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Diffstat (limited to 'theories/Strings/String.v')
| -rw-r--r-- | theories/Strings/String.v | 34 |
1 files changed, 34 insertions, 0 deletions
diff --git a/theories/Strings/String.v b/theories/Strings/String.v index 2be6618a..be9a10c6 100644 --- a/theories/Strings/String.v +++ b/theories/Strings/String.v @@ -14,6 +14,7 @@ Require Import Arith. Require Import Ascii. +Require Import Bool. Declare ML Module "string_syntax_plugin". (** *** Definition of strings *) @@ -35,6 +36,39 @@ Proof. decide equality; apply ascii_dec. Defined. +Local Open Scope lazy_bool_scope. + +Fixpoint eqb s1 s2 : bool := + match s1, s2 with + | EmptyString, EmptyString => true + | String c1 s1', String c2 s2' => Ascii.eqb c1 c2 &&& eqb s1' s2' + | _,_ => false + end. + +Infix "=?" := eqb : string_scope. + +Lemma eqb_spec s1 s2 : Bool.reflect (s1 = s2) (s1 =? s2)%string. +Proof. + revert s2. induction s1; destruct s2; try (constructor; easy); simpl. + case Ascii.eqb_spec; simpl; [intros -> | constructor; now intros [= ]]. + case IHs1; [intros ->; now constructor | constructor; now intros [= ]]. +Qed. + +Local Ltac t_eqb := + repeat first [ congruence + | progress subst + | apply conj + | match goal with + | [ |- context[eqb ?x ?y] ] => destruct (eqb_spec x y) + end + | intro ]. +Lemma eqb_refl x : (x =? x)%string = true. Proof. t_eqb. Qed. +Lemma eqb_sym x y : (x =? y)%string = (y =? x)%string. Proof. t_eqb. Qed. +Lemma eqb_eq n m : (n =? m)%string = true <-> n = m. Proof. t_eqb. Qed. +Lemma eqb_neq x y : (x =? y)%string = false <-> x <> y. Proof. t_eqb. Qed. +Lemma eqb_compat: Morphisms.Proper (Morphisms.respectful eq (Morphisms.respectful eq eq)) eqb. +Proof. t_eqb. Qed. + (** *** Concatenation of strings *) Reserved Notation "x ++ y" (right associativity, at level 60). |