move constant 'Respects' into Lifting.thy;
add quantifier transfer rules for quotients
(* Author: Lukas Bulwahn, TU Muenchen *)
theory New_Random_Sequence
imports Quickcheck New_DSequence
begin
type_synonym 'a pos_random_dseq = "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> 'a New_DSequence.pos_dseq"
type_synonym 'a neg_random_dseq = "code_numeral \<Rightarrow> code_numeral \<Rightarrow> Random.seed \<Rightarrow> 'a New_DSequence.neg_dseq"
definition pos_empty :: "'a pos_random_dseq"
where
"pos_empty = (%nrandom size seed. New_DSequence.pos_empty)"
definition pos_single :: "'a => 'a pos_random_dseq"
where
"pos_single x = (%nrandom size seed. New_DSequence.pos_single x)"
definition pos_bind :: "'a pos_random_dseq => ('a \<Rightarrow> 'b pos_random_dseq) \<Rightarrow> 'b pos_random_dseq"
where
"pos_bind R f = (\<lambda>nrandom size seed. New_DSequence.pos_bind (R nrandom size seed) (%a. f a nrandom size seed))"
definition pos_decr_bind :: "'a pos_random_dseq => ('a \<Rightarrow> 'b pos_random_dseq) \<Rightarrow> 'b pos_random_dseq"
where
"pos_decr_bind R f = (\<lambda>nrandom size seed. New_DSequence.pos_decr_bind (R nrandom size seed) (%a. f a nrandom size seed))"
definition pos_union :: "'a pos_random_dseq => 'a pos_random_dseq => 'a pos_random_dseq"
where
"pos_union R1 R2 = (\<lambda>nrandom size seed. New_DSequence.pos_union (R1 nrandom size seed) (R2 nrandom size seed))"
definition pos_if_random_dseq :: "bool => unit pos_random_dseq"
where
"pos_if_random_dseq b = (if b then pos_single () else pos_empty)"
definition pos_iterate_upto :: "(code_numeral => 'a) => code_numeral => code_numeral => 'a pos_random_dseq"
where
"pos_iterate_upto f n m = (\<lambda>nrandom size seed. New_DSequence.pos_iterate_upto f n m)"
definition pos_not_random_dseq :: "unit neg_random_dseq => unit pos_random_dseq"
where
"pos_not_random_dseq R = (\<lambda>nrandom size seed. New_DSequence.pos_not_seq (R nrandom size seed))"
fun iter :: "(code_numeral * code_numeral => ('a * (unit => term)) * code_numeral * code_numeral) => code_numeral => code_numeral * code_numeral => 'a Lazy_Sequence.lazy_sequence"
where
"iter random nrandom seed =
(if nrandom = 0 then Lazy_Sequence.empty else Lazy_Sequence.Lazy_Sequence (%u. let ((x, _), seed') = random seed in Some (x, iter random (nrandom - 1) seed')))"
definition Random :: "(code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed)) \<Rightarrow> 'a pos_random_dseq"
where
"Random g = (%nrandom size seed depth. iter (g size) nrandom seed)"
definition pos_map :: "('a => 'b) => 'a pos_random_dseq => 'b pos_random_dseq"
where
"pos_map f P = pos_bind P (pos_single o f)"
definition neg_empty :: "'a neg_random_dseq"
where
"neg_empty = (%nrandom size seed. New_DSequence.neg_empty)"
definition neg_single :: "'a => 'a neg_random_dseq"
where
"neg_single x = (%nrandom size seed. New_DSequence.neg_single x)"
definition neg_bind :: "'a neg_random_dseq => ('a \<Rightarrow> 'b neg_random_dseq) \<Rightarrow> 'b neg_random_dseq"
where
"neg_bind R f = (\<lambda>nrandom size seed. New_DSequence.neg_bind (R nrandom size seed) (%a. f a nrandom size seed))"
definition neg_decr_bind :: "'a neg_random_dseq => ('a \<Rightarrow> 'b neg_random_dseq) \<Rightarrow> 'b neg_random_dseq"
where
"neg_decr_bind R f = (\<lambda>nrandom size seed. New_DSequence.neg_decr_bind (R nrandom size seed) (%a. f a nrandom size seed))"
definition neg_union :: "'a neg_random_dseq => 'a neg_random_dseq => 'a neg_random_dseq"
where
"neg_union R1 R2 = (\<lambda>nrandom size seed. New_DSequence.neg_union (R1 nrandom size seed) (R2 nrandom size seed))"
definition neg_if_random_dseq :: "bool => unit neg_random_dseq"
where
"neg_if_random_dseq b = (if b then neg_single () else neg_empty)"
definition neg_iterate_upto :: "(code_numeral => 'a) => code_numeral => code_numeral => 'a neg_random_dseq"
where
"neg_iterate_upto f n m = (\<lambda>nrandom size seed. New_DSequence.neg_iterate_upto f n m)"
definition neg_not_random_dseq :: "unit pos_random_dseq => unit neg_random_dseq"
where
"neg_not_random_dseq R = (\<lambda>nrandom size seed. New_DSequence.neg_not_seq (R nrandom size seed))"
(*
fun iter :: "(code_numeral * code_numeral => ('a * (unit => term)) * code_numeral * code_numeral) => code_numeral => code_numeral * code_numeral => 'a Lazy_Sequence.lazy_sequence"
where
"iter random nrandom seed =
(if nrandom = 0 then Lazy_Sequence.empty else Lazy_Sequence.Lazy_Sequence (%u. let ((x, _), seed') = random seed in Some (x, iter random (nrandom - 1) seed')))"
definition Random :: "(code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed)) \<Rightarrow> 'a pos_random_dseq"
where
"Random g = (%nrandom size seed depth. iter (g size) nrandom seed)"
*)
definition neg_map :: "('a => 'b) => 'a neg_random_dseq => 'b neg_random_dseq"
where
"neg_map f P = neg_bind P (neg_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)
pos_empty pos_single pos_bind pos_decr_bind pos_union pos_if_random_dseq pos_iterate_upto pos_not_random_dseq iter Random pos_map
neg_empty neg_single neg_bind neg_decr_bind neg_union neg_if_random_dseq neg_iterate_upto neg_not_random_dseq neg_map
hide_type New_DSequence.pos_dseq New_DSequence.neg_dseq pos_random_dseq neg_random_dseq
(* FIXME: hide facts *)
(*hide_fact (open) empty_def single_def bind_def union_def if_random_dseq_def not_random_dseq_def Random.simps map_def*)
end