X-Git-Url: http://matita.cs.unibo.it/gitweb/?p=helm.git;a=blobdiff_plain;f=matita%2Fcontribs%2Fassembly%2Ffreescale%2Fextra.ma;fp=matita%2Fcontribs%2Fassembly%2Ffreescale%2Fextra.ma;h=94f4a47547eebf1a1048c94474c14f35e4e90625;hp=0000000000000000000000000000000000000000;hb=f61af501fb4608cc4fb062a0864c774e677f0d76;hpb=58ae1809c352e71e7b5530dc41e2bfc834e1aef1

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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:                                                         *)
+(*   Cosimo Oliboni, oliboni@cs.unibo.it                                  *)
+(*                                                                        *)
+(* Questo materiale fa parte della tesi:                                  *)
+(*   "Formalizzazione Interattiva dei Microcontroller a 8bit FreeScale"   *)
+(*                                                                        *)
+(*                    data ultima modifica 15/11/2007                     *)
+(* ********************************************************************** *)
+
+include "nat/div_and_mod.ma".
+include "nat/primes.ma".
+include "list/list.ma".
+include "datatypes/constructors.ma".
+include "logic/connectives.ma".
+
+(* BOOLEANI *)
+
+(* ridefinizione degli operatori booleani, per evitare l'overloading di quelli normali *)
+definition not_bool ≝
+λb:bool.match b with [ true ⇒ false | false ⇒ true ].
+
+definition and_bool ≝
+λb1,b2:bool.match b1 with
+ [ true ⇒ b2 | false ⇒ false ].
+
+definition or_bool ≝
+λb1,b2:bool.match b1 with
+ [ true ⇒ true | false ⇒ b2 ].
+
+definition xor_bool ≝
+λb1,b2:bool.match b1 with
+ [ true ⇒ not_bool b2
+ | false ⇒ b2 ].
+
+definition eq_bool ≝
+λb1,b2:bool.match b1 with
+ [ true ⇒ b2
+ | false ⇒ not_bool b2 ].
+
+(* \ominus *)
+notation "hvbox(⊖ a)" non associative with precedence 36
+ for @{ 'not_bool $a }.
+interpretation "not_bool" 'not_bool x = 
+ (cic:/matita/freescale/extra/not_bool.con x).
+
+(* \otimes *)
+notation "hvbox(a break ⊗ b)" left associative with precedence 35
+ for @{ 'and_bool $a $b }.
+interpretation "and_bool" 'and_bool x y = 
+ (cic:/matita/freescale/extra/and_bool.con x y).
+
+(* \oplus *)
+notation "hvbox(a break ⊕ b)" left associative with precedence 34
+ for @{ 'or_bool $a $b }.
+interpretation "or_bool" 'or_bool x y = 
+ (cic:/matita/freescale/extra/or_bool.con x y).
+
+(* \odot *)
+notation "hvbox(a break ⊙ b)" left associative with precedence 33
+ for @{ 'xor_bool $a $b }.
+interpretation "xor_bool" 'xor_bool x y = 
+ (cic:/matita/freescale/extra/xor_bool.con x y).
+
+(* ProdT e' gia' definito, aggiungo Prod3T e Prod4T e Prod5T *)
+
+inductive Prod3T (T1:Type) (T2:Type) (T3:Type) : Type ≝
+tripleT : T1 → T2 → T3 → Prod3T T1 T2 T3.
+
+definition fst3T ≝
+λT1.λT2.λT3.λp:Prod3T T1 T2 T3.match p with [ tripleT x _ _ ⇒ x ].
+
+definition snd3T ≝
+λT1.λT2.λT3.λp:Prod3T T1 T2 T3.match p with [ tripleT _ x _ ⇒ x ].
+
+definition thd3T ≝
+λT1.λT2.λT3.λp:Prod3T T1 T2 T3.match p with [ tripleT _ _ x ⇒ x ].
+
+inductive Prod4T (T1:Type) (T2:Type) (T3:Type) (T4:Type) : Type ≝
+quadrupleT : T1 → T2 → T3 → T4 → Prod4T T1 T2 T3 T4.
+
+definition fst4T ≝
+λT1.λT2.λT3.λT4.λp:Prod4T T1 T2 T3 T4.match p with [ quadrupleT x _ _ _ ⇒ x ].
+
+definition snd4T ≝
+λT1.λT2.λT3.λT4.λp:Prod4T T1 T2 T3 T4.match p with [ quadrupleT _ x _ _ ⇒ x ].
+
+definition thd4T ≝
+λT1.λT2.λT3.λT4.λp:Prod4T T1 T2 T3 T4.match p with [ quadrupleT _ _ x _ ⇒ x ].
+
+definition fth4T ≝
+λT1.λT2.λT3.λT4.λp:Prod4T T1 T2 T3 T4.match p with [ quadrupleT _ _ _ x ⇒ x ].
+
+inductive Prod5T (T1:Type) (T2:Type) (T3:Type) (T4:Type) (T5:Type) : Type ≝
+quintupleT : T1 → T2 → T3 → T4 → T5 → Prod5T T1 T2 T3 T4 T5.
+
+definition fst5T ≝
+λT1.λT2.λT3.λT4.λT5.λp:Prod5T T1 T2 T3 T4 T5.match p with [ quintupleT x _ _ _ _ ⇒ x ].
+
+definition snd5T ≝
+λT1.λT2.λT3.λT4.λT5.λp:Prod5T T1 T2 T3 T4 T5.match p with [ quintupleT _ x _ _ _ ⇒ x ].
+
+definition thd5T ≝
+λT1.λT2.λT3.λT4.λT5.λp:Prod5T T1 T2 T3 T4 T5.match p with [ quintupleT _ _ x _ _ ⇒ x ].
+
+definition frth5T ≝
+λT1.λT2.λT3.λT4.λT5.λp:Prod5T T1 T2 T3 T4 T5.match p with [ quintupleT _ _ _ x _ ⇒ x ].
+
+definition ffth5T ≝
+λT1.λT2.λT3.λT4.λT5.λp:Prod5T T1 T2 T3 T4 T5.match p with [ quintupleT _ _ _ _ x ⇒ x ].
+
+(* OPTIOTN MAP *)
+
+(* option map = match ... with [ None ⇒ None ? | Some .. ⇒ .. ] *)
+definition opt_map ≝
+λT1,T2:Type.λt:option T1.λf:T1 → option T2.
+ match t with [ None ⇒ None ? | Some x ⇒ (f x) ].
+
+(* ********************** *)
+(* TEOREMI/LEMMMI/ASSIOMI *)
+(* ********************** *)
+
+axiom mod_plus: ∀a,b,m. (a + b) \mod m = (a \mod m + b \mod m) \mod m.
+axiom mod_mod: ∀a,n,m. n∣m → a \mod n = a \mod n \mod m.
+axiom eq_mod_times_n_m_m_O: ∀n,m. O < m → n * m \mod m = O.
+axiom eq_mod_to_eq_plus_mod: ∀a,b,c,m. a \mod m = b \mod m → (a+c) \mod m = (b+c) \mod m.
+axiom eq_mod_times_times_mod: ∀a,b,n,m. m = a*n → (a*b) \mod m = a * (b \mod n).
+axiom divides_to_eq_mod_mod_mod: ∀a,n,m. n∣m → a \mod m \mod n = a \mod n.
+axiom le_to_le_plus_to_le : ∀a,b,c,d.b\leq d\rarr a+b\leq c+d\rarr a\leq c.
+axiom or_lt_le : ∀n,m. n < m ∨ m ≤ n.
+
+lemma le_to_lt: ∀n,m. n ≤ m → n < S m.
+ intros;
+ autobatch.
+qed.
+
+alias num (instance 0) = "natural number".
+definition nat_of_bool ≝
+ λb:bool.match b return λ_.nat with [ true ⇒ 1 | false ⇒ 0 ].
+
+theorem lt_trans: ∀x,y,z. x < y → y < z → x < z.
+ unfold lt;
+ intros;
+ autobatch.
+qed.
+
+lemma leq_m_n_to_eq_div_n_m_S: ∀n,m:nat. 0 < m → m ≤ n → ∃z. n/m = S z.
+ intros;
+ unfold div;
+ apply (ex_intro ? ? (div_aux (pred n) (n-m) (pred m)));
+ cut (∃w.m = S w);
+  [ elim Hcut;
+    rewrite > H2;
+    rewrite > H2 in H1;
+    clear Hcut; clear H2; clear H;
+    simplify;
+    unfold in ⊢ (? ? % ?);
+    cut (∃z.n = S z);
+     [ elim Hcut; clear Hcut;
+       rewrite > H in H1;
+       rewrite > H; clear m;
+       change in ⊢ (? ? % ?)  with
+        (match leb (S a1) a with
+         [ true ⇒ O
+         | false ⇒ S (div_aux a1 ((S a1) - S a) a)]);
+       cut (S a1 ≰ a);
+        [ apply (leb_elim (S a1) a);
+           [ intro;
+             elim (Hcut H2)
+           | intro;
+             simplify;
+             reflexivity
+           ]
+        | intro;
+          autobatch
+        ]
+     | elim H1; autobatch
+     ]
+  | autobatch
+  ].
+qed.
+
+axiom daemon: False.