author | hoelzl |
Mon, 03 Dec 2012 18:19:08 +0100 | |
changeset 50328 | 25b1e8686ce0 |
parent 50055 | 94041d602ecb |
child 51126 | df86080de4cb |
permissions | -rw-r--r-- |
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(* Author: Lukas Bulwahn, TU Muenchen *) |
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theory Random_Sequence |
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imports Quickcheck |
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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 |