src/HOL/Random_Pred.thy
author blanchet
Sun May 04 18:14:58 2014 +0200 (2014-05-04)
changeset 56846 9df717fef2bb
parent 51143 0a2371e7ced3
child 58889 5b7a9633cfa8
permissions -rw-r--r--
renamed 'xxx_size' to 'size_xxx' for old datatype package
     1 
     2 (* Author: Lukas Bulwahn, TU Muenchen *)
     3 
     4 header {* The Random-Predicate Monad *}
     5 
     6 theory Random_Pred
     7 imports Quickcheck_Random
     8 begin
     9 
    10 fun iter' :: "'a itself \<Rightarrow> natural \<Rightarrow> natural \<Rightarrow> Random.seed \<Rightarrow> ('a::random) Predicate.pred"
    11 where
    12   "iter' T nrandom sz seed = (if nrandom = 0 then bot_class.bot else
    13      let ((x, _), seed') = Quickcheck_Random.random sz seed
    14    in Predicate.Seq (%u. Predicate.Insert x (iter' T (nrandom - 1) sz seed')))"
    15 
    16 definition iter :: "natural \<Rightarrow> natural \<Rightarrow> Random.seed \<Rightarrow> ('a::random) Predicate.pred"
    17 where
    18   "iter nrandom sz seed = iter' (TYPE('a)) nrandom sz seed"
    19 
    20 lemma [code]:
    21   "iter nrandom sz seed = (if nrandom = 0 then bot_class.bot else
    22      let ((x, _), seed') = Quickcheck_Random.random sz seed
    23    in Predicate.Seq (%u. Predicate.Insert x (iter (nrandom - 1) sz seed')))"
    24    unfolding iter_def iter'.simps [of _ nrandom] ..
    25 
    26 type_synonym 'a random_pred = "Random.seed \<Rightarrow> ('a Predicate.pred \<times> Random.seed)"
    27 
    28 definition empty :: "'a random_pred"
    29   where "empty = Pair bot"
    30 
    31 definition single :: "'a => 'a random_pred"
    32   where "single x = Pair (Predicate.single x)"
    33 
    34 definition bind :: "'a random_pred \<Rightarrow> ('a \<Rightarrow> 'b random_pred) \<Rightarrow> 'b random_pred"
    35   where
    36     "bind R f = (\<lambda>s. let
    37        (P, s') = R s;
    38        (s1, s2) = Random.split_seed s'
    39      in (Predicate.bind P (%a. fst (f a s1)), s2))"
    40 
    41 definition union :: "'a random_pred \<Rightarrow> 'a random_pred \<Rightarrow> 'a random_pred"
    42 where
    43   "union R1 R2 = (\<lambda>s. let
    44      (P1, s') = R1 s; (P2, s'') = R2 s'
    45    in (sup_class.sup P1 P2, s''))"
    46 
    47 definition if_randompred :: "bool \<Rightarrow> unit random_pred"
    48 where
    49   "if_randompred b = (if b then single () else empty)"
    50 
    51 definition iterate_upto :: "(natural \<Rightarrow> 'a) => natural \<Rightarrow> natural \<Rightarrow> 'a random_pred"
    52 where
    53   "iterate_upto f n m = Pair (Predicate.iterate_upto f n m)"
    54 
    55 definition not_randompred :: "unit random_pred \<Rightarrow> unit random_pred"
    56 where
    57   "not_randompred P = (\<lambda>s. let
    58      (P', s') = P s
    59    in if Predicate.eval P' () then (Orderings.bot, s') else (Predicate.single (), s'))"
    60 
    61 definition Random :: "(Random.seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed) \<Rightarrow> 'a random_pred"
    62   where "Random g = scomp g (Pair o (Predicate.single o fst))"
    63 
    64 definition map :: "('a \<Rightarrow> 'b) \<Rightarrow> 'a random_pred \<Rightarrow> 'b random_pred"
    65   where "map f P = bind P (single o f)"
    66 
    67 hide_const (open) iter' iter empty single bind union if_randompred
    68   iterate_upto not_randompred Random map
    69 
    70 hide_fact iter'.simps
    71   
    72 hide_fact (open) iter_def empty_def single_def bind_def union_def
    73   if_randompred_def iterate_upto_def not_randompred_def Random_def map_def 
    74 
    75 end
    76