src/HOL/New_DSequence.thy

+
+(* Author: Lukas Bulwahn, TU Muenchen *)
+
+header {* Depth-Limited Sequences with failure element *}
+
+theory New_DSequence
+imports Random_Sequence
+begin
+
+section {* Positive Depth-Limited Sequence *}
+
+types 'a pos_dseq = "code_numeral => 'a Lazy_Sequence.lazy_sequence"
+
+definition pos_empty :: "'a pos_dseq"
+where
+  "pos_empty = (%i. Lazy_Sequence.empty)"
+
+definition pos_single :: "'a => 'a pos_dseq"
+where
+  "pos_single x = (%i. Lazy_Sequence.single x)"
+
+definition pos_bind :: "'a pos_dseq => ('a => 'b pos_dseq) => 'b pos_dseq"
+where
+  "pos_bind x f = (%i. 
+     if i = 0 then
+       Lazy_Sequence.empty
+     else
+       Lazy_Sequence.bind (x (i - 1)) (%a. f a i))"
+
+definition pos_union :: "'a pos_dseq => 'a pos_dseq => 'a pos_dseq"
+where
+  "pos_union xq yq = (%i. Lazy_Sequence.append (xq i) (yq i))"
+
+definition pos_if_seq :: "bool => unit pos_dseq"
+where
+  "pos_if_seq b = (if b then pos_single () else pos_empty)"
+
+definition pos_map :: "('a => 'b) => 'a pos_dseq => 'b pos_dseq"
+where
+  "pos_map f xq = (%i. Lazy_Sequence.map f (xq i))"
+
+section {* Negative Depth-Limited Sequence *}
+
+types 'a neg_dseq = "code_numeral => 'a Lazy_Sequence.hit_bound_lazy_sequence"
+
+definition neg_empty :: "'a neg_dseq"
+where
+  "neg_empty = (%i. Lazy_Sequence.empty)"
+
+definition neg_single :: "'a => 'a neg_dseq"
+where
+  "neg_single x = (%i. Lazy_Sequence.hb_single x)"
+
+definition neg_bind :: "'a neg_dseq => ('a => 'b neg_dseq) => 'b neg_dseq"
+where
+  "neg_bind x f = (%i. 
+     if i = 0 then
+       Lazy_Sequence.hit_bound
+     else
+       hb_bind (x (i - 1)) (%a. f a i))"
+
+definition neg_union :: "'a neg_dseq => 'a neg_dseq => 'a neg_dseq"
+where
+  "neg_union x y = (%i. Lazy_Sequence.append (x i) (y i))"
+
+definition neg_if_seq :: "bool => unit neg_dseq"
+where
+  "neg_if_seq b = (if b then neg_single () else neg_empty)"
+
+definition neg_map :: "('a => 'b) => 'a neg_dseq => 'b neg_dseq"
+where
+  "neg_map f xq = (%i. Lazy_Sequence.hb_map f (xq i))"
+
+section {* Negation *}
+
+definition pos_not_seq :: "unit neg_dseq => unit pos_dseq"
+where
+  "pos_not_seq xq = (%i. Lazy_Sequence.hb_not_seq (xq i))"
+
+definition neg_not_seq :: "unit pos_dseq => unit neg_dseq"
+where
+  "neg_not_seq x = (%i. case Lazy_Sequence.yield (x i) of
+    None => Lazy_Sequence.hb_single ()
+  | Some ((), xq) => Lazy_Sequence.empty)"
+
+hide (open) type pos_dseq neg_dseq
+
+hide (open) const 
+  pos_empty pos_single pos_bind pos_union pos_if_seq pos_not_seq
+  neg_empty neg_single neg_bind neg_union neg_if_seq neg_not_seq
+hide (open) fact
+  pos_empty_def pos_single_def pos_bind_def pos_union_def pos_if_seq_def pos_not_seq_def pos_map_def
+  neg_empty_def neg_single_def neg_bind_def neg_union_def neg_if_seq_def neg_not_seq_def neg_map_def
+
+end