A orelse exhaustive (\<lambda>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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62979  216 
fun full_exhaustive_set 
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where 
62979  218 
"full_exhaustive_set f i = 
219 
(if i = 0 then None 

220 
else 

221 
f valterm_emptyset orelse 

222 
full_exhaustive_set 

223 
(\<lambda>A. f A orelse Quickcheck_Exhaustive.full_exhaustive 

224 
(\<lambda>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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62979  230 
instantiation "fun" :: ("{equal,exhaustive}", exhaustive) exhaustive 
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begin 
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62979  233 
fun exhaustive_fun' :: 
234 
"(('a \<Rightarrow> 'b) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> natural \<Rightarrow> natural \<Rightarrow> (bool \<times> term list) option" 

42304  235 
where 
62979  236 
"exhaustive_fun' f i d = 
237 
(exhaustive (\<lambda>b. f (\<lambda>_. b)) d) orelse 

238 
(if i > 1 then 

239 
exhaustive_fun' 

240 
(\<lambda>g. exhaustive (\<lambda>a. exhaustive (\<lambda>b. f (g(a := b))) d) d) (i  1) d else None)" 

42304  241 

62979  242 
definition exhaustive_fun :: 
243 
"(('a \<Rightarrow> 'b) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> natural \<Rightarrow> (bool \<times> term list) option" 

244 
where "exhaustive_fun f d = exhaustive_fun' f d d" 

42304  245 

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instance .. 
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end 
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62979  250 
definition [code_unfold]: 
251 
"valtermify_absdummy = 

252 
(\<lambda>(v, t). 

253 
(\<lambda>_::'a. v, 

254 
\<lambda>u::unit. Code_Evaluation.Abs (STR ''x'') (Typerep.typerep TYPE('a::typerep)) (t ())))" 

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62979  256 
definition (in term_syntax) 
257 
[code_unfold]: "valtermify_fun_upd g a b = 

258 
Code_Evaluation.valtermify 

259 
(fun_upd :: ('a::typerep \<Rightarrow> 'b::typerep) \<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> 'a \<Rightarrow> 'b) {\<cdot>} g {\<cdot>} a {\<cdot>} b" 

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62979  261 
instantiation "fun" :: ("{equal,full_exhaustive}", full_exhaustive) full_exhaustive 
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begin 
42304  263 

62979  264 
fun full_exhaustive_fun' :: 
265 
"(('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> 

266 
natural \<Rightarrow> natural \<Rightarrow> (bool \<times> term list) option" 

42304  267 
where 
62979  268 
"full_exhaustive_fun' f i d = 
269 
full_exhaustive (\<lambda>v. f (valtermify_absdummy v)) d orelse 

270 
(if i > 1 then 

271 
full_exhaustive_fun' 

272 
(\<lambda>g. full_exhaustive 

273 
(\<lambda>a. full_exhaustive (\<lambda>b. f (valtermify_fun_upd g a b)) d) d) (i  1) d 

274 
else None)" 

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62979  276 
definition full_exhaustive_fun :: 
277 
"(('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> 

278 
natural \<Rightarrow> (bool \<times> term list) option" 

279 
where "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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60758  285 
subsubsection \<open>A smarter enumeration scheme for functions over finite datatypes\<close> 
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class check_all = enum + term_of + 
62979  288 
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fixes enum_term_of :: "'a itself \<Rightarrow> unit \<Rightarrow> term list" 
62979  290 

291 
fun check_all_n_lists :: "('a::check_all list \<times> (unit \<Rightarrow> term list) \<Rightarrow> 

292 
(bool \<times> term list) option) \<Rightarrow> natural \<Rightarrow> (bool * term list) option" 

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where 
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"check_all_n_lists f n = 
62979  295 
(if n = 0 then f ([], (\<lambda>_. [])) 
296 
else check_all (\<lambda>(x, xt). 

297 
check_all_n_lists (\<lambda>(xs, xst). f ((x # xs), (\<lambda>_. (xt () # xst ())))) (n  1)))" 

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62979  299 
definition (in term_syntax) 
300 
[code_unfold]: "termify_fun_upd g a b = 

301 
(Code_Evaluation.termify 

302 
(fun_upd :: ('a::typerep \<Rightarrow> 'b::typerep) \<Rightarrow> 'a \<Rightarrow> 'b \<Rightarrow> 'a \<Rightarrow> 'b) <\<cdot>> g <\<cdot>> a <\<cdot>> b)" 

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62979  304 
definition mk_map_term :: 
305 
"(unit \<Rightarrow> typerep) \<Rightarrow> (unit \<Rightarrow> typerep) \<Rightarrow> 

306 
(unit \<Rightarrow> term list) \<Rightarrow> (unit \<Rightarrow> term list) \<Rightarrow> unit \<Rightarrow> term" 

307 
where "mk_map_term T1 T2 domm rng = 

308 
(\<lambda>_. 

309 
let 

310 
T1 = T1 (); 

311 
T2 = T2 (); 

312 
update_term = 

313 
(\<lambda>g (a, b). 

314 
Code_Evaluation.App (Code_Evaluation.App (Code_Evaluation.App 

315 
(Code_Evaluation.Const (STR ''Fun.fun_upd'') 

316 
(Typerep.Typerep (STR ''fun'') [Typerep.Typerep (STR ''fun'') [T1, T2], 

317 
Typerep.Typerep (STR ''fun'') [T1, 

318 
Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''fun'') [T1, T2]]]])) 

319 
g) a) b) 

320 
in 

321 
List.foldl update_term 

322 
(Code_Evaluation.Abs (STR ''x'') T1 

323 
(Code_Evaluation.Const (STR ''HOL.undefined'') T2)) (zip (domm ()) (rng ())))" 

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62979  325 
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 
62979  331 
mk_term = 
332 
mk_map_term 

333 
(\<lambda>_. Typerep.typerep (TYPE('a))) 

334 
(\<lambda>_. Typerep.typerep (TYPE('b))) 

335 
(enum_term_of (TYPE('a))); 

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enum = (Enum.enum :: 'a list) 
62979  337 
in 
338 
check_all_n_lists 

339 
(\<lambda>(ys, yst). f (the o map_of (zip enum ys), mk_term yst)) 

340 
(natural_of_nat (length enum)))" 

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62979  342 
definition enum_term_of_fun :: "('a \<Rightarrow> 'b) itself \<Rightarrow> unit \<Rightarrow> term list" 
343 
where "enum_term_of_fun = 

344 
(\<lambda>_ _. 

345 
let 

346 
enum_term_of_a = enum_term_of (TYPE('a)); 

347 
mk_term = 

348 
mk_map_term 

349 
(\<lambda>_. Typerep.typerep (TYPE('a))) 

350 
(\<lambda>_. Typerep.typerep (TYPE('b))) 

351 
enum_term_of_a 

352 
in 

353 
map (\<lambda>ys. mk_term (\<lambda>_. ys) ()) 

354 
(List.n_lists (length (enum_term_of_a ())) (enum_term_of (TYPE('b)) ())))" 

355 

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356 
instance .. 
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358 
end 
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359 

62979  360 
fun (in term_syntax) check_all_subsets :: 
361 
"(('a::typerep) set \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> 

362 
('a \<times> (unit \<Rightarrow> term)) list \<Rightarrow> (bool \<times> term list) option" 

46305  363 
where 
364 
"check_all_subsets f [] = f valterm_emptyset" 

62979  365 
 "check_all_subsets f (x # xs) = 
366 
check_all_subsets (\<lambda>s. case f s of Some ts \<Rightarrow> Some ts  None \<Rightarrow> f (valtermify_insert x s)) xs" 

46305  367 

368 

62979  369 
definition (in term_syntax) 
370 
[code_unfold]: "term_emptyset = Code_Evaluation.termify ({} :: ('a::typerep) set)" 

46305  371 

62979  372 
definition (in term_syntax) 
373 
[code_unfold]: "termify_insert x s = 

374 
Code_Evaluation.termify (insert :: ('a::typerep) \<Rightarrow> 'a set \<Rightarrow> 'a set) <\<cdot>> x <\<cdot>> s" 

375 

376 
definition (in term_syntax) setify :: "('a::typerep) itself \<Rightarrow> term list \<Rightarrow> term" 

46305  377 
where 
62979  378 
"setify T ts = foldr (termify_insert T) ts (term_emptyset T)" 
46305  379 

380 
instantiation set :: (check_all) check_all 

381 
begin 

382 

383 
definition 

384 
"check_all_set f = 

62979  385 
check_all_subsets f 
386 
(zip (Enum.enum :: 'a list) 

387 
(map (\<lambda>a. \<lambda>u :: unit. a) (Quickcheck_Exhaustive.enum_term_of (TYPE ('a)) ())))" 

46305  388 

62979  389 
definition enum_term_of_set :: "'a set itself \<Rightarrow> unit \<Rightarrow> term list" 
390 
where "enum_term_of_set _ _ = 

391 
map (setify (TYPE('a))) (sublists (Quickcheck_Exhaustive.enum_term_of (TYPE('a)) ()))" 

46305  392 

393 
instance .. 

394 

395 
end 

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396 

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397 
instantiation unit :: check_all 
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398 
begin 
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399 

62979  400 
definition "check_all f = f (Code_Evaluation.valtermify ())" 
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401 

62979  402 
definition enum_term_of_unit :: "unit itself \<Rightarrow> unit \<Rightarrow> term list" 
403 
where "enum_term_of_unit = (\<lambda>_ _. [Code_Evaluation.term_of ()])" 

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404 

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405 
instance .. 
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406 

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407 
end 
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408 

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409 

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410 
instantiation bool :: check_all 
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411 
begin 
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412 

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definition 
62979  414 
"check_all f = 
415 
(case f (Code_Evaluation.valtermify False) of 

416 
Some x' \<Rightarrow> Some x' 

417 
 None \<Rightarrow> f (Code_Evaluation.valtermify True))" 

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418 

62979  419 
definition enum_term_of_bool :: "bool itself \<Rightarrow> unit \<Rightarrow> term list" 
420 
where "enum_term_of_bool = (\<lambda>_ _. map Code_Evaluation.term_of (Enum.enum :: bool list))" 

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421 

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422 
instance .. 
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423 

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424 
end 
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425 

62979  426 
definition (in term_syntax) [code_unfold]: 
427 
"termify_pair x y = 

428 
Code_Evaluation.termify (Pair :: 'a::typerep \<Rightarrow> 'b :: typerep \<Rightarrow> 'a * 'b) <\<cdot>> x <\<cdot>> y" 

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429 

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430 
instantiation prod :: (check_all, check_all) check_all 
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431 
begin 
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432 

62979  433 
definition "check_all f = check_all (\<lambda>x. check_all (\<lambda>y. f (valtermify_pair x y)))" 
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434 

62979  435 
definition enum_term_of_prod :: "('a * 'b) itself \<Rightarrow> unit \<Rightarrow> term list" 
436 
where "enum_term_of_prod = 

437 
(\<lambda>_ _. 

438 
map (\<lambda>(x, y). termify_pair TYPE('a) TYPE('b) x y) 

439 
(List.product (enum_term_of (TYPE('a)) ()) (enum_term_of (TYPE('b)) ())))" 

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440 

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441 
instance .. 
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442 

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443 
end 
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444 

62979  445 
definition (in term_syntax) 
446 
[code_unfold]: "valtermify_Inl x = 

447 
Code_Evaluation.valtermify (Inl :: 'a::typerep \<Rightarrow> 'a + 'b :: typerep) {\<cdot>} x" 

448 

449 
definition (in term_syntax) 

450 
[code_unfold]: "valtermify_Inr x = 

451 
Code_Evaluation.valtermify (Inr :: 'b::typerep \<Rightarrow> 'a::typerep + 'b) {\<cdot>} x" 

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452 

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instantiation sum :: (check_all, check_all) check_all 
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454 
begin 
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455 

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456 
definition 
62979  457 
"check_all f = check_all (\<lambda>a. f (valtermify_Inl a)) orelse check_all (\<lambda>b. f (valtermify_Inr b))" 
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458 

62979  459 
definition enum_term_of_sum :: "('a + 'b) itself \<Rightarrow> unit \<Rightarrow> term list" 
460 
where "enum_term_of_sum = 

461 
(\<lambda>_ _. 

462 
let 

463 
T1 = Typerep.typerep (TYPE('a)); 

464 
T2 = Typerep.typerep (TYPE('b)) 

465 
in 

466 
map 

467 
(Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inl'') 

468 
(Typerep.Typerep (STR ''fun'') [T1, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]]))) 

469 
(enum_term_of (TYPE('a)) ()) @ 

470 
map 

471 
(Code_Evaluation.App (Code_Evaluation.Const (STR ''Sum_Type.Inr'') 

472 
(Typerep.Typerep (STR ''fun'') [T2, Typerep.Typerep (STR ''Sum_Type.sum'') [T1, T2]]))) 

473 
(enum_term_of (TYPE('b)) ()))" 

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474 

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475 
instance .. 
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476 

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477 
end 
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478 

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479 
instantiation char :: check_all 
41105
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480 
begin 
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481 

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482 
primrec check_all_char' :: 
f77b946d18aa
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483 
"(char \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> char list \<Rightarrow> (bool \<times> term list) option" 
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484 
where "check_all_char' f [] = None" 
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485 
 "check_all_char' f (c # cs) = f (c, \<lambda>_. Code_Evaluation.term_of c) 
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486 
orelse check_all_char' f cs" 
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62979
diff
changeset

487 

f77b946d18aa
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488 
definition check_all_char :: 
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489 
"(char \<times> (unit \<Rightarrow> term) \<Rightarrow> (bool \<times> term list) option) \<Rightarrow> (bool \<times> term list) option" 
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490 
where "check_all f = check_all_char' f Enum.enum" 
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491 

62979  492 
definition enum_term_of_char :: "char itself \<Rightarrow> unit \<Rightarrow> term list" 
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493 
where 
62979  494 
"enum_term_of_char = (\<lambda>_ _. map Code_Evaluation.term_of (Enum.enum :: char list))" 
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changeset

495 

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496 
instance .. 
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497 

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498 
end 
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499 

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500 
instantiation option :: (check_all) check_all 
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501 
begin 
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502 

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503 
definition 
62979  504 
"check_all f = 
505 
f (Code_Evaluation.valtermify (None :: 'a option)) orelse 

506 
check_all 

507 
(\<lambda>(x, t). 

508 
f 

509 
(Some x, 

510 
\<lambda>_. Code_Evaluation.App 

511 
(Code_Evaluation.Const (STR ''Option.option.Some'') 

512 
(Typerep.Typerep (STR ''fun'') 

513 
[Typerep.typerep TYPE('a), 

514 
Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]])) (t ())))" 

41105
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515 

62979  516 
definition enum_term_of_option :: "'a option itself \<Rightarrow> unit \<Rightarrow> term list" 
517 
where "enum_term_of_option = 

518 
(\<lambda> _ _. 

519 
Code_Evaluation.term_of (None :: 'a option) # 

520 
(map 

521 
(Code_Evaluation.App 

522 
(Code_Evaluation.Const (STR ''Option.option.Some'') 

523 
(Typerep.Typerep (STR ''fun'') 

524 
[Typerep.typerep TYPE('a), 

525 
Typerep.Typerep (STR ''Option.option'') [Typerep.typerep TYPE('a)]]))) 

526 
(enum_term_of (TYPE('a)) ())))" 

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527 

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528 
instance .. 
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529 

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530 
end 
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changeset

531 

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changeset

532 

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533 
instantiation Enum.finite_1 :: check_all 
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534 
begin 
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535 

62979  536 
definition "check_all f = f (Code_Evaluation.valtermify Enum.finite_1.a\<^sub>1)" 
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537 

62979  538 
definition enum_term_of_finite_1 :: "Enum.finite_1 itself \<Rightarrow> unit \<Rightarrow> term list" 
539 
where "enum_term_of_finite_1 = (\<lambda>_ _. [Code_Evaluation.term_of Enum.finite_1.a\<^sub>1])" 

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540 

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541 
instance .. 
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542 

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543 
end 
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544 

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545 
instantiation Enum.finite_2 :: check_all 
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546 
begin 
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547 

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548 
definition 
62979  549 
"check_all f = 
550 
(f (Code_Evaluation.valtermify Enum.finite_2.a\<^sub>1) orelse 

551 
f (Code_Evaluation.valtermify Enum.finite_2.a\<^sub>2))" 

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552 

62979  553 
definition enum_term_of_finite_2 :: "Enum.finite_2 itself \<Rightarrow> unit \<Rightarrow> term list" 
554 
where "enum_term_of_finite_2 = 

555 
(\<lambda>_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_2 list))" 

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556 

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557 
instance .. 
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558 

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559 
end 
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560 

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561 
instantiation Enum.finite_3 :: check_all 
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562 
begin 
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563 

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564 
definition 
62979  565 
"check_all f = 
566 
(f (Code_Evaluation.valtermify Enum.finite_3.a\<^sub>1) orelse 

567 
f (Code_Evaluation.valtermify Enum.finite_3.a\<^sub>2) orelse 

568 
f (Code_Evaluation.valtermify Enum.finite_3.a\<^sub>3))" 

41085
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569 

62979  570 
definition enum_term_of_finite_3 :: "Enum.finite_3 itself \<Rightarrow> unit \<Rightarrow> term list" 
571 
where "enum_term_of_finite_3 = 

572 
(\<lambda>_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_3 list))" 

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573 

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574 
instance .. 
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575 

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576 
end 
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changeset

577 

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578 
instantiation Enum.finite_4 :: check_all 
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579 
begin 
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changeset

580 

1a68fcb80b62
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581 
definition 
62979  582 
"check_all f = 
583 
f (Code_Evaluation.valtermify Enum.finite_4.a\<^sub>1) orelse 

584 
f (Code_Evaluation.valtermify Enum.finite_4.a\<^sub>2) orelse 

585 
f (Code_Evaluation.valtermify Enum.finite_4.a\<^sub>3) orelse 

586 
f (Code_Evaluation.valtermify Enum.finite_4.a\<^sub>4)" 

46417
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587 

62979  588 
definition enum_term_of_finite_4 :: "Enum.finite_4 itself \<Rightarrow> unit \<Rightarrow> term list" 
589 
where "enum_term_of_finite_4 = 

590 
(\<lambda>_ _. map Code_Evaluation.term_of (Enum.enum :: Enum.finite_4 list))" 

46417
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591 

1a68fcb80b62
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592 
instance .. 
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changeset

593 

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594 
end 
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595 

60758  596 
subsection \<open>Bounded universal quantifiers\<close> 
41085
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changeset

597 

42195
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changeset

598 
class bounded_forall = 
51143
0a2371e7ced3
two target language numeral types: integer and natural, as replacement for code_numeral;
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599 
fixes bounded_forall :: "('a \<Rightarrow> bool) \<Rightarrow> natural \<Rightarrow> bool" 
42195
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600 

62979  601 

60758  602 
subsection \<open>Fast exhaustive combinators\<close> 
42305
494c31fdec95
theory definitions for fast exhaustive quickcheck compilation
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diff
changeset

603 

494c31fdec95
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604 
class fast_exhaustive = term_of + 
51143
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605 
fixes fast_exhaustive :: "('a \<Rightarrow> unit) \<Rightarrow> natural \<Rightarrow> unit" 
42305
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changeset

606 

62979  607 
axiomatization throw_Counterexample :: "term list \<Rightarrow> unit" 
608 
axiomatization catch_Counterexample :: "unit \<Rightarrow> term list option" 

42305
494c31fdec95
theory definitions for fast exhaustive quickcheck compilation
bulwahn
parents:
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diff
changeset

609 

52435
6646bb548c6b
migration from code_(consttypeclassinstance) to code_printing and from code_module to code_identifier
haftmann
parents:
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diff
changeset

610 
code_printing 
6646bb548c6b
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parents:
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diff
changeset

611 
constant throw_Counterexample \<rightharpoonup> 
6646bb548c6b
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612 
(Quickcheck) "raise (Exhaustive'_Generators.Counterexample _)" 
6646bb548c6b
migration from code_(consttypeclassinstance) to code_printing and from code_module to code_identifier
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613 
 constant catch_Counterexample \<rightharpoonup> 
62979  614 
(Quickcheck) "(((_); NONE) handle Exhaustive'_Generators.Counterexample ts \<Rightarrow> SOME ts)" 
615 

42305
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changeset

616 

60758  617 
subsection \<open>Continuation passing style functions as plus monad\<close> 
62979  618 

619 
type_synonym 'a cps = "('a \<Rightarrow> term list option) \<Rightarrow> term list option" 

45450  620 

621 
definition cps_empty :: "'a cps" 

62979  622 
where "cps_empty = (\<lambda>cont. None)" 
45450  623 

62979  624 
definition cps_single :: "'a \<Rightarrow> 'a cps" 
625 
where "cps_single v = (\<lambda>cont. cont v)" 

45450  626 

62979  627 
definition cps_bind :: "'a cps \<Rightarrow> ('a \<Rightarrow> 'b cps) \<Rightarrow> 'b cps" 
628 
where "cps_bind m f = (\<lambda>cont. m (\<lambda>a. (f a) cont))" 

45450  629 

62979  630 
definition cps_plus :: "'a cps \<Rightarrow> 'a cps \<Rightarrow> 'a cps" 
631 
where "cps_plus a b = (\<lambda>c. case a c of None \<Rightarrow> b c  Some x \<Rightarrow> Some x)" 

632 

633 
definition cps_if :: "bool \<Rightarrow> unit cps" 

634 
where "cps_if b = (if b then cps_single () else cps_empty)" 

45450  635 

62979  636 
definition cps_not :: "unit cps \<Rightarrow> unit cps" 
637 
where "cps_not n = (\<lambda>c. case n (\<lambda>u. Some []) of None \<Rightarrow> c ()  Some _ \<Rightarrow> None)" 

45450  638 

62979  639 
type_synonym 'a pos_bound_cps = 
640 
"('a \<Rightarrow> (bool * term list) option) \<Rightarrow> natural \<Rightarrow> (bool * term list) option" 

45450  641 

642 
definition pos_bound_cps_empty :: "'a pos_bound_cps" 

62979  643 
where "pos_bound_cps_empty = (\<lambda>cont i. None)" 
45450  644 

62979  645 
definition pos_bound_cps_single :: "'a \<Rightarrow> 'a pos_bound_cps" 
646 
where "pos_bound_cps_single v = (\<lambda>cont i. cont v)" 

45450  647 

62979  648 
definition pos_bound_cps_bind :: "'a pos_bound_cps \<Rightarrow> ('a \<Rightarrow> 'b pos_bound_cps) \<Rightarrow> 'b pos_bound_cps" 
649 
where "pos_bound_cps_bind m f = (\<lambda>cont i. if i = 0 then None else (m (\<lambda>a. (f a) cont i) (i  1)))" 

45450  650 

62979  651 
definition pos_bound_cps_plus :: "'a pos_bound_cps \<Rightarrow> 'a pos_bound_cps \<Rightarrow> 'a pos_bound_cps" 
652 
where "pos_bound_cps_plus a b = (\<lambda>c i. case a c i of None \<Rightarrow> b c i  Some x \<Rightarrow> Some x)" 

45450  653 

62979  654 
definition pos_bound_cps_if :: "bool \<Rightarrow> unit pos_bound_cps" 
655 
where "pos_bound_cps_if b = (if b then pos_bound_cps_single () else pos_bound_cps_empty)" 

45450  656 

58350
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changeset

657 
datatype (plugins only: code extraction) (dead 'a) unknown = 
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blanchet
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changeset

658 
Unknown  Known 'a 
919149921e46
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diff
changeset

659 

919149921e46
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diff
changeset

660 
datatype (plugins only: code extraction) (dead 'a) three_valued = 
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blanchet
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58334
diff
changeset

661 
Unknown_value  Value 'a  No_value 
45450  662 

62979  663 
type_synonym 'a neg_bound_cps = 
664 
"('a unknown \<Rightarrow> term list three_valued) \<Rightarrow> natural \<Rightarrow> term list three_valued" 

45450  665 

666 
definition neg_bound_cps_empty :: "'a neg_bound_cps" 

62979  667 
where "neg_bound_cps_empty = (\<lambda>cont i. No_value)" 
668 

669 
definition neg_bound_cps_single :: "'a \<Rightarrow> 'a neg_bound_cps" 

670 
where "neg_bound_cps_single v = (\<lambda>cont i. cont (Known v))" 

45450  671 

62979  672 
definition neg_bound_cps_bind :: "'a neg_bound_cps \<Rightarrow> ('a \<Rightarrow> 'b neg_bound_cps) \<Rightarrow> 'b neg_bound_cps" 
673 
where "neg_bound_cps_bind m f = 

674 
(\<lambda>cont i. 

675 
if i = 0 then cont Unknown 

676 
else m (\<lambda>a. case a of Unknown \<Rightarrow> cont Unknown  Known a' \<Rightarrow> f a' cont i) (i  1))" 

45450  677 

62979  678 
definition neg_bound_cps_plus :: "'a neg_bound_cps \<Rightarrow> 'a neg_bound_cps \<Rightarrow> 'a neg_bound_cps" 
679 
where "neg_bound_cps_plus a b = 

680 
(\<lambda>c i. 

681 
case a c i of 

682 
No_value \<Rightarrow> b c i 

683 
 Value x \<Rightarrow> Value x 

684 
 Unknown_value \<Rightarrow> 

685 
(case b c i of 

686 
No_value \<Rightarrow> Unknown_value 

687 
 Value x \<Rightarrow> Value x 

688 
 Unknown_value \<Rightarrow> Unknown_value))" 

45450  689 

62979  690 
definition neg_bound_cps_if :: "bool \<Rightarrow> unit neg_bound_cps" 
691 
where "neg_bound_cps_if b = (if b then neg_bound_cps_single () else neg_bound_cps_empty)" 

45450  692 

62979  693 
definition neg_bound_cps_not :: "unit pos_bound_cps \<Rightarrow> unit neg_bound_cps" 
694 
where "neg_bound_cps_not n = 

695 
(\<lambda>c i. case n (\<lambda>u. Some (True, [])) i of None \<Rightarrow> c (Known ())  Some _ \<Rightarrow> No_value)" 

696 

697 
definition pos_bound_cps_not :: "unit neg_bound_cps \<Rightarrow> unit pos_bound_cps" 

698 
where "pos_bound_cps_not n = 

699 
(\<lambda>c i. case n (\<lambda>u. Value []) i of No_value \<Rightarrow> c ()  Value _ \<Rightarrow> None  Unknown_value \<Rightarrow> None)" 

700 

45450  701 

60758  702 
subsection \<open>Defining generators for any firstorder data type\<close> 
40420
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adding code and theory for smallvalue generators, but do not setup the interpretation yet
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703 

45697
3b7c35a08723
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diff
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704 
axiomatization unknown :: 'a 
3b7c35a08723
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diff
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705 

3b7c35a08723
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706 
notation (output) unknown ("?") 
51143
0a2371e7ced3
two target language numeral types: integer and natural, as replacement for code_numeral;
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707 

48891  708 
ML_file "Tools/Quickcheck/exhaustive_generators.ML" 
40420
552563ea3304
adding code and theory for smallvalue generators, but do not setup the interpretation yet
bulwahn
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diff
changeset

709 

43882
05d5696f177f
renaming quickcheck_tester to quickcheck_batch_tester; tuned
bulwahn
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42310
diff
changeset

710 
declare [[quickcheck_batch_tester = exhaustive]] 
40915
a4c956d1f91f
declaring quickcheck testers as default after their setup
bulwahn
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40914
diff
changeset

711 

62979  712 

60758  713 
subsection \<open>Defining generators for abstract types\<close> 
45925  714 

48891  715 
ML_file "Tools/Quickcheck/abstract_generators.ML" 
45925  716 

62597  717 
(* FIXME instantiation char :: full_exhaustive 
62364
9209770bdcdf
more direct bootstrap of char type, still retaining the nibble representation for syntax
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718 
begin 
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diff
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719 

9209770bdcdf
more direct bootstrap of char type, still retaining the nibble representation for syntax
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diff
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720 
definition full_exhaustive_char 
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diff
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721 
where 
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722 
"full_exhaustive f i = 
59484
a130ae7a9398
slightly more standard code setup for String.literal, with explicit special case in predicate compiler
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diff
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723 
(if 0 < i then full_exhaustive_class.full_exhaustive 
a130ae7a9398
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724 
(\<lambda>(a, b). full_exhaustive_class.full_exhaustive 
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725 
(\<lambda>(c, d). 
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diff
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726 
f (char_of_nat (nat_of_nibble a * 16 + nat_of_nibble c), 
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727 
\<lambda>_. Code_Evaluation.App (Code_Evaluation.App 
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slightly more standard code setup for String.literal, with explicit special case in predicate compiler
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728 
(Code_Evaluation.Const (STR ''String.char.Char'') 
a130ae7a9398
slightly more standard code setup for String.literal, with explicit special case in predicate compiler
haftmann
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diff
changeset

729 
(TYPEREP(nibble \<Rightarrow> nibble \<Rightarrow> char))) 
a130ae7a9398
slightly more standard code setup for String.literal, with explicit special case in predicate compiler
haftmann
parents:
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diff
changeset

730 
(b ())) (d ()))) (i  1)) (i  1) 
a130ae7a9398
slightly more standard code setup for String.literal, with explicit special case in predicate compiler
haftmann
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diff
changeset

731 
else None)" 
62364
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haftmann
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diff
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732 

9209770bdcdf
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haftmann
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diff
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733 
instance .. 
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haftmann
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734 

62597  735 
end *) 
59484
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736 

47203  737 
hide_fact (open) orelse_def 
62979  738 
no_notation orelse (infixr "orelse" 55) 
45818
53a697f5454a
hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
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45750
diff
changeset

739 

62979  740 
hide_const valtermify_absdummy valtermify_fun_upd 
741 
valterm_emptyset valtermify_insert 

742 
valtermify_pair valtermify_Inl valtermify_Inr 

46307
ec8f975c059b
shortened definitions by adding some termify constants
bulwahn
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46305
diff
changeset

743 
termify_fun_upd term_emptyset termify_insert termify_pair setify 
46305  744 

45818
53a697f5454a
hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
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diff
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745 
hide_const (open) 
51143
0a2371e7ced3
two target language numeral types: integer and natural, as replacement for code_numeral;
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746 
exhaustive full_exhaustive 
0a2371e7ced3
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747 
exhaustive_int' full_exhaustive_int' 
0a2371e7ced3
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748 
exhaustive_integer' full_exhaustive_integer' 
0a2371e7ced3
two target language numeral types: integer and natural, as replacement for code_numeral;
haftmann
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51126
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749 
exhaustive_natural' full_exhaustive_natural' 
45818
53a697f5454a
hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents:
45750
diff
changeset

750 
throw_Counterexample catch_Counterexample 
53a697f5454a
hiding constants and facts in the Quickcheck_Exhaustive and Quickcheck_Narrowing theory;
bulwahn
parents:
45750
diff
changeset

751 
check_all enum_term_of 
46305  752 
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

753 

45450  754 
hide_type (open) cps pos_bound_cps neg_bound_cps unknown three_valued 
62979  755 

45450  756 
hide_const (open) cps_empty cps_single cps_bind cps_plus cps_if cps_not 
62979  757 
pos_bound_cps_empty pos_bound_cps_single pos_bound_cps_bind 
758 
pos_bound_cps_plus pos_bound_cps_if pos_bound_cps_not 

759 
neg_bound_cps_empty neg_bound_cps_single neg_bound_cps_bind 

760 
neg_bound_cps_plus neg_bound_cps_if neg_bound_cps_not 

45450  761 
Unknown Known Unknown_value Value No_value 
762 

763 
end 