bulwahn@36017: 
bulwahn@36017: (* Author: Lukas Bulwahn, TU Muenchen *)
bulwahn@36017: 
bulwahn@36017: header {* Depth-Limited Sequences with failure element *}
bulwahn@36017: 
bulwahn@36017: theory New_DSequence
bulwahn@36017: imports Random_Sequence
bulwahn@36017: begin
bulwahn@36017: 
huffman@36902: subsection {* Positive Depth-Limited Sequence *}
bulwahn@36017: 
bulwahn@36017: types 'a pos_dseq = "code_numeral => 'a Lazy_Sequence.lazy_sequence"
bulwahn@36017: 
bulwahn@36017: definition pos_empty :: "'a pos_dseq"
bulwahn@36017: where
bulwahn@36017:   "pos_empty = (%i. Lazy_Sequence.empty)"
bulwahn@36017: 
bulwahn@36017: definition pos_single :: "'a => 'a pos_dseq"
bulwahn@36017: where
bulwahn@36017:   "pos_single x = (%i. Lazy_Sequence.single x)"
bulwahn@36017: 
bulwahn@36017: definition pos_bind :: "'a pos_dseq => ('a => 'b pos_dseq) => 'b pos_dseq"
bulwahn@36017: where
bulwahn@36017:   "pos_bind x f = (%i. 
bulwahn@36017:      if i = 0 then
bulwahn@36017:        Lazy_Sequence.empty
bulwahn@36017:      else
bulwahn@36017:        Lazy_Sequence.bind (x (i - 1)) (%a. f a i))"
bulwahn@36017: 
bulwahn@36017: definition pos_union :: "'a pos_dseq => 'a pos_dseq => 'a pos_dseq"
bulwahn@36017: where
bulwahn@36017:   "pos_union xq yq = (%i. Lazy_Sequence.append (xq i) (yq i))"
bulwahn@36017: 
bulwahn@36017: definition pos_if_seq :: "bool => unit pos_dseq"
bulwahn@36017: where
bulwahn@36017:   "pos_if_seq b = (if b then pos_single () else pos_empty)"
bulwahn@36017: 
bulwahn@36049: definition pos_iterate_upto :: "(code_numeral => 'a) => code_numeral => code_numeral => 'a pos_dseq"
bulwahn@36049: where
bulwahn@36049:   "pos_iterate_upto f n m = (%i. Lazy_Sequence.iterate_upto f n m)"
bulwahn@36049:  
bulwahn@36017: definition pos_map :: "('a => 'b) => 'a pos_dseq => 'b pos_dseq"
bulwahn@36017: where
bulwahn@36017:   "pos_map f xq = (%i. Lazy_Sequence.map f (xq i))"
bulwahn@36017: 
huffman@36902: subsection {* Negative Depth-Limited Sequence *}
bulwahn@36017: 
bulwahn@36017: types 'a neg_dseq = "code_numeral => 'a Lazy_Sequence.hit_bound_lazy_sequence"
bulwahn@36017: 
bulwahn@36017: definition neg_empty :: "'a neg_dseq"
bulwahn@36017: where
bulwahn@36017:   "neg_empty = (%i. Lazy_Sequence.empty)"
bulwahn@36017: 
bulwahn@36017: definition neg_single :: "'a => 'a neg_dseq"
bulwahn@36017: where
bulwahn@36017:   "neg_single x = (%i. Lazy_Sequence.hb_single x)"
bulwahn@36017: 
bulwahn@36017: definition neg_bind :: "'a neg_dseq => ('a => 'b neg_dseq) => 'b neg_dseq"
bulwahn@36017: where
bulwahn@36017:   "neg_bind x f = (%i. 
bulwahn@36017:      if i = 0 then
bulwahn@36017:        Lazy_Sequence.hit_bound
bulwahn@36017:      else
bulwahn@36017:        hb_bind (x (i - 1)) (%a. f a i))"
bulwahn@36017: 
bulwahn@36017: definition neg_union :: "'a neg_dseq => 'a neg_dseq => 'a neg_dseq"
bulwahn@36017: where
bulwahn@36017:   "neg_union x y = (%i. Lazy_Sequence.append (x i) (y i))"
bulwahn@36017: 
bulwahn@36017: definition neg_if_seq :: "bool => unit neg_dseq"
bulwahn@36017: where
bulwahn@36017:   "neg_if_seq b = (if b then neg_single () else neg_empty)"
bulwahn@36017: 
bulwahn@36049: definition neg_iterate_upto 
bulwahn@36049: where
bulwahn@36049:   "neg_iterate_upto f n m = (%i. Lazy_Sequence.iterate_upto (%i. Some (f i)) n m)"
bulwahn@36049: 
bulwahn@36017: definition neg_map :: "('a => 'b) => 'a neg_dseq => 'b neg_dseq"
bulwahn@36017: where
bulwahn@36017:   "neg_map f xq = (%i. Lazy_Sequence.hb_map f (xq i))"
bulwahn@36017: 
huffman@36902: subsection {* Negation *}
bulwahn@36017: 
bulwahn@36017: definition pos_not_seq :: "unit neg_dseq => unit pos_dseq"
bulwahn@36017: where
bulwahn@36017:   "pos_not_seq xq = (%i. Lazy_Sequence.hb_not_seq (xq i))"
bulwahn@36017: 
bulwahn@36017: definition neg_not_seq :: "unit pos_dseq => unit neg_dseq"
bulwahn@36017: where
bulwahn@36017:   "neg_not_seq x = (%i. case Lazy_Sequence.yield (x i) of
bulwahn@36017:     None => Lazy_Sequence.hb_single ()
bulwahn@36017:   | Some ((), xq) => Lazy_Sequence.empty)"
bulwahn@36017: 
wenzelm@36176: hide_type (open) pos_dseq neg_dseq
bulwahn@36017: 
wenzelm@36176: hide_const (open)
bulwahn@36049:   pos_empty pos_single pos_bind pos_union pos_if_seq pos_iterate_upto pos_not_seq pos_map
bulwahn@36049:   neg_empty neg_single neg_bind neg_union neg_if_seq neg_iterate_upto neg_not_seq neg_map
wenzelm@36176: hide_fact (open)
bulwahn@36049:   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:   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: 
bulwahn@36017: end