src/HOL/Random_Sequence.thy

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Random_Sequence.thy	Wed Jan 20 11:56:45 2010 +0100
@@ -0,0 +1,61 @@
+
+(* Author: Lukas Bulwahn, TU Muenchen *)
+
+theory Random_Sequence
+imports Quickcheck DSequence
+begin
+
+types 'a random_dseq = "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a DSequence.dseq \<times> Random.seed)"
+
+definition empty :: "'a random_dseq"
+where
+  "empty = (%nrandom size. Pair (DSequence.empty))"
+
+definition single :: "'a => 'a random_dseq"
+where
+  "single x = (%nrandom size. Pair (DSequence.single x))"
+
+definition bind :: "'a random_dseq => ('a \<Rightarrow> 'b random_dseq) \<Rightarrow> 'b random_dseq"
+where
+  "bind R f = (\<lambda>nrandom size s. let
+     (P, s') = R nrandom size s;
+     (s1, s2) = Random.split_seed s'
+  in (DSequence.bind P (%a. fst (f a nrandom size s1)), s2))"
+
+definition union :: "'a random_dseq => 'a random_dseq => 'a random_dseq"
+where
+  "union R1 R2 = (\<lambda>nrandom size s. let
+     (S1, s') = R1 nrandom size s; (S2, s'') = R2 nrandom size s'
+  in (DSequence.union S1 S2, s''))"
+
+definition if_random_dseq :: "bool => unit random_dseq"
+where
+  "if_random_dseq b = (if b then single () else empty)"
+
+definition not_random_dseq :: "unit random_dseq => unit random_dseq"
+where
+  "not_random_dseq R = (\<lambda>nrandom size s. let
+     (S, s') = R nrandom size s
+   in (DSequence.not_seq S, s'))"
+
+fun Random :: "(code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed)) \<Rightarrow> 'a random_dseq"
+where
+  "Random g nrandom = (%size. if nrandom <= 0 then (Pair DSequence.empty) else
+     (scomp (g size) (%r. scomp (Random g (nrandom - 1) size) (%rs. Pair (DSequence.union (DSequence.single (fst r)) rs)))))"
+
+definition map :: "('a => 'b) => 'a random_dseq => 'b random_dseq"
+where
+  "map f P = bind P (single o f)"
+
+(*
+hide const DSequence.empty DSequence.single DSequence.eval
+  DSequence.map_seq DSequence.bind DSequence.union DSequence.if_seq DSequence.not_seq
+  DSequence.map
+*)
+
+hide (open) const empty single bind union if_random_dseq not_random_dseq Random map
+
+hide type DSequence.dseq random_dseq
+hide (open) fact empty_def single_def bind_def union_def if_random_dseq_def not_random_dseq_def Random_def map_def
+
+end
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