src/HOL/Random_Sequence.thy
author bulwahn
Wed Mar 30 11:32:52 2011 +0200 (2011-03-30)
changeset 42163 392fd6c4669c
parent 36176 3fe7e97ccca8
child 50055 94041d602ecb
permissions -rw-r--r--
renewing specifications in HOL: replacing types by type_synonym
     1 
     2 (* Author: Lukas Bulwahn, TU Muenchen *)
     3 
     4 theory Random_Sequence
     5 imports Quickcheck DSequence
     6 begin
     7 
     8 type_synonym 'a random_dseq = "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a DSequence.dseq \<times> Random.seed)"
     9 
    10 definition empty :: "'a random_dseq"
    11 where
    12   "empty = (%nrandom size. Pair (DSequence.empty))"
    13 
    14 definition single :: "'a => 'a random_dseq"
    15 where
    16   "single x = (%nrandom size. Pair (DSequence.single x))"
    17 
    18 definition bind :: "'a random_dseq => ('a \<Rightarrow> 'b random_dseq) \<Rightarrow> 'b random_dseq"
    19 where
    20   "bind R f = (\<lambda>nrandom size s. let
    21      (P, s') = R nrandom size s;
    22      (s1, s2) = Random.split_seed s'
    23   in (DSequence.bind P (%a. fst (f a nrandom size s1)), s2))"
    24 
    25 definition union :: "'a random_dseq => 'a random_dseq => 'a random_dseq"
    26 where
    27   "union R1 R2 = (\<lambda>nrandom size s. let
    28      (S1, s') = R1 nrandom size s; (S2, s'') = R2 nrandom size s'
    29   in (DSequence.union S1 S2, s''))"
    30 
    31 definition if_random_dseq :: "bool => unit random_dseq"
    32 where
    33   "if_random_dseq b = (if b then single () else empty)"
    34 
    35 definition not_random_dseq :: "unit random_dseq => unit random_dseq"
    36 where
    37   "not_random_dseq R = (\<lambda>nrandom size s. let
    38      (S, s') = R nrandom size s
    39    in (DSequence.not_seq S, s'))"
    40 
    41 fun Random :: "(code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed)) \<Rightarrow> 'a random_dseq"
    42 where
    43   "Random g nrandom = (%size. if nrandom <= 0 then (Pair DSequence.empty) else
    44      (scomp (g size) (%r. scomp (Random g (nrandom - 1) size) (%rs. Pair (DSequence.union (DSequence.single (fst r)) rs)))))"
    45 
    46 definition map :: "('a => 'b) => 'a random_dseq => 'b random_dseq"
    47 where
    48   "map f P = bind P (single o f)"
    49 
    50 (*
    51 hide_const DSequence.empty DSequence.single DSequence.eval
    52   DSequence.map_seq DSequence.bind DSequence.union DSequence.if_seq DSequence.not_seq
    53   DSequence.map
    54 *)
    55 
    56 hide_const (open) empty single bind union if_random_dseq not_random_dseq Random map
    57 
    58 hide_type DSequence.dseq random_dseq
    59 hide_fact (open) empty_def single_def bind_def union_def if_random_dseq_def not_random_dseq_def Random.simps map_def
    60 
    61 end