(* 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_const (open) empty single bind union if_random_dseq not_random_dseq Random map
hide_type DSequence.dseq random_dseq
hide_fact (open) empty_def single_def bind_def union_def if_random_dseq_def not_random_dseq_def Random.simps map_def
end