src/HOL/New_DSequence.thy
 author huffman Sun Apr 01 16:09:58 2012 +0200 (2012-04-01) changeset 47255 30a1692557b0 parent 42163 392fd6c4669c child 50055 94041d602ecb permissions -rw-r--r--
removed Nat_Numeral.thy, moving all theorems elsewhere
 bulwahn@36017 ` 1` bulwahn@36017 ` 2` ```(* Author: Lukas Bulwahn, TU Muenchen *) ``` bulwahn@36017 ` 3` bulwahn@36017 ` 4` ```header {* Depth-Limited Sequences with failure element *} ``` bulwahn@36017 ` 5` bulwahn@36017 ` 6` ```theory New_DSequence ``` bulwahn@36017 ` 7` ```imports Random_Sequence ``` bulwahn@36017 ` 8` ```begin ``` bulwahn@36017 ` 9` huffman@36902 ` 10` ```subsection {* Positive Depth-Limited Sequence *} ``` bulwahn@36017 ` 11` bulwahn@42163 ` 12` ```type_synonym 'a pos_dseq = "code_numeral => 'a Lazy_Sequence.lazy_sequence" ``` bulwahn@36017 ` 13` bulwahn@36017 ` 14` ```definition pos_empty :: "'a pos_dseq" ``` bulwahn@36017 ` 15` ```where ``` bulwahn@36017 ` 16` ``` "pos_empty = (%i. Lazy_Sequence.empty)" ``` bulwahn@36017 ` 17` bulwahn@36017 ` 18` ```definition pos_single :: "'a => 'a pos_dseq" ``` bulwahn@36017 ` 19` ```where ``` bulwahn@36017 ` 20` ``` "pos_single x = (%i. Lazy_Sequence.single x)" ``` bulwahn@36017 ` 21` bulwahn@36017 ` 22` ```definition pos_bind :: "'a pos_dseq => ('a => 'b pos_dseq) => 'b pos_dseq" ``` bulwahn@36017 ` 23` ```where ``` bulwahn@40049 ` 24` ``` "pos_bind x f = (%i. Lazy_Sequence.bind (x i) (%a. f a i))" ``` bulwahn@40049 ` 25` bulwahn@40049 ` 26` ```definition pos_decr_bind :: "'a pos_dseq => ('a => 'b pos_dseq) => 'b pos_dseq" ``` bulwahn@40049 ` 27` ```where ``` bulwahn@40049 ` 28` ``` "pos_decr_bind x f = (%i. ``` bulwahn@36017 ` 29` ``` if i = 0 then ``` bulwahn@36017 ` 30` ``` Lazy_Sequence.empty ``` bulwahn@36017 ` 31` ``` else ``` bulwahn@36017 ` 32` ``` Lazy_Sequence.bind (x (i - 1)) (%a. f a i))" ``` bulwahn@36017 ` 33` bulwahn@36017 ` 34` ```definition pos_union :: "'a pos_dseq => 'a pos_dseq => 'a pos_dseq" ``` bulwahn@36017 ` 35` ```where ``` bulwahn@36017 ` 36` ``` "pos_union xq yq = (%i. Lazy_Sequence.append (xq i) (yq i))" ``` bulwahn@36017 ` 37` bulwahn@36017 ` 38` ```definition pos_if_seq :: "bool => unit pos_dseq" ``` bulwahn@36017 ` 39` ```where ``` bulwahn@36017 ` 40` ``` "pos_if_seq b = (if b then pos_single () else pos_empty)" ``` bulwahn@36017 ` 41` bulwahn@36049 ` 42` ```definition pos_iterate_upto :: "(code_numeral => 'a) => code_numeral => code_numeral => 'a pos_dseq" ``` bulwahn@36049 ` 43` ```where ``` bulwahn@36049 ` 44` ``` "pos_iterate_upto f n m = (%i. Lazy_Sequence.iterate_upto f n m)" ``` bulwahn@36049 ` 45` ``` ``` bulwahn@36017 ` 46` ```definition pos_map :: "('a => 'b) => 'a pos_dseq => 'b pos_dseq" ``` bulwahn@36017 ` 47` ```where ``` bulwahn@36017 ` 48` ``` "pos_map f xq = (%i. Lazy_Sequence.map f (xq i))" ``` bulwahn@36017 ` 49` huffman@36902 ` 50` ```subsection {* Negative Depth-Limited Sequence *} ``` bulwahn@36017 ` 51` bulwahn@42163 ` 52` ```type_synonym 'a neg_dseq = "code_numeral => 'a Lazy_Sequence.hit_bound_lazy_sequence" ``` bulwahn@36017 ` 53` bulwahn@36017 ` 54` ```definition neg_empty :: "'a neg_dseq" ``` bulwahn@36017 ` 55` ```where ``` bulwahn@36017 ` 56` ``` "neg_empty = (%i. Lazy_Sequence.empty)" ``` bulwahn@36017 ` 57` bulwahn@36017 ` 58` ```definition neg_single :: "'a => 'a neg_dseq" ``` bulwahn@36017 ` 59` ```where ``` bulwahn@36017 ` 60` ``` "neg_single x = (%i. Lazy_Sequence.hb_single x)" ``` bulwahn@36017 ` 61` bulwahn@36017 ` 62` ```definition neg_bind :: "'a neg_dseq => ('a => 'b neg_dseq) => 'b neg_dseq" ``` bulwahn@36017 ` 63` ```where ``` bulwahn@40049 ` 64` ``` "neg_bind x f = (%i. hb_bind (x i) (%a. f a i))" ``` bulwahn@40049 ` 65` bulwahn@40049 ` 66` ```definition neg_decr_bind :: "'a neg_dseq => ('a => 'b neg_dseq) => 'b neg_dseq" ``` bulwahn@40049 ` 67` ```where ``` bulwahn@40049 ` 68` ``` "neg_decr_bind x f = (%i. ``` bulwahn@36017 ` 69` ``` if i = 0 then ``` bulwahn@36017 ` 70` ``` Lazy_Sequence.hit_bound ``` bulwahn@36017 ` 71` ``` else ``` bulwahn@36017 ` 72` ``` hb_bind (x (i - 1)) (%a. f a i))" ``` bulwahn@36017 ` 73` bulwahn@36017 ` 74` ```definition neg_union :: "'a neg_dseq => 'a neg_dseq => 'a neg_dseq" ``` bulwahn@36017 ` 75` ```where ``` bulwahn@36017 ` 76` ``` "neg_union x y = (%i. Lazy_Sequence.append (x i) (y i))" ``` bulwahn@36017 ` 77` bulwahn@36017 ` 78` ```definition neg_if_seq :: "bool => unit neg_dseq" ``` bulwahn@36017 ` 79` ```where ``` bulwahn@36017 ` 80` ``` "neg_if_seq b = (if b then neg_single () else neg_empty)" ``` bulwahn@36017 ` 81` bulwahn@36049 ` 82` ```definition neg_iterate_upto ``` bulwahn@36049 ` 83` ```where ``` bulwahn@36049 ` 84` ``` "neg_iterate_upto f n m = (%i. Lazy_Sequence.iterate_upto (%i. Some (f i)) n m)" ``` bulwahn@36049 ` 85` bulwahn@36017 ` 86` ```definition neg_map :: "('a => 'b) => 'a neg_dseq => 'b neg_dseq" ``` bulwahn@36017 ` 87` ```where ``` bulwahn@36017 ` 88` ``` "neg_map f xq = (%i. Lazy_Sequence.hb_map f (xq i))" ``` bulwahn@36017 ` 89` huffman@36902 ` 90` ```subsection {* Negation *} ``` bulwahn@36017 ` 91` bulwahn@36017 ` 92` ```definition pos_not_seq :: "unit neg_dseq => unit pos_dseq" ``` bulwahn@36017 ` 93` ```where ``` bulwahn@39183 ` 94` ``` "pos_not_seq xq = (%i. Lazy_Sequence.hb_not_seq (xq (3 * i)))" ``` bulwahn@36017 ` 95` bulwahn@36017 ` 96` ```definition neg_not_seq :: "unit pos_dseq => unit neg_dseq" ``` bulwahn@36017 ` 97` ```where ``` bulwahn@36017 ` 98` ``` "neg_not_seq x = (%i. case Lazy_Sequence.yield (x i) of ``` bulwahn@36017 ` 99` ``` None => Lazy_Sequence.hb_single () ``` bulwahn@36017 ` 100` ``` | Some ((), xq) => Lazy_Sequence.empty)" ``` bulwahn@36017 ` 101` wenzelm@36176 ` 102` ```hide_type (open) pos_dseq neg_dseq ``` bulwahn@36017 ` 103` wenzelm@36176 ` 104` ```hide_const (open) ``` bulwahn@40049 ` 105` ``` pos_empty pos_single pos_bind pos_decr_bind pos_union pos_if_seq pos_iterate_upto pos_not_seq pos_map ``` bulwahn@40049 ` 106` ``` neg_empty neg_single neg_bind neg_decr_bind neg_union neg_if_seq neg_iterate_upto neg_not_seq neg_map ``` wenzelm@36176 ` 107` ```hide_fact (open) ``` bulwahn@36049 ` 108` ``` pos_empty_def pos_single_def pos_bind_def pos_union_def pos_if_seq_def pos_iterate_upto_def pos_not_seq_def pos_map_def ``` bulwahn@36049 ` 109` ``` neg_empty_def neg_single_def neg_bind_def neg_union_def neg_if_seq_def neg_iterate_upto_def neg_not_seq_def neg_map_def ``` bulwahn@36017 ` 110` bulwahn@36017 ` 111` ```end ```