+++ /dev/null
-(**************************************************************************)
-(* ___ *)
-(* ||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 *)
-(* Cosimo Oliboni, oliboni@cs.unibo.it *)
-(* *)
-(* ********************************************************************** *)
-
-include "compiler/ast_type.ma".
-include "utility/utility_lemmas.ma".
-
-(* ************************* *)
-(* dimensioni degli elementi *)
-(* ************************* *)
-
-ndefinition astbasetype_destruct_aux ≝
-Πb1,b2:ast_base_type.ΠP:Prop.b1 = b2 →
- match b1 with
- [ AST_BASE_TYPE_BYTE8 ⇒ match b2 with [ AST_BASE_TYPE_BYTE8 ⇒ P → P | _ ⇒ P ]
- | AST_BASE_TYPE_WORD16 ⇒ match b2 with [ AST_BASE_TYPE_WORD16 ⇒ P → P | _ ⇒ P ]
- | AST_BASE_TYPE_WORD32 ⇒ match b2 with [ AST_BASE_TYPE_WORD32 ⇒ P → P | _ ⇒ P ]
- ].
-
-ndefinition astbasetype_destruct : astbasetype_destruct_aux.
- #b1; #b2; #P;
- nelim b1;
- nelim b2;
- nnormalize;
- #H;
- ##[ ##1,5,9: napply (λx:P.x)
- ##| ##2,3: napply (False_ind (λ_.?) ?);
- nchange with (match AST_BASE_TYPE_BYTE8 with [ AST_BASE_TYPE_BYTE8 ⇒ False | _ ⇒ True]);
- nrewrite > H;
- nnormalize;
- napply I
- ##| ##4,6: napply (False_ind (λ_.?) ?);
- nchange with (match AST_BASE_TYPE_WORD16 with [ AST_BASE_TYPE_WORD16 ⇒ False | _ ⇒ True]);
- nrewrite > H;
- nnormalize;
- napply I
- ##| ##7,8: napply (False_ind (λ_.?) ?);
- nchange with (match AST_BASE_TYPE_WORD32 with [ AST_BASE_TYPE_WORD32 ⇒ False | _ ⇒ True]);
- nrewrite > H;
- nnormalize;
- napply I
- ##]
-nqed.
-
-nlemma symmetric_eqastbasetype : symmetricT ast_base_type bool eq_ast_base_type.
- #b1; #b2; ncases b1; ncases b2; nnormalize; napply refl_eq. nqed.
-
-nlemma eqastbasetype_to_eq : ∀b1,b2.eq_ast_base_type b1 b2 = true → b1 = b2.
- #b1; #b2; ncases b1; ncases b2; nnormalize;
- ##[ ##1,5,9: #H; napply refl_eq
- ##| ##*: #H; napply (bool_destruct … H)
- ##]
-nqed.
-
-nlemma eq_to_eqastbasetype : ∀b1,b2.b1 = b2 → eq_ast_base_type b1 b2 = true.
- #b1; #b2; ncases b1; ncases b2; nnormalize;
- ##[ ##1,5,9: #H; napply refl_eq
- ##| ##*: #H; napply (astbasetype_destruct … H)
- ##]
-nqed.
-
-nlemma asttype_destruct_base_base : ∀b1,b2.AST_TYPE_BASE b1 = AST_TYPE_BASE b2 → b1 = b2.
- #b1; #b2; #H;
- nchange with (match AST_TYPE_BASE b2 with [ AST_TYPE_BASE a ⇒ b1 = a | _ ⇒ False ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma asttype_destruct_array_array_1 : ∀x1,x2,y1,y2.AST_TYPE_ARRAY x1 y1 = AST_TYPE_ARRAY x2 y2 → x1 = x2.
- #x1; #x2; #y1; #y2; #H;
- nchange with (match AST_TYPE_ARRAY x2 y2 with [ AST_TYPE_ARRAY a _ ⇒ x1 = a | _ ⇒ False ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma asttype_destruct_array_array_2 : ∀x1,x2,y1,y2.AST_TYPE_ARRAY x1 y1 = AST_TYPE_ARRAY x2 y2 → y1 = y2.
- #x1; #x2; #y1; #y2; #H;
- nchange with (match AST_TYPE_ARRAY x2 y2 with [ AST_TYPE_ARRAY _ b ⇒ y1 = b | _ ⇒ False ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-nlemma asttype_destruct_struct_struct : ∀b1,b2.AST_TYPE_STRUCT b1 = AST_TYPE_STRUCT b2 → b1 = b2.
- #b1; #b2; #H;
- nchange with (match AST_TYPE_STRUCT b2 with [ AST_TYPE_STRUCT a ⇒ b1 = a | _ ⇒ False ]);
- nrewrite < H;
- nnormalize;
- napply refl_eq.
-nqed.
-
-ndefinition asttype_destruct_aux ≝
-Πb1,b2:ast_type.ΠP:Prop.b1 = b2 →
- match b1 with
- [ AST_TYPE_BASE s1 ⇒ match b2 with
- [ AST_TYPE_BASE s2 ⇒ match s1 with
- [ AST_BASE_TYPE_BYTE8 ⇒ match s2 with [ AST_BASE_TYPE_BYTE8 ⇒ P → P | _ ⇒ P ]
- | AST_BASE_TYPE_WORD16 ⇒ match s2 with [ AST_BASE_TYPE_WORD16 ⇒ P → P | _ ⇒ P ]
- | AST_BASE_TYPE_WORD32 ⇒ match s2 with [ AST_BASE_TYPE_WORD32 ⇒ P → P | _ ⇒ P ]
- ] | _ ⇒ P ]
- | AST_TYPE_ARRAY _ _ ⇒ match b2 with [ AST_TYPE_ARRAY _ _ ⇒ P → P | _ ⇒ P ]
- | AST_TYPE_STRUCT _ ⇒ match b2 with [ AST_TYPE_STRUCT _ ⇒ P → P | _ ⇒ P ]
- ].
-
-ndefinition asttype_destruct : asttype_destruct_aux.
- #b1; #b2; #P;
- ncases b1;
- ##[ ##1: ncases b2;
- ##[ ##1: nnormalize; #s1; #s2; ncases s1; ncases s2; nnormalize;
- ##[ ##1,5,9: #H; napply (λx:P.x)
- ##| ##*: #H; napply (astbasetype_destruct … (asttype_destruct_base_base … H))
- ##]
- ##| ##2: #t; #n; #b; nnormalize; #H
- ##| ##3: #l; #b; nnormalize; #H
- ##]
- napply (False_ind (λ_.?) ?);
- nchange with (match AST_TYPE_BASE b with [ AST_TYPE_BASE _ ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##| ##2: ncases b2;
- ##[ ##2: #t1; #n1; #t2; #n2; nnormalize; #H; napply (λx:P.x)
- ##| ##1: #b; #t; #n; nnormalize; #H
- ##| ##3: #l; #t; #n; nnormalize; #H
- ##]
- napply (False_ind (λ_.?) ?);
- nchange with (match AST_TYPE_ARRAY t n with [ AST_TYPE_ARRAY _ _ ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##| ##3: ncases b2;
- ##[ ##3: #l1; #l2; nnormalize; #H; napply (λx:P.x)
- ##| ##1: #b; #l; nnormalize; #H
- ##| ##2: #t; #n; #l; nnormalize; #H
- ##]
- napply (False_ind (λ_.?) ?);
- nchange with (match AST_TYPE_STRUCT l with [ AST_TYPE_STRUCT _ ⇒ False | _ ⇒ True ]);
- nrewrite > H; nnormalize; napply I
- ##]
-nqed.
-
-nlemma symmetric_eqasttype_aux1
- : ∀nl1,nl2.
- (eq_ast_type (AST_TYPE_STRUCT nl1) (AST_TYPE_STRUCT nl2)) = (eq_ast_type (AST_TYPE_STRUCT nl2) (AST_TYPE_STRUCT nl1)) →
- (bfold_right_neList2 ? (λx,y.eq_ast_type x y) nl1 nl2) = (bfold_right_neList2 ? (λx,y.eq_ast_type x y) nl2 nl1).
- #nl1; #nl2; #H;
- napply H.
-nqed.
-
-nlemma symmetric_eqasttype : symmetricT ast_type bool eq_ast_type.
- #t1; napply (ast_type_index … t1);
- ##[ ##1: #b1; #t2; ncases t2;
- ##[ ##1: #b2; nchange with ((eq_ast_base_type b1 b2) = (eq_ast_base_type b2 b1));
- nrewrite > (symmetric_eqastbasetype b1 b2);
- napply refl_eq
- ##| ##2: #st2; #n2; nnormalize; napply refl_eq
- ##| ##3: #nl2; nnormalize; napply refl_eq
- ##]
- ##| ##2: #st1; #n1; #H; #t2; ncases t2;
- ##[ ##2: #st2; #n2; nchange with (((eq_ast_type st1 st2)⊗(eq_nat n1 n2)) = ((eq_ast_type st2 st1)⊗(eq_nat n2 n1)));
- nrewrite > (symmetric_eqnat n1 n2);
- nrewrite > (H st2);
- napply refl_eq
- ##| ##1: #b2; nnormalize; napply refl_eq
- ##| ##3: #nl2; nnormalize; napply refl_eq
- ##]
- ##| ##3: #hh1; #H; #t2; ncases t2;
- ##[ ##3: #nl2; ncases nl2;
- ##[ ##1: #hh2; nchange with ((eq_ast_type hh1 hh2) = (eq_ast_type hh2 hh1));
- nrewrite > (H hh2);
- napply refl_eq
- ##| ##2: #hh2; #ll2; nnormalize; napply refl_eq
- ##]
- ##| ##1: #b2; nnormalize; napply refl_eq
- ##| ##2: #st2; #n2; nnormalize; napply refl_eq
- ##]
- ##| ##4: #hh1; #ll1; #H; #H1; #t2; ncases t2;
- ##[ ##3: #nl2; ncases nl2;
- ##[ ##1: #hh2; nnormalize; napply refl_eq
- ##| ##2: #hh2; #ll2; nnormalize;
- nrewrite > (H hh2);
- nrewrite > (symmetric_eqasttype_aux1 ll1 ll2 (H1 (AST_TYPE_STRUCT ll2)));
- napply refl_eq
- ##]
- ##| ##1: #b2; nnormalize; napply refl_eq
- ##| ##2: #st2; #n2; nnormalize; napply refl_eq
- ##]
- ##]
-nqed.
-
-nlemma eqasttype_to_eq : ∀t1,t2.eq_ast_type t1 t2 = true → t1 = t2.
- #t1;
- napply (ast_type_index … t1);
- ##[ ##1: #b1; #t2; ncases t2;
- ##[ ##1: #b2; #H; nchange in H:(%) with ((eq_ast_base_type b1 b2) = true);
- nrewrite > (eqastbasetype_to_eq b1 b2 H);
- napply refl_eq
- ##| ##2: #st2; #n2; nnormalize; #H; napply (bool_destruct … H)
- ##| ##3: #nl2; nnormalize; #H; napply (bool_destruct … H)
- ##]
- ##| ##2: #st1; #n1; #H; #t2; ncases t2;
- ##[ ##2: #st2; #n2; #H1; nchange in H1:(%) with (((eq_ast_type st1 st2)⊗(eq_nat n1 n2)) = true);
- nrewrite > (H st2 (andb_true_true_l … H1));
- nrewrite > (eqnat_to_eq n1 n2 (andb_true_true_r … H1));
- napply refl_eq
- ##| ##1: #b2; nnormalize; #H1; napply (bool_destruct … H1)
- ##| ##3: #nl2; nnormalize; #H1; napply (bool_destruct … H1)
- ##]
- ##| ##3: #hh1; #H; #t2; ncases t2;
- ##[ ##3: #nl2; ncases nl2;
- ##[ ##1: #hh2; #H1; nchange in H1:(%) with ((eq_ast_type hh1 hh2) = true);
- nrewrite > (H hh2 H1);
- napply refl_eq
- ##| ##2: #hh2; #ll2; nnormalize; #H1; napply (bool_destruct … H1)
- ##]
- ##| ##1: #b2; nnormalize; #H1; napply (bool_destruct … H1)
- ##| ##2: #st2; #n2; nnormalize; #H1; napply (bool_destruct … H1)
- ##]
- ##| ##4: #hh1; #ll1; #H; #H1; #t2; ncases t2;
- ##[ ##3: #nl2; ncases nl2;
- ##[ ##1: #hh2; nnormalize; #H2; napply (bool_destruct … H2)
- ##| ##2: #hh2; #ll2; #H2; nchange in H2:(%) with (((eq_ast_type hh1 hh2)⊗(bfold_right_neList2 ? (λx,y.eq_ast_type x y) ll1 ll2)) = true);
- nrewrite > (H hh2 (andb_true_true_l … H2));
- nrewrite > (asttype_destruct_struct_struct ll1 ll2 (H1 (AST_TYPE_STRUCT ll2) (andb_true_true_r … H2)));
- napply refl_eq
- ##]
- ##| ##1: #b2; nnormalize; #H2; napply (bool_destruct … H2)
- ##| ##2: #st2; #n2; nnormalize; #H2; napply (bool_destruct … H2)
- ##]
- ##]
-nqed.
-
-nlemma eq_to_eqasttype_aux1
- : ∀nl1,nl2.
- ((eq_ast_type (AST_TYPE_STRUCT nl1) (AST_TYPE_STRUCT nl2)) = true) →
- ((bfold_right_neList2 ? (λx,y.eq_ast_type x y) nl1 nl2) = true).
- #nl1; #nl2; #H;
- napply H.
-nqed.
-
-nlemma eq_to_eqasttype : ∀t1,t2.t1 = t2 → eq_ast_type t1 t2 = true.
- #t1;
- napply (ast_type_index … t1);
- ##[ ##1: #b1; #t2; ncases t2;
- ##[ ##1: #b2; #H; nrewrite > (asttype_destruct_base_base … H);
- nchange with ((eq_ast_base_type b2 b2) = true);
- nrewrite > (eq_to_eqastbasetype b2 b2 (refl_eq …));
- napply refl_eq
- ##| ##2: #st2; #n2; #H; napply (asttype_destruct … H)
- ##| ##3: #nl2; #H; napply (asttype_destruct … H)
- ##]
- ##| ##2: #st1; #n1; #H; #t2; ncases t2;
- ##[ ##2: #st2; #n2; #H1; nchange with (((eq_ast_type st1 st2)⊗(eq_nat n1 n2)) = true);
- nrewrite > (H st2 (asttype_destruct_array_array_1 … H1));
- nrewrite > (eq_to_eqnat n1 n2 (asttype_destruct_array_array_2 … H1));
- nnormalize;
- napply refl_eq
- ##| ##1: #b2; #H1; napply (asttype_destruct … H1)
- ##| ##3: #nl2; #H1; napply (asttype_destruct … H1)
- ##]
- ##| ##3: #hh1; #H; #t2; ncases t2;
- ##[ ##3: #nl2; ncases nl2;
- ##[ ##1: #hh2; #H1; nchange with ((eq_ast_type hh1 hh2) = true);
- nrewrite > (H hh2 (nelist_destruct_nil_nil ? hh1 hh2 (asttype_destruct_struct_struct … H1)));
- napply refl_eq
- ##| ##2: #hh2; #ll2; #H1; nelim (nelist_destruct_nil_cons ? hh1 hh2 ll2 (asttype_destruct_struct_struct … H1))
- ##]
- ##| ##1: #b2; #H1; napply (asttype_destruct … H1)
- ##| ##2: #st2; #n2; #H1; napply (asttype_destruct … H1)
- ##]
- ##| ##4: #hh1; #ll1; #H; #H1; #t2; ncases t2;
- ##[ ##3: #nl2; ncases nl2;
- ##[ ##1: #hh2; #H2; nelim (nelist_destruct_cons_nil ? hh1 hh2 ll1 (asttype_destruct_struct_struct … H2))
- ##| ##2: #hh2; #ll2; #H2; nchange with (((eq_ast_type hh1 hh2)⊗(bfold_right_neList2 ? (λx,y.eq_ast_type x y) ll1 ll2)) = true);
- nrewrite > (H hh2 (nelist_destruct_cons_cons_1 … (asttype_destruct_struct_struct … H2)));
- nrewrite > (eq_to_eqasttype_aux1 ll1 ll2 (H1 (AST_TYPE_STRUCT ll2) ?));
- ##[ ##1: nnormalize; napply refl_eq
- ##| ##2: nrewrite > (nelist_destruct_cons_cons_2 … (asttype_destruct_struct_struct … H2));
- napply refl_eq
- ##]
- ##]
- ##| ##1: #b2; #H2; napply (asttype_destruct … H2)
- ##| ##2: #st2; #n2; #H2; napply (asttype_destruct … H2)
- ##]
- ##]
-nqed.
-
-nlemma isbastbasetype_to_isastbasetype : ∀ast.isb_ast_base_type ast = true → is_ast_base_type ast.
- #ast;
- ncases ast;
- nnormalize;
- ##[ ##1: #t; #H; napply I
- ##| ##2: #t; #n; #H; napply (bool_destruct … H)
- ##| ##3: #t; #H; napply (bool_destruct … H)
- ##]
-nqed.
-
-nlemma isntbastbasetype_to_isntastbasetype : ∀ast.isntb_ast_base_type ast = true → isnt_ast_base_type ast.
- #ast;
- ncases ast;
- nnormalize;
- ##[ ##1: #t; #H; napply (bool_destruct … H)
- ##| ##2: #t; #n; #H; napply I
- ##| ##3: #l; #H; napply I
- ##]
-nqed.
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