prefer implementation in HOL;
n.b. code_reflect cannot reflect type synonyms
(* Author: Lukas Bulwahn, TU Muenchen *)
header {* Depth-Limited Sequences with failure element *}
theory DSequence
imports Lazy_Sequence
begin
type_synonym 'a dseq = "code_numeral => bool => 'a Lazy_Sequence.lazy_sequence option"
definition empty :: "'a dseq"
where
"empty = (%i pol. Some Lazy_Sequence.empty)"
definition single :: "'a => 'a dseq"
where
"single x = (%i pol. Some (Lazy_Sequence.single x))"
fun eval :: "'a dseq => code_numeral => bool => 'a Lazy_Sequence.lazy_sequence option"
where
"eval f i pol = f i pol"
definition yield :: "'a dseq => code_numeral => bool => ('a * 'a dseq) option"
where
"yield dseq i pol = (case eval dseq i pol of
None => None
| Some s => Option.map (apsnd (%r i pol. Some r)) (Lazy_Sequence.yield s))"
definition yieldn :: "code_numeral \<Rightarrow> 'a dseq \<Rightarrow> code_numeral \<Rightarrow> bool \<Rightarrow> 'a list \<times> 'a dseq"
where
"yieldn n dseq i pol = (case dseq i pol of
None \<Rightarrow> ([], \<lambda>i pol. None)
| Some s \<Rightarrow> let (xs, s') = Lazy_Sequence.yieldn n s in (xs, \<lambda>i pol. Some s'))"
fun map_seq :: "('a => 'b dseq) => 'a Lazy_Sequence.lazy_sequence => 'b dseq"
where
"map_seq f xq i pol = (case Lazy_Sequence.yield xq of
None => Some Lazy_Sequence.empty
| Some (x, xq') => (case eval (f x) i pol of
None => None
| Some yq => (case map_seq f xq' i pol of
None => None
| Some zq => Some (Lazy_Sequence.append yq zq))))"
definition bind :: "'a dseq => ('a => 'b dseq) => 'b dseq"
where
"bind x f = (%i pol.
if i = 0 then
(if pol then Some Lazy_Sequence.empty else None)
else
(case x (i - 1) pol of
None => None
| Some xq => map_seq f xq i pol))"
definition union :: "'a dseq => 'a dseq => 'a dseq"
where
"union x y = (%i pol. case (x i pol, y i pol) of
(Some xq, Some yq) => Some (Lazy_Sequence.append xq yq)
| _ => None)"
definition if_seq :: "bool => unit dseq"
where
"if_seq b = (if b then single () else empty)"
definition not_seq :: "unit dseq => unit dseq"
where
"not_seq x = (%i pol. case x i (\<not>pol) of
None => Some Lazy_Sequence.empty
| Some xq => (case Lazy_Sequence.yield xq of
None => Some (Lazy_Sequence.single ())
| Some _ => Some (Lazy_Sequence.empty)))"
definition map :: "('a => 'b) => 'a dseq => 'b dseq"
where
"map f g = (%i pol. case g i pol of
None => None
| Some xq => Some (Lazy_Sequence.map f xq))"
ML {*
signature DSEQUENCE =
sig
type 'a dseq = int -> bool -> 'a Lazy_Sequence.lazy_sequence option
val yield : 'a dseq -> int -> bool -> ('a * 'a dseq) option
val yieldn : int -> 'a dseq -> int -> bool -> 'a list * 'a dseq
val map : ('a -> 'b) -> 'a dseq -> 'b dseq
end;
structure DSequence : DSEQUENCE =
struct
type 'a dseq = int -> bool -> 'a Lazy_Sequence.lazy_sequence option
val yield = @{code yield}
val yieldn = @{code yieldn}
val map = @{code map}
end;
*}
code_reserved Eval DSequence
(*
hide_type Sequence.seq
hide_const Sequence.Seq Sequence.yield Sequence.yieldn Sequence.empty Sequence.single
Sequence.append Sequence.flat Sequence.map Sequence.bind Sequence.ifpred Sequence.not_seq
*)
hide_const (open) empty single eval map_seq bind union if_seq not_seq map
hide_fact (open) empty_def single_def eval.simps map_seq.simps bind_def union_def
if_seq_def not_seq_def map_def
end