Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / assembly / string / string.ma

diff --git a/matita/matita/contribs/assembly/string/string.ma b/matita/matita/contribs/assembly/string/string.ma
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+(**************************************************************************)
+(*       ___                                                              *)
+(*      ||M||                                                             *)
+(*      ||A||       A project by Andrea Asperti                           *)
+(*      ||T||                                                             *)
+(*      ||I||       Developers:                                           *)
+(*      ||T||         The HELM team.                                      *)
+(*      ||A||         http://helm.cs.unibo.it                             *)
+(*      \   /                                                             *)
+(*       \ /        This file is distributed under the terms of the       *)
+(*        v         GNU General Public License Version 2                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                                                                        *)
+(* Sviluppato da:                                                         *)
+(*   Cosimo Oliboni, oliboni@cs.unibo.it                                  *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "string/ascii_min.ma".
+include "compiler/utility.ma".
+
+(* ************************ *)
+(* MANIPOLAZIONE DI STRINGA *)
+(* ************************ *)
+
+(* tipo pubblico *)
+definition aux_str_type ≝ list ascii_min.
+
+(* empty string *)
+definition empty_str ≝ nil ascii_min.
+
+(* is empty ? *)
+definition isNull_str ≝
+λstr:aux_str_type.match str with
+ [ nil ⇒ true | cons _ _ ⇒ false ].
+
+(* strcmp *)
+let rec eqStr_str (str,str':aux_str_type) ≝
+ match str with
+  [ nil ⇒ match str' with
+   [ nil => true
+   | cons _ _ => false ]
+  | cons h t ⇒ match str' with
+   [ nil ⇒ false
+   | cons h' t' ⇒ (eqAsciiMin h h')⊗(eqStr_str t t')
+   ]
+  ].
+
+lemma eqex_switch : ∀e1,e2.eq_ex e1 e2 = eq_ex e2 e1.
+ intros;
+ elim e1;
+ elim e2;
+ reflexivity.
+qed.
+
+lemma eqb8_switch : ∀b1,b2.eq_b8 b1 b2 = eq_b8 b2 b1.
+ intros;
+ elim b1;
+ elim b2;
+ unfold eq_b8;
+ rewrite > eqex_switch in ⊢ (? ? % ?);
+ rewrite > eqex_switch in ⊢ (? ? (? ? %) ?);
+ reflexivity.
+qed.
+
+lemma eqasciimin_switch : ∀a1,a2.eqAsciiMin a1 a2 = eqAsciiMin a2 a1.
+ intros;
+ unfold eqAsciiMin;
+ rewrite > eqb8_switch in ⊢ (? ? % ?);
+ reflexivity.
+qed.
+
+lemma eq_to_eqstr : ∀s,s'.s = s' → eqStr_str s s' = true.
+ do 2 intro;
+ intro;
+ rewrite < H;
+ elim s;
+ [ 1: reflexivity
+ | 2: simplify;
+      rewrite > (eq_to_eqasciimin a a (refl_eq ??));
+      rewrite > H1;
+      reflexivity
+ ].
+qed.
+
+lemma eqstr_to_eq : ∀s,s'.eqStr_str s s' = true → s = s'.
+ intros 1;
+ elim s 0;
+ intros;
+ [ simplify in H:(%);
+   cases s' in H;
+   simplify;
+   intros;
+   [ reflexivity
+   | destruct H
+   ]
+ | elim s' in H1;
+   [ simplify in H1;
+     destruct H1
+   | simplify in H2;
+     lapply (andb_true_true ?? H2);
+     lapply (andb_true_true_r ?? H2);
+     rewrite > (H ? Hletin1);
+     rewrite > (eqasciimin_to_eq ?? Hletin);
+     reflexivity
+   ]
+ ].
+qed.
+
+(* strcat *)
+definition strCat_str ≝
+λstr,str':aux_str_type.str@str'.
+
+(* strlen *)
+definition strLen_str ≝ λstr:aux_str_type.len_list ? str.
+
+(* ************ *)
+(* STRINGA + ID *)
+(* ************ *)
+
+(* tipo pubblico *)
+inductive aux_strId_type : Type ≝
+ STR_ID: aux_str_type → nat → aux_strId_type.
+
+(* getter *)
+definition get_name_strId ≝ λsid:aux_strId_type.match sid with [ STR_ID n _ ⇒ n ].
+definition get_id_strId ≝ λsid:aux_strId_type.match sid with [ STR_ID _ d ⇒ d ].
+
+(* confronto *)
+definition eqStrId_str ≝
+λsid,sid':aux_strId_type.(eqStr_str (get_name_strId sid) (get_name_strId sid'))⊗(eqb (get_id_strId sid) (get_id_strId sid')).
+
+lemma eq_to_eqstrid : ∀s,s'.s = s' → eqStrId_str s s' = true.
+ intros 3;
+ rewrite < H;
+ elim s;
+ simplify;
+ rewrite > (eq_to_eqstr a a (refl_eq ??));
+ rewrite > (eq_to_eqb_true n n (refl_eq ??));
+ reflexivity.
+qed.
+
+lemma eqstrid_to_eq : ∀s,s'.eqStrId_str s s' = true → s = s'.
+ intros 2;
+ elim s 0;
+ elim s' 0;
+ intros 4;
+ simplify;
+ intro;
+ rewrite > (eqstr_to_eq a1 a (andb_true_true ?? H));
+ rewrite > (eqb_true_to_eq n1 n (andb_true_true_r ?? H));
+ reflexivity.
+qed.