--- a/src/HOL/ex/Random.thy Thu Feb 05 11:49:15 2009 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,183 +0,0 @@
-(* ID: $Id$
- Author: Florian Haftmann, TU Muenchen
-*)
-
-header {* A HOL random engine *}
-
-theory Random
-imports State_Monad Code_Index
-begin
-
-subsection {* Auxiliary functions *}
-
-definition
- inc_shift :: "index \<Rightarrow> index \<Rightarrow> index"
-where
- "inc_shift v k = (if v = k then 1 else k + 1)"
-
-definition
- minus_shift :: "index \<Rightarrow> index \<Rightarrow> index \<Rightarrow> index"
-where
- "minus_shift r k l = (if k < l then r + k - l else k - l)"
-
-fun
- log :: "index \<Rightarrow> index \<Rightarrow> index"
-where
- "log b i = (if b \<le> 1 \<or> i < b then 1 else 1 + log b (i div b))"
-
-subsection {* Random seeds *}
-
-types seed = "index \<times> index"
-
-primrec
- "next" :: "seed \<Rightarrow> index \<times> seed"
-where
- "next (v, w) = (let
- k = v div 53668;
- v' = minus_shift 2147483563 (40014 * (v mod 53668)) (k * 12211);
- l = w div 52774;
- w' = minus_shift 2147483399 (40692 * (w mod 52774)) (l * 3791);
- z = minus_shift 2147483562 v' (w' + 1) + 1
- in (z, (v', w')))"
-
-lemma next_not_0:
- "fst (next s) \<noteq> 0"
-apply (cases s)
-apply (auto simp add: minus_shift_def Let_def)
-done
-
-primrec
- seed_invariant :: "seed \<Rightarrow> bool"
-where
- "seed_invariant (v, w) \<longleftrightarrow> 0 < v \<and> v < 9438322952 \<and> 0 < w \<and> True"
-
-lemma if_same:
- "(if b then f x else f y) = f (if b then x else y)"
- by (cases b) simp_all
-
-definition
- split_seed :: "seed \<Rightarrow> seed \<times> seed"
-where
- "split_seed s = (let
- (v, w) = s;
- (v', w') = snd (next s);
- v'' = inc_shift 2147483562 v;
- s'' = (v'', w');
- w'' = inc_shift 2147483398 w;
- s''' = (v', w'')
- in (s'', s'''))"
-
-
-subsection {* Base selectors *}
-
-function
- range_aux :: "index \<Rightarrow> index \<Rightarrow> seed \<Rightarrow> index \<times> seed"
-where
- "range_aux k l s = (if k = 0 then (l, s) else
- let (v, s') = next s
- in range_aux (k - 1) (v + l * 2147483561) s')"
-by pat_completeness auto
-termination
- by (relation "measure (nat_of_index o fst)")
- (auto simp add: index)
-
-definition
- range :: "index \<Rightarrow> seed \<Rightarrow> index \<times> seed"
-where
- "range k = (do
- v \<leftarrow> range_aux (log 2147483561 k) 1;
- return (v mod k)
- done)"
-
-lemma range:
- assumes "k > 0"
- shows "fst (range k s) < k"
-proof -
- obtain v w where range_aux:
- "range_aux (log 2147483561 k) 1 s = (v, w)"
- by (cases "range_aux (log 2147483561 k) 1 s")
- with assms show ?thesis
- by (simp add: monad_collapse range_def del: range_aux.simps log.simps)
-qed
-
-definition
- select :: "'a list \<Rightarrow> seed \<Rightarrow> 'a \<times> seed"
-where
- "select xs = (do
- k \<leftarrow> range (index_of_nat (length xs));
- return (nth xs (nat_of_index k))
- done)"
-
-lemma select:
- assumes "xs \<noteq> []"
- shows "fst (select xs s) \<in> set xs"
-proof -
- from assms have "index_of_nat (length xs) > 0" by simp
- with range have
- "fst (range (index_of_nat (length xs)) s) < index_of_nat (length xs)" by best
- then have
- "nat_of_index (fst (range (index_of_nat (length xs)) s)) < length xs" by simp
- then show ?thesis
- by (auto simp add: monad_collapse select_def)
-qed
-
-definition
- select_default :: "index \<Rightarrow> 'a \<Rightarrow> 'a \<Rightarrow> seed \<Rightarrow> 'a \<times> seed"
-where
- [code del]: "select_default k x y = (do
- l \<leftarrow> range k;
- return (if l + 1 < k then x else y)
- done)"
-
-lemma select_default_zero:
- "fst (select_default 0 x y s) = y"
- by (simp add: monad_collapse select_default_def)
-
-lemma select_default_code [code]:
- "select_default k x y = (if k = 0 then do
- _ \<leftarrow> range 1;
- return y
- done else do
- l \<leftarrow> range k;
- return (if l + 1 < k then x else y)
- done)"
-proof (cases "k = 0")
- case False then show ?thesis by (simp add: select_default_def)
-next
- case True then show ?thesis
- by (simp add: monad_collapse select_default_def range_def)
-qed
-
-
-subsection {* @{text ML} interface *}
-
-ML {*
-structure Random_Engine =
-struct
-
-type seed = int * int;
-
-local
-
-val seed = ref
- (let
- val now = Time.toMilliseconds (Time.now ());
- val (q, s1) = IntInf.divMod (now, 2147483562);
- val s2 = q mod 2147483398;
- in (s1 + 1, s2 + 1) end);
-
-in
-
-fun run f =
- let
- val (x, seed') = f (! seed);
- val _ = seed := seed'
- in x end;
-
-end;
-
-end;
-*}
-
-end
-