Library Cshmgenproof1
Require Import Coqlib.
Require Import Errors.
Require Import Maps.
Require Import Integers.
Require Import Floats.
Require Import AST.
Require Import Values.
Require Import Events.
Require Import Mem.
Require Import Globalenvs.
Require Import Csyntax.
Require Import Csem.
Require Import Ctyping.
Require Import Cminor.
Require Import Csharpminor.
Require Import Cshmgen.
Lemma transl_fundef_sig1:
forall f tf args res,
transl_fundef f = OK tf ->
classify_fun (type_of_fundef f) = fun_case_f args res ->
funsig tf = signature_of_type args res.
Lemma transl_fundef_sig2:
forall f tf args res,
transl_fundef f = OK tf ->
type_of_fundef f = Tfunction args res ->
funsig tf = signature_of_type args res.
Lemma var_kind_by_value:
forall ty chunk,
access_mode ty = By_value chunk ->
var_kind_of_type ty = OK(Vscalar chunk).
Lemma sizeof_var_kind_of_type:
forall ty vk,
var_kind_of_type ty = OK vk ->
Csharpminor.sizeof vk = Csyntax.sizeof ty.
Lemma map_partial_names:
forall (A B: Type) (f: A -> res B)
(l: list (ident * A)) (tl: list (ident * B)),
map_partial prefix_var_name f l = OK tl ->
List.map (@fst ident B) tl = List.map (@fst ident A) l.
Lemma map_partial_append:
forall (A B: Type) (f: A -> res B)
(l1 l2: list (ident * A)) (tl1 tl2: list (ident * B)),
map_partial prefix_var_name f l1 = OK tl1 ->
map_partial prefix_var_name f l2 = OK tl2 ->
map_partial prefix_var_name f (l1 ++ l2) = OK (tl1 ++ tl2).
Lemma transl_params_names:
forall vars tvars,
transl_params vars = OK tvars ->
List.map (@fst ident memory_chunk) tvars = Ctyping.var_names vars.
Lemma transl_vars_names:
forall vars tvars,
transl_vars vars = OK tvars ->
List.map (@fst ident var_kind) tvars = Ctyping.var_names vars.
Lemma transl_names_norepet:
forall params vars sg tparams tvars body,
list_norepet (var_names params ++ var_names vars) ->
transl_params params = OK tparams ->
transl_vars vars = OK tvars ->
let f := Csharpminor.mkfunction sg tparams tvars body in
list_norepet (fn_params_names f ++ fn_vars_names f).
Lemma transl_vars_append:
forall l1 l2 tl1 tl2,
transl_vars l1 = OK tl1 -> transl_vars l2 = OK tl2 ->
transl_vars (l1 ++ l2) = OK (tl1 ++ tl2).
Lemma transl_params_vars:
forall params tparams,
transl_params params = OK tparams ->
transl_vars params =
OK (List.map (fun id_chunk => (fst id_chunk, Vscalar (snd id_chunk))) tparams).
Lemma transl_fn_variables:
forall params vars sg tparams tvars body,
transl_params params = OK tparams ->
transl_vars vars = OK tvars ->
let f := Csharpminor.mkfunction sg tparams tvars body in
transl_vars (params ++ vars) = OK (fn_variables f).
Transformation of expressions and statements.
Lemma is_variable_correct:
forall a id,
is_variable a = Some id ->
a = Csyntax.Expr (Csyntax.Evar id) (typeof a).
Lemma transl_expr_lvalue:
forall ge e m a ty loc ofs ta,
Csem.eval_lvalue ge e m (Expr a ty) loc ofs ->
transl_expr (Expr a ty) = OK ta ->
(exists id, a = Csyntax.Evar id /\ var_get id ty = OK ta) \/
(exists tb, transl_lvalue (Expr a ty) = OK tb /\
make_load tb ty = OK ta).
Lemma is_Sskip_true:
forall (A: Type) (a b: A),
(if is_Sskip Csyntax.Sskip then a else b) = a.
Lemma is_Sskip_false:
forall (A: Type) (a b: A) s,
s <> Csyntax.Sskip ->
(if is_Sskip s then a else b) = b.
Properties of labeled statements
Lemma transl_lbl_stmt_1:
forall nbrk ncnt n sl tsl,
transl_lbl_stmt nbrk ncnt sl = OK tsl ->
transl_lbl_stmt nbrk ncnt (Csem.select_switch n sl) = OK (select_switch n tsl).
Lemma transl_lbl_stmt_2:
forall nbrk ncnt sl tsl,
transl_lbl_stmt nbrk ncnt sl = OK tsl ->
transl_statement nbrk ncnt (seq_of_labeled_statement sl) = OK (seq_of_lbl_stmt tsl).
Lemma wt_select_switch:
forall n tyenv sl,
wt_lblstmts tyenv sl ->
wt_lblstmts tyenv (Csem.select_switch n sl).
Lemma wt_seq_of_labeled_statement:
forall tyenv sl,
wt_lblstmts tyenv sl ->
wt_stmt tyenv (seq_of_labeled_statement sl).