@@ -17,119 +17,119 @@ Section working_environment.
1717
1818Variable R : realFieldType.
1919
20- (* Notation prefix, dupplicated from cells_alg.v *)
21- Notation pt := (pt (RealField.sort R)).
22- Notation p_x := (p_x (RealField.sort R)).
23- Notation p_y := (p_y (RealField.sort R)).
24- Notation Bpt := (Bpt (RealField.sort R)).
20+ (* Notation prefix, duplicated from cells_alg.v *)
21+ Notation pt := (pt (Num. RealField.sort R)).
22+ Notation p_x := (p_x (Num. RealField.sort R)).
23+ Notation p_y := (p_y (Num. RealField.sort R)).
24+ Notation Bpt := (Bpt (Num. RealField.sort R)).
2525Notation edge := (edge R).
2626Notation left_pt := (@left_pt R).
2727Notation right_pt := (@right_pt R).
28- Notation event := (event (RealField.sort R) edge).
29- Notation outgoing := (outgoing (RealField.sort R) edge).
30- Notation point := (point (RealField.sort R) edge).
31- Notation cell := (cell (RealField.sort R) edge).
28+ Notation event := (event (Num. RealField.sort R) edge).
29+ Notation outgoing := (outgoing (Num. RealField.sort R) edge).
30+ Notation point := (point (Num. RealField.sort R) edge).
31+ Notation cell := (cell (Num. RealField.sort R) edge).
3232
33- Notation dummy_pt := (dummy_pt (RealField.sort R) 1).
34- Notation dummy_edge := (dummy_edge (RealField.sort R) 1 edge (@unsafe_Bedge _)).
33+ Notation dummy_pt := (dummy_pt (Num. RealField.sort R) 1).
34+ Notation dummy_edge := (dummy_edge (Num. RealField.sort R) 1 edge (@unsafe_Bedge _)).
3535Notation dummy_cell :=
36- (dummy_cell (RealField.sort R) 1 edge (@unsafe_Bedge _)).
37- Notation dummy_event := (dummy_event (RealField.sort R) 1 edge).
36+ (dummy_cell (Num. RealField.sort R) 1 edge (@unsafe_Bedge _)).
37+ Notation dummy_event := (dummy_event (Num. RealField.sort R) 1 edge).
3838Notation edge_below :=
39- (generic_trajectories.edge_below (RealField.sort R) eq_op <=%R +%R
39+ (generic_trajectories.edge_below (Num. RealField.sort R) eq_op <=%R +%R
4040 (fun x y => x - y) *%R 1 edge left_pt right_pt).
4141Notation "x <| y" := (edge_below x y).
4242Notation valid_edge :=
43- (generic_trajectories.valid_edge (RealField.sort R)
43+ (generic_trajectories.valid_edge (Num. RealField.sort R)
4444 le edge left_pt right_pt).
4545Notation vertical_intersection_point :=
46- (vertical_intersection_point (RealField.sort R)
46+ (vertical_intersection_point (Num. RealField.sort R)
4747 le +%R (fun x y => x - y) *%R
4848 (fun x y => x / y) edge left_pt right_pt).
4949Notation point_under_edge :=
50- (point_under_edge (RealField.sort R) le +%R (fun x y => x - y) *%R 1
50+ (point_under_edge (Num. RealField.sort R) le +%R (fun x y => x - y) *%R 1
5151 edge left_pt right_pt).
5252Notation "p <<= g" := (point_under_edge p g).
5353Notation "p >>> g" := (~~ (point_under_edge p g)).
5454Notation point_strictly_under_edge :=
55- (point_strictly_under_edge (RealField.sort R) eq_op <=%R +%R
55+ (point_strictly_under_edge (Num. RealField.sort R) eq_op <=%R +%R
5656 (fun x y => x - y) *%R 1 edge left_pt right_pt).
5757Notation "p <<< g" := (point_strictly_under_edge p g).
5858Notation "p >>= g" := (~~ (point_strictly_under_edge p g)).
5959
6060Notation contains_point :=
61- (contains_point (RealField.sort R) eq_op <=%R +%R (fun x y => x - y) *%R 1
61+ (contains_point (Num. RealField.sort R) eq_op <=%R +%R (fun x y => x - y) *%R 1
6262 edge left_pt right_pt).
6363
6464Notation open_cells_decomposition_contact :=
65- (open_cells_decomposition_contact (RealField.sort R) eq_op le +%R
65+ (open_cells_decomposition_contact (Num. RealField.sort R) eq_op le +%R
6666 (fun x y => x - y) *%R 1 edge left_pt right_pt).
6767Notation open_cells_decomposition_rec :=
68- (open_cells_decomposition_rec (RealField.sort R) eq_op le +%R
68+ (open_cells_decomposition_rec (Num. RealField.sort R) eq_op le +%R
6969 (fun x y => x - y) *%R 1 edge (@unsafe_Bedge R) left_pt
7070 right_pt).
7171Notation open_cells_decomposition :=
72- (open_cells_decomposition (RealField.sort R) eq_op le +%R
72+ (open_cells_decomposition (Num. RealField.sort R) eq_op le +%R
7373 (fun x y => x - y) *%R 1 edge (@unsafe_Bedge R) left_pt
7474 right_pt).
7575
76- Notation scan_state := (scan_state (RealField.sort R) edge).
77- Notation sc_open1 := (sc_open1 (RealField.sort R) edge).
78- Notation lst_open := (lst_open (RealField.sort R) edge).
79- Notation sc_open2 := (sc_open2 (RealField.sort R) edge).
80- Notation sc_closed := (sc_closed (RealField.sort R) edge).
81- Notation lst_closed := (lst_closed (RealField.sort R) edge).
76+ Notation scan_state := (scan_state (Num. RealField.sort R) edge).
77+ Notation sc_open1 := (sc_open1 (Num. RealField.sort R) edge).
78+ Notation lst_open := (lst_open (Num. RealField.sort R) edge).
79+ Notation sc_open2 := (sc_open2 (Num. RealField.sort R) edge).
80+ Notation sc_closed := (sc_closed (Num. RealField.sort R) edge).
81+ Notation lst_closed := (lst_closed (Num. RealField.sort R) edge).
8282
8383Notation update_closed_cell :=
84- (update_closed_cell (RealField.sort R) 1 edge).
84+ (update_closed_cell (Num. RealField.sort R) 1 edge).
8585
8686Notation set_left_pts :=
87- (set_left_pts (RealField.sort R) edge).
87+ (set_left_pts (Num. RealField.sort R) edge).
8888
89- Notation low := (low (RealField.sort R) edge).
90- Notation high := (high (RealField.sort R) edge).
91- Notation left_pts := (left_pts (RealField.sort R) edge).
92- Notation right_pts := (right_pts (RealField.sort R) edge).
93- Notation Bcell := (Bcell (RealField.sort R) edge).
89+ Notation low := (low (Num. RealField.sort R) edge).
90+ Notation high := (high (Num. RealField.sort R) edge).
91+ Notation left_pts := (left_pts (Num. RealField.sort R) edge).
92+ Notation right_pts := (right_pts (Num. RealField.sort R) edge).
93+ Notation Bcell := (Bcell (Num. RealField.sort R) edge).
9494Notation cell_center :=
95- (cell_center (RealField.sort R) +%R (fun x y => x / y) 1%:R edge).
95+ (cell_center (Num. RealField.sort R) +%R (fun x y => x / y) 1%:R edge).
9696
9797Notation closing_cells :=
98- (generic_trajectories.closing_cells (RealField.sort R) eq_op <=%R +%R (fun x y => x - y)
98+ (generic_trajectories.closing_cells (Num. RealField.sort R) eq_op <=%R +%R (fun x y => x - y)
9999 *%R (fun x y => x / y) edge left_pt right_pt).
100100Notation close_cell :=
101- (generic_trajectories.close_cell (RealField.sort R) eq_op <=%R +%R (fun x y => x - y)
101+ (generic_trajectories.close_cell (Num. RealField.sort R) eq_op <=%R +%R (fun x y => x - y)
102102 *%R (fun x y => x / y) edge left_pt right_pt).
103103
104- Notation set_pts := (set_pts (RealField.sort R) edge).
104+ Notation set_pts := (set_pts (Num. RealField.sort R) edge).
105105
106106(* This function is to be called only when the event is in the middle
107107 of the last opening cell. The point e needs to be added to the left
108108 points of one of the newly created open cells, but the one that receives
109109 the first segment of the last opening cells should keep its existing
110110 left points. *)
111111Notation update_open_cell :=
112- (update_open_cell (RealField.sort R) eq_op le +%R (fun x y => x - y)
112+ (update_open_cell (Num. RealField.sort R) eq_op le +%R (fun x y => x - y)
113113 *%R (fun x y => x / y) 1 edge (@unsafe_Bedge R) left_pt right_pt).
114114
115115Notation update_open_cell_top :=
116- (update_open_cell_top (RealField.sort R) eq_op le +%R (fun x y => x - y)
116+ (update_open_cell_top (Num. RealField.sort R) eq_op le +%R (fun x y => x - y)
117117 *%R (fun x y => x / y) 1
118118 edge (@unsafe_Bedge R) left_pt right_pt).
119119
120- Notation Bscan := (Bscan (RealField.sort R) edge).
120+ Notation Bscan := (Bscan (Num. RealField.sort R) edge).
121121
122122Notation opening_cells_aux :=
123- (opening_cells_aux (RealField.sort R) eq_op <=%R +%R (fun x y => x - y)
123+ (opening_cells_aux (Num. RealField.sort R) eq_op <=%R +%R (fun x y => x - y)
124124 *%R (fun x y => x / y) 1 edge (@unsafe_Bedge R) left_pt right_pt).
125125
126126Notation simple_step :=
127- (generic_trajectories.simple_step (RealField.sort R) eq_op le +%R
127+ (generic_trajectories.simple_step (Num. RealField.sort R) eq_op le +%R
128128 (fun x y => x - y) *%R (fun x y => x / y)
129129 1 edge (@unsafe_Bedge R) left_pt right_pt).
130130
131131Notation step :=
132- (step (RealField.sort R) eq_op le +%R (fun x y => x - y) *%R
132+ (step (Num. RealField.sort R) eq_op le +%R (fun x y => x - y) *%R
133133 (fun x y => x / y) 1 edge (@unsafe_Bedge R) left_pt right_pt).
134134(*
135135Definition scan events st : seq cell * seq cell :=
@@ -138,7 +138,7 @@ Definition scan events st : seq cell * seq cell :=
138138 lst_closed final_state :: sc_closed final_state). *)
139139
140140Notation start_open_cell :=
141- (start_open_cell (RealField.sort R) eq_op le +%R (fun x y => x - y)
141+ (start_open_cell (Num. RealField.sort R) eq_op le +%R (fun x y => x - y)
142142 *%R (fun x y => x / y) edge left_pt right_pt).
143143
144144Notation open_cell_side_limit_ok :=
@@ -1531,4 +1531,4 @@ have lo_lb' : {in state_open_seq rstate, forall c,
15311531by constructor.
15321532Qed .
15331533
1534- End working_environment.
1534+ End working_environment.
0 commit comments