src/HOL/New_DSequence.thy
 author haftmann Mon Nov 29 13:44:54 2010 +0100 (2010-11-29) changeset 40815 6e2d17cc0d1d parent 40049 75d9f57123d6 child 42163 392fd6c4669c permissions -rw-r--r--
equivI has replaced equiv.intro
```     1
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```     2 (* Author: Lukas Bulwahn, TU Muenchen *)
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```     3
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```     4 header {* Depth-Limited Sequences with failure element *}
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```     5
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```     6 theory New_DSequence
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```     7 imports Random_Sequence
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```     8 begin
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```     9
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```    10 subsection {* Positive Depth-Limited Sequence *}
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```    11
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```    12 types 'a pos_dseq = "code_numeral => 'a Lazy_Sequence.lazy_sequence"
```
```    13
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```    14 definition pos_empty :: "'a pos_dseq"
```
```    15 where
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```    16   "pos_empty = (%i. Lazy_Sequence.empty)"
```
```    17
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```    18 definition pos_single :: "'a => 'a pos_dseq"
```
```    19 where
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```    20   "pos_single x = (%i. Lazy_Sequence.single x)"
```
```    21
```
```    22 definition pos_bind :: "'a pos_dseq => ('a => 'b pos_dseq) => 'b pos_dseq"
```
```    23 where
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```    24   "pos_bind x f = (%i. Lazy_Sequence.bind (x i) (%a. f a i))"
```
```    25
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```    26 definition pos_decr_bind :: "'a pos_dseq => ('a => 'b pos_dseq) => 'b pos_dseq"
```
```    27 where
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```    28   "pos_decr_bind x f = (%i.
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```    29      if i = 0 then
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```    30        Lazy_Sequence.empty
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```    31      else
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```    32        Lazy_Sequence.bind (x (i - 1)) (%a. f a i))"
```
```    33
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```    34 definition pos_union :: "'a pos_dseq => 'a pos_dseq => 'a pos_dseq"
```
```    35 where
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```    36   "pos_union xq yq = (%i. Lazy_Sequence.append (xq i) (yq i))"
```
```    37
```
```    38 definition pos_if_seq :: "bool => unit pos_dseq"
```
```    39 where
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```    40   "pos_if_seq b = (if b then pos_single () else pos_empty)"
```
```    41
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```    42 definition pos_iterate_upto :: "(code_numeral => 'a) => code_numeral => code_numeral => 'a pos_dseq"
```
```    43 where
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```    44   "pos_iterate_upto f n m = (%i. Lazy_Sequence.iterate_upto f n m)"
```
```    45
```
```    46 definition pos_map :: "('a => 'b) => 'a pos_dseq => 'b pos_dseq"
```
```    47 where
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```    48   "pos_map f xq = (%i. Lazy_Sequence.map f (xq i))"
```
```    49
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```    50 subsection {* Negative Depth-Limited Sequence *}
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```    51
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```    52 types 'a neg_dseq = "code_numeral => 'a Lazy_Sequence.hit_bound_lazy_sequence"
```
```    53
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```    54 definition neg_empty :: "'a neg_dseq"
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```    55 where
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```    56   "neg_empty = (%i. Lazy_Sequence.empty)"
```
```    57
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```    58 definition neg_single :: "'a => 'a neg_dseq"
```
```    59 where
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```    60   "neg_single x = (%i. Lazy_Sequence.hb_single x)"
```
```    61
```
```    62 definition neg_bind :: "'a neg_dseq => ('a => 'b neg_dseq) => 'b neg_dseq"
```
```    63 where
```
```    64   "neg_bind x f = (%i. hb_bind (x i) (%a. f a i))"
```
```    65
```
```    66 definition neg_decr_bind :: "'a neg_dseq => ('a => 'b neg_dseq) => 'b neg_dseq"
```
```    67 where
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```    68   "neg_decr_bind x f = (%i.
```
```    69      if i = 0 then
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```    70        Lazy_Sequence.hit_bound
```
```    71      else
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```    72        hb_bind (x (i - 1)) (%a. f a i))"
```
```    73
```
```    74 definition neg_union :: "'a neg_dseq => 'a neg_dseq => 'a neg_dseq"
```
```    75 where
```
```    76   "neg_union x y = (%i. Lazy_Sequence.append (x i) (y i))"
```
```    77
```
```    78 definition neg_if_seq :: "bool => unit neg_dseq"
```
```    79 where
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```    80   "neg_if_seq b = (if b then neg_single () else neg_empty)"
```
```    81
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```    82 definition neg_iterate_upto
```
```    83 where
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```    84   "neg_iterate_upto f n m = (%i. Lazy_Sequence.iterate_upto (%i. Some (f i)) n m)"
```
```    85
```
```    86 definition neg_map :: "('a => 'b) => 'a neg_dseq => 'b neg_dseq"
```
```    87 where
```
```    88   "neg_map f xq = (%i. Lazy_Sequence.hb_map f (xq i))"
```
```    89
```
```    90 subsection {* Negation *}
```
```    91
```
```    92 definition pos_not_seq :: "unit neg_dseq => unit pos_dseq"
```
```    93 where
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```    94   "pos_not_seq xq = (%i. Lazy_Sequence.hb_not_seq (xq (3 * i)))"
```
```    95
```
```    96 definition neg_not_seq :: "unit pos_dseq => unit neg_dseq"
```
```    97 where
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```    98   "neg_not_seq x = (%i. case Lazy_Sequence.yield (x i) of
```
```    99     None => Lazy_Sequence.hb_single ()
```
```   100   | Some ((), xq) => Lazy_Sequence.empty)"
```
```   101
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```   102 hide_type (open) pos_dseq neg_dseq
```
```   103
```
```   104 hide_const (open)
```
```   105   pos_empty pos_single pos_bind pos_decr_bind pos_union pos_if_seq pos_iterate_upto pos_not_seq pos_map
```
```   106   neg_empty neg_single neg_bind neg_decr_bind neg_union neg_if_seq neg_iterate_upto neg_not_seq neg_map
```
```   107 hide_fact (open)
```
```   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
```
```   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
```
```   110
```
```   111 end
```