strings.v 3.75 KB
Newer Older
1
(* Copyright (c) 2012-2017, Coq-std++ developers. *)
Robbert Krebbers's avatar
Robbert Krebbers committed
2
(* This file is distributed under the terms of the BSD license. *)
3
4
From Coq Require Import Ascii.
From Coq Require Export String.
5
6
From stdpp Require Export list.
From stdpp Require Import countable.
7
Set Default Proof Using "Type".
8
9
10
11

(* To avoid randomly ending up with String.length because this module is
imported hereditarily somewhere. *)
Notation length := List.length.
Robbert Krebbers's avatar
Robbert Krebbers committed
12
13
14
15

(** * Fix scopes *)
Open Scope string_scope.
Open Scope list_scope.
16
Infix "+:+" := String.append (at level 60, right associativity) : stdpp_scope.
17
Arguments String.append : simpl never.
Robbert Krebbers's avatar
Robbert Krebbers committed
18
19

(** * Decision of equality *)
20
21
Instance assci_eq_dec : EqDecision ascii := ascii_dec.
Instance string_eq_dec : EqDecision string.
Robbert Krebbers's avatar
Robbert Krebbers committed
22
Proof. solve_decision. Defined.
23
Instance string_app_inj : Inj (=) (=) (String.append s1).
24
Proof. intros s1 ???. induction s1; simplify_eq/=; f_equal/=; auto. Qed.
Robbert Krebbers's avatar
Robbert Krebbers committed
25

26
27
28
29
30
31
32
33
(* Reverse *)
Fixpoint string_rev_app (s1 s2 : string) : string :=
  match s1 with
  | "" => s2
  | String a s1 => string_rev_app s1 (String a s2)
  end.
Definition string_rev (s : string) : string := string_rev_app s "".

34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
Definition is_nat (x : ascii) : option nat :=
  match x with
  | "0" => Some 0
  | "1" => Some 1
  | "2" => Some 2
  | "3" => Some 3
  | "4" => Some 4
  | "5" => Some 5
  | "6" => Some 6
  | "7" => Some 7
  | "8" => Some 8
  | "9" => Some 9
  | _ => None
  end%char.

49
(* Break a string up into lists of words, delimited by white space *)
50
51
52
53
54
Definition is_space (x : Ascii.ascii) : bool :=
  match x with
  | "009" | "010" | "011" | "012" | "013" | " " => true | _ => false
  end%char.

55
56
57
Fixpoint words_go (cur : option string) (s : string) : list string :=
  match s with
  | "" => option_list (string_rev <$> cur)
58
59
  | String a s =>
     if is_space a then option_list (string_rev <$> cur) ++ words_go None s
60
     else words_go (Some (from_option (String a) (String a "") cur)) s
61
62
63
64
65
66
67
68
69
  end.
Definition words : string  list string := words_go None.

Ltac words s :=
  match type of s with
  | list string => s
  | string => eval vm_compute in (words s)
  end.

Robbert Krebbers's avatar
Robbert Krebbers committed
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
(** * Encoding and decoding *)
(** In order to reuse or existing implementation of radix-2 search trees over
positive binary naturals [positive], we define an injection [string_to_pos]
from [string] into [positive]. *)
Fixpoint digits_to_pos (βs : list bool) : positive :=
  match βs with
  | [] => xH
  | false :: βs => (digits_to_pos βs)~0
  | true :: βs => (digits_to_pos βs)~1
  end%positive.
Definition ascii_to_digits (a : Ascii.ascii) : list bool :=
  match a with
  | Ascii.Ascii β1 β2 β3 β4 β5 β6 β7 β8 => [β1;β2;β3;β4;β5;β6;β7;β8]
  end.
Fixpoint string_to_pos (s : string) : positive :=
  match s with
  | EmptyString => xH
  | String a s => string_to_pos s ++ digits_to_pos (ascii_to_digits a)
  end%positive.
Fixpoint digits_of_pos (p : positive) : list bool :=
  match p with
  | xH => []
  | p~0 => false :: digits_of_pos p
  | p~1 => true :: digits_of_pos p
  end%positive.
Fixpoint ascii_of_digits (βs : list bool) : ascii :=
  match βs with
  | [] => zero
  | β :: βs => Ascii.shift β (ascii_of_digits βs)
  end.
Fixpoint string_of_digits (βs : list bool) : string :=
  match βs with
  | β1 :: β2 :: β3 :: β4 :: β5 :: β6 :: β7 :: β8 :: βs =>
     String (ascii_of_digits [β1;β2;β3;β4;β5;β6;β7;β8]) (string_of_digits βs)
  | _ => EmptyString
  end.
Definition string_of_pos (p : positive) : string :=
  string_of_digits (digits_of_pos p).
Lemma string_of_to_pos s : string_of_pos (string_to_pos s) = s.
Proof.
110
  unfold string_of_pos. by induction s as [|[[][][][][][][][]]]; f_equal/=.
Robbert Krebbers's avatar
Robbert Krebbers committed
111
112
113
114
115
Qed.
Program Instance string_countable : Countable string := {|
  encode := string_to_pos; decode p := Some (string_of_pos p)
|}.
Solve Obligations with naive_solver eauto using string_of_to_pos with f_equal.