freescale porting

[helm.git] / helm / software / matita / contribs / ng_assembly2 / compiler / ast_base_type.ma

diff --git a/helm/software/matita/contribs/ng_assembly2/compiler/ast_base_type.ma b/helm/software/matita/contribs/ng_assembly2/compiler/ast_base_type.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                  *)
+(*                                                                        *)
+(**************************************************************************)
+
+(* ********************************************************************** *)
+(*                          Progetto FreeScale                            *)
+(*                                                                        *)
+(*   Sviluppato da: Ing. Cosimo Oliboni, oliboni@cs.unibo.it              *)
+(*   Sviluppo: 2008-2010                                                  *)
+(*                                                                        *)
+(* ********************************************************************** *)
+
+include "compiler/ast_base_type_base.ma".
+include "common/comp.ma".
+include "num/bool_lemmas.ma".
+
+(* ************************* *)
+(* dimensioni degli elementi *)
+(* ************************* *)
+
+ndefinition astbasetype_destruct_aux ≝
+Πb1,b2:ast_base_type.ΠP:Prop.b1 = b2 →
+ match eq_astbasetype b1 b2 with [ true ⇒ P → P | false ⇒ P ].
+
+ndefinition astbasetype_destruct : astbasetype_destruct_aux.
+ #b1; #b2; #P; #H;
+ nrewrite < H;
+ nelim b1;
+ nnormalize;
+ napply (λx.x).
+nqed.
+
+nlemma eq_to_eqastbasetype : ∀n1,n2.n1 = n2 → eq_astbasetype n1 n2 = true.
+ #n1; #n2; #H;
+ nrewrite > H;
+ nelim n2;
+ nnormalize;
+ napply refl_eq.
+nqed.
+
+nlemma neqastbasetype_to_neq : ∀n1,n2.eq_astbasetype n1 n2 = false → n1 ≠ n2.
+ #n1; #n2; #H;
+ napply (not_to_not (n1 = n2) (eq_astbasetype n1 n2 = true) …);
+ ##[ ##1: napply (eq_to_eqastbasetype n1 n2)
+ ##| ##2: napply (eqfalse_to_neqtrue … H)
+ ##]
+nqed.
+
+nlemma eqastbasetype_to_eq : ∀b1,b2.eq_astbasetype b1 b2 = true → b1 = b2.
+ #b1; #b2; ncases b1; ncases b2; nnormalize;
+ ##[ ##1,5,9: #H; napply refl_eq
+ ##| ##*: #H; ndestruct (*napply (bool_destruct … H)*)
+ ##]
+nqed.
+
+nlemma neq_to_neqastbasetype : ∀n1,n2.n1 ≠ n2 → eq_astbasetype n1 n2 = false.
+ #n1; #n2; #H;
+ napply (neqtrue_to_eqfalse (eq_astbasetype n1 n2));
+ napply (not_to_not (eq_astbasetype n1 n2 = true) (n1 = n2) ? H);
+ napply (eqastbasetype_to_eq n1 n2).
+nqed.
+
+nlemma decidable_astbasetype : ∀x,y:ast_base_type.decidable (x = y).
+ #x; #y; nnormalize;
+ napply (or2_elim (eq_astbasetype x y = true) (eq_astbasetype x y = false) ? (decidable_bexpr ?));
+ ##[ ##1: #H; napply (or2_intro1 (x = y) (x ≠ y) (eqastbasetype_to_eq … H))
+ ##| ##2: #H; napply (or2_intro2 (x = y) (x ≠ y) (neqastbasetype_to_neq … H))
+ ##]
+nqed.
+
+nlemma symmetric_eqastbasetype : symmetricT ast_base_type bool eq_astbasetype.
+ #n1; #n2;
+ napply (or2_elim (n1 = n2) (n1 ≠ n2) ? (decidable_astbasetype n1 n2));
+ ##[ ##1: #H; nrewrite > H; napply refl_eq
+ ##| ##2: #H; nrewrite > (neq_to_neqastbasetype n1 n2 H);
+          napply (symmetric_eq ? (eq_astbasetype n2 n1) false);
+          napply (neq_to_neqastbasetype n2 n1 (symmetric_neq ? n1 n2 H))
+ ##]
+nqed.
+
+nlemma astbasetype_is_comparable : comparable.
+ @ ast_base_type
+  ##[ napply AST_BASE_TYPE_BYTE8
+  ##| napply forall_astbasetype
+  ##| napply eq_astbasetype
+  ##| napply eqastbasetype_to_eq
+  ##| napply eq_to_eqastbasetype
+  ##| napply neqastbasetype_to_neq
+  ##| napply neq_to_neqastbasetype
+  ##| napply decidable_astbasetype
+  ##| napply symmetric_eqastbasetype
+  ##]
+nqed.
+
+unification hint 0 ≔ ⊢ carr astbasetype_is_comparable ≡ ast_base_type.
+