1.1 --- a/src/HOL/Quickcheck.thy Fri Mar 16 22:48:38 2012 +0100
1.2 +++ b/src/HOL/Quickcheck.thy Sat Mar 17 00:17:30 2012 +0100
1.3 @@ -43,8 +43,9 @@
1.4 instantiation itself :: (typerep) random
1.5 begin
1.6
1.7 -definition random_itself :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a itself \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
1.8 - "random_itself _ = Pair (Code_Evaluation.valtermify TYPE('a))"
1.9 +definition
1.10 + random_itself :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a itself \<times> (unit \<Rightarrow> term)) \<times> Random.seed"
1.11 +where "random_itself _ = Pair (Code_Evaluation.valtermify TYPE('a))"
1.12
1.13 instance ..
1.14
1.15 @@ -73,7 +74,9 @@
1.16 instantiation nat :: random
1.17 begin
1.18
1.19 -definition random_nat :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (nat \<times> (unit \<Rightarrow> Code_Evaluation.term)) \<times> Random.seed" where
1.20 +definition random_nat :: "code_numeral \<Rightarrow> Random.seed
1.21 + \<Rightarrow> (nat \<times> (unit \<Rightarrow> Code_Evaluation.term)) \<times> Random.seed"
1.22 +where
1.23 "random_nat i = Random.range (i + 1) \<circ>\<rightarrow> (\<lambda>k. Pair (
1.24 let n = Code_Numeral.nat_of k
1.25 in (n, \<lambda>_. Code_Evaluation.term_of n)))"
1.26 @@ -100,18 +103,22 @@
1.27 text {* Towards @{typ "'a \<Rightarrow> 'b"} *}
1.28
1.29 axiomatization random_fun_aux :: "typerep \<Rightarrow> typerep \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> term)
1.30 - \<Rightarrow> (Random.seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> Random.seed) \<Rightarrow> (Random.seed \<Rightarrow> Random.seed \<times> Random.seed)
1.31 + \<Rightarrow> (Random.seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> Random.seed)
1.32 + \<Rightarrow> (Random.seed \<Rightarrow> Random.seed \<times> Random.seed)
1.33 \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed"
1.34
1.35 definition random_fun_lift :: "(Random.seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> Random.seed)
1.36 - \<Rightarrow> Random.seed \<Rightarrow> (('a\<Colon>term_of \<Rightarrow> 'b\<Colon>typerep) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
1.37 - "random_fun_lift f = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Evaluation.term_of f Random.split_seed"
1.38 + \<Rightarrow> Random.seed \<Rightarrow> (('a\<Colon>term_of \<Rightarrow> 'b\<Colon>typerep) \<times> (unit \<Rightarrow> term)) \<times> Random.seed"
1.39 +where
1.40 + "random_fun_lift f =
1.41 + random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Evaluation.term_of f Random.split_seed"
1.42
1.43 instantiation "fun" :: ("{equal, term_of}", random) random
1.44 begin
1.45
1.46 -definition random_fun :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where
1.47 - "random i = random_fun_lift (random i)"
1.48 +definition
1.49 + random_fun :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed"
1.50 + where "random i = random_fun_lift (random i)"
1.51
1.52 instance ..
1.53
1.54 @@ -119,19 +126,21 @@
1.55
1.56 text {* Towards type copies and datatypes *}
1.57
1.58 -definition collapse :: "('a \<Rightarrow> ('a \<Rightarrow> 'b \<times> 'a) \<times> 'a) \<Rightarrow> 'a \<Rightarrow> 'b \<times> 'a" where
1.59 - "collapse f = (f \<circ>\<rightarrow> id)"
1.60 +definition collapse :: "('a \<Rightarrow> ('a \<Rightarrow> 'b \<times> 'a) \<times> 'a) \<Rightarrow> 'a \<Rightarrow> 'b \<times> 'a"
1.61 + where "collapse f = (f \<circ>\<rightarrow> id)"
1.62
1.63 -definition beyond :: "code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral" where
1.64 - "beyond k l = (if l > k then l else 0)"
1.65 +definition beyond :: "code_numeral \<Rightarrow> code_numeral \<Rightarrow> code_numeral"
1.66 + where "beyond k l = (if l > k then l else 0)"
1.67
1.68 -lemma beyond_zero:
1.69 - "beyond k 0 = 0"
1.70 +lemma beyond_zero: "beyond k 0 = 0"
1.71 by (simp add: beyond_def)
1.72
1.73
1.74 -definition (in term_syntax) [code_unfold]: "valterm_emptyset = Code_Evaluation.valtermify ({} :: ('a :: typerep) set)"
1.75 -definition (in term_syntax) [code_unfold]: "valtermify_insert x s = Code_Evaluation.valtermify insert {\<cdot>} (x :: ('a :: typerep * _)) {\<cdot>} s"
1.76 +definition (in term_syntax) [code_unfold]:
1.77 + "valterm_emptyset = Code_Evaluation.valtermify ({} :: ('a :: typerep) set)"
1.78 +
1.79 +definition (in term_syntax) [code_unfold]:
1.80 + "valtermify_insert x s = Code_Evaluation.valtermify insert {\<cdot>} (x :: ('a :: typerep * _)) {\<cdot>} s"
1.81
1.82 instantiation set :: (random) random
1.83 begin
1.84 @@ -139,12 +148,17 @@
1.85 primrec random_aux_set
1.86 where
1.87 "random_aux_set 0 j = collapse (Random.select_weight [(1, Pair valterm_emptyset)])"
1.88 -| "random_aux_set (Code_Numeral.Suc i) j = collapse (Random.select_weight [(1, Pair valterm_emptyset), (Code_Numeral.Suc i, random j \<circ>\<rightarrow> (%x. random_aux_set i j \<circ>\<rightarrow> (%s. Pair (valtermify_insert x s))))])"
1.89 +| "random_aux_set (Code_Numeral.Suc i) j =
1.90 + collapse (Random.select_weight
1.91 + [(1, Pair valterm_emptyset),
1.92 + (Code_Numeral.Suc i,
1.93 + random j \<circ>\<rightarrow> (%x. random_aux_set i j \<circ>\<rightarrow> (%s. Pair (valtermify_insert x s))))])"
1.94
1.95 lemma [code]:
1.96 - "random_aux_set i j = collapse (Random.select_weight [(1, Pair valterm_emptyset), (i, random j \<circ>\<rightarrow> (%x. random_aux_set (i - 1) j \<circ>\<rightarrow> (%s. Pair (valtermify_insert x s))))])"
1.97 + "random_aux_set i j =
1.98 + collapse (Random.select_weight [(1, Pair valterm_emptyset),
1.99 + (i, random j \<circ>\<rightarrow> (%x. random_aux_set (i - 1) j \<circ>\<rightarrow> (%s. Pair (valtermify_insert x s))))])"
1.100 proof (induct i rule: code_numeral.induct)
1.101 -print_cases
1.102 case zero
1.103 show ?case by (subst select_weight_drop_zero[symmetric])
1.104 (simp add: filter.simps random_aux_set.simps[simplified])
1.105 @@ -153,9 +167,7 @@
1.106 show ?case by (simp only: random_aux_set.simps(2)[of "i"] Suc_code_numeral_minus_one)
1.107 qed
1.108
1.109 -definition random_set
1.110 -where
1.111 - "random_set i = random_aux_set i i"
1.112 +definition "random_set i = random_aux_set i i"
1.113
1.114 instance ..
1.115
1.116 @@ -190,13 +202,15 @@
1.117 subsection {* The Random-Predicate Monad *}
1.118
1.119 fun iter' ::
1.120 - "'a itself => code_numeral => code_numeral => code_numeral * code_numeral => ('a::random) Predicate.pred"
1.121 + "'a itself => code_numeral => code_numeral => code_numeral * code_numeral
1.122 + => ('a::random) Predicate.pred"
1.123 where
1.124 "iter' T nrandom sz seed = (if nrandom = 0 then bot_class.bot else
1.125 let ((x, _), seed') = random sz seed
1.126 in Predicate.Seq (%u. Predicate.Insert x (iter' T (nrandom - 1) sz seed')))"
1.127
1.128 -definition iter :: "code_numeral => code_numeral => code_numeral * code_numeral => ('a::random) Predicate.pred"
1.129 +definition iter :: "code_numeral => code_numeral => code_numeral * code_numeral
1.130 + => ('a::random) Predicate.pred"
1.131 where
1.132 "iter nrandom sz seed = iter' (TYPE('a)) nrandom sz seed"
1.133
1.134 @@ -262,8 +276,10 @@
1.135
1.136 hide_const (open) catch_match random collapse beyond random_fun_aux random_fun_lift
1.137
1.138 -hide_fact (open) iter'.simps iter_def empty_def single_def bind_def union_def if_randompred_def iterate_upto_def not_randompred_def Random_def map_def
1.139 +hide_fact (open) iter'.simps iter_def empty_def single_def bind_def union_def
1.140 + if_randompred_def iterate_upto_def not_randompred_def Random_def map_def
1.141 hide_type (open) randompred
1.142 -hide_const (open) iter' iter empty single bind union if_randompred iterate_upto not_randompred Random map
1.143 +hide_const (open) iter' iter empty single bind union if_randompred
1.144 + iterate_upto not_randompred Random map
1.145
1.146 end