src/HOL/Random_Sequence.thy
author webertj
Fri, 19 Oct 2012 15:12:52 +0200
changeset 49962 a8cc904a6820
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child 50055 94041d602ecb
permissions -rw-r--r--
Renamed {left,right}_distrib to distrib_{right,left}.
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(* Author: Lukas Bulwahn, TU Muenchen *)
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theory Random_Sequence
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imports Quickcheck DSequence
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begin
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type_synonym 'a random_dseq = "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a DSequence.dseq \<times> Random.seed)"
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definition empty :: "'a random_dseq"
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where
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  "empty = (%nrandom size. Pair (DSequence.empty))"
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definition single :: "'a => 'a random_dseq"
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where
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  "single x = (%nrandom size. Pair (DSequence.single x))"
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definition bind :: "'a random_dseq => ('a \<Rightarrow> 'b random_dseq) \<Rightarrow> 'b random_dseq"
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where
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  "bind R f = (\<lambda>nrandom size s. let
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     (P, s') = R nrandom size s;
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     (s1, s2) = Random.split_seed s'
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  in (DSequence.bind P (%a. fst (f a nrandom size s1)), s2))"
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definition union :: "'a random_dseq => 'a random_dseq => 'a random_dseq"
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where
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  "union R1 R2 = (\<lambda>nrandom size s. let
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     (S1, s') = R1 nrandom size s; (S2, s'') = R2 nrandom size s'
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  in (DSequence.union S1 S2, s''))"
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definition if_random_dseq :: "bool => unit random_dseq"
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where
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  "if_random_dseq b = (if b then single () else empty)"
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definition not_random_dseq :: "unit random_dseq => unit random_dseq"
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where
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  "not_random_dseq R = (\<lambda>nrandom size s. let
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     (S, s') = R nrandom size s
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   in (DSequence.not_seq S, s'))"
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fun Random :: "(code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed)) \<Rightarrow> 'a random_dseq"
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where
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  "Random g nrandom = (%size. if nrandom <= 0 then (Pair DSequence.empty) else
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     (scomp (g size) (%r. scomp (Random g (nrandom - 1) size) (%rs. Pair (DSequence.union (DSequence.single (fst r)) rs)))))"
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definition map :: "('a => 'b) => 'a random_dseq => 'b random_dseq"
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where
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  "map f P = bind P (single o f)"
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(*
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hide_const DSequence.empty DSequence.single DSequence.eval
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  DSequence.map_seq DSequence.bind DSequence.union DSequence.if_seq DSequence.not_seq
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  DSequence.map
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*)
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hide_const (open) empty single bind union if_random_dseq not_random_dseq Random map
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hide_type DSequence.dseq random_dseq
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hide_fact (open) empty_def single_def bind_def union_def if_random_dseq_def not_random_dseq_def Random.simps map_def
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end