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From Coq Require Import FSets.FMapPositive.
From compcert Require RTL Op Maps.
From coqup Require Import Coquplib Verilog Veriloggen Value.
(** * Relational specification of the translation *)
(** We now define inductive predicates that characterise the fact that the
statemachine that is created by the translation contains the correct
translations for each of the elements *)
Inductive tr_op : Op.operation -> list reg -> expr -> Prop :=
| tr_op_Omove : forall r, tr_op Op.Omove (r::nil) (Vvar r)
| tr_op_Ointconst : forall n l, tr_op (Op.Ointconst n) l (Vlit (intToValue n))
| tr_op_Oneg : forall r, tr_op Op.Oneg (r::nil) (Vunop Vneg (Vvar r))
| tr_op_Osub : forall r1 r2, tr_op Op.Osub (r1::r2::nil) (bop Vsub r1 r2)
| tr_op_Omul : forall r1 r2, tr_op Op.Omul (r1::r2::nil) (bop Vmul r1 r2)
| tr_op_Omulimm : forall r n, tr_op (Op.Omulimm n) (r::nil) (boplit Vmul r n)
| tr_op_Odiv : forall r1 r2, tr_op Op.Odiv (r1::r2::nil) (bop Vdiv r1 r2)
| tr_op_Odivu : forall r1 r2, tr_op Op.Odivu (r1::r2::nil) (bop Vdivu r1 r2)
| tr_op_Omod : forall r1 r2, tr_op Op.Omod (r1::r2::nil) (bop Vmod r1 r2)
| tr_op_Omodu : forall r1 r2, tr_op Op.Omodu (r1::r2::nil) (bop Vmodu r1 r2)
| tr_op_Oand : forall r1 r2, tr_op Op.Oand (r1::r2::nil) (bop Vand r1 r2)
| tr_op_Oandimm : forall n r, tr_op (Op.Oandimm n) (r::nil) (boplit Vand r n)
| tr_op_Oor : forall r1 r2, tr_op Op.Oor (r1::r2::nil) (bop Vor r1 r2)
| tr_op_Oorimm : forall n r, tr_op (Op.Oorimm n) (r::nil) (boplit Vor r n)
| tr_op_Oxor : forall r1 r2, tr_op Op.Oxor (r1::r2::nil) (bop Vxor r1 r2)
| tr_op_Oxorimm : forall n r, tr_op (Op.Oxorimm n) (r::nil) (boplit Vxor r n)
| tr_op_Onot : forall r, tr_op Op.Onot (r::nil) (Vunop Vnot (Vvar r))
| tr_op_Oshl : forall r1 r2, tr_op Op.Oshl (r1::r2::nil) (bop Vshl r1 r2)
| tr_op_Oshlimm : forall n r, tr_op (Op.Oshlimm n) (r::nil) (boplit Vshl r n)
| tr_op_Oshr : forall r1 r2, tr_op Op.Oshr (r1::r2::nil) (bop Vshr r1 r2)
| tr_op_Oshrimm : forall n r, tr_op (Op.Oshrimm n) (r::nil) (boplit Vshr r n)
| tr_op_Ocmp : forall c l e s s' i, translate_condition c l s = OK e s' i -> tr_op (Op.Ocmp c) l e
| tr_op_Olea : forall a l e s s' i, translate_eff_addressing a l s = OK e s' i -> tr_op (Op.Olea a) l e.
Inductive tr_instr (fin rtrn st : reg) : RTL.instruction -> stmnt -> stmnt -> Prop :=
| tr_instr_Inop :
forall n,
tr_instr fin rtrn st (RTL.Inop n) Vskip (state_goto st n)
| tr_instr_Iop :
forall n op args e dst,
tr_op op args e ->
tr_instr fin rtrn st (RTL.Iop op args dst n) (Vnonblock (Vvar dst) e) (state_goto st n)
| tr_instr_Icond :
forall n1 n2 cond args s s' i c,
translate_condition cond args s = OK c s' i ->
tr_instr fin rtrn st (RTL.Icond cond args n1 n2) Vskip (state_cond st c n1 n2)
| tr_instr_Ireturn_None :
tr_instr fin rtrn st (RTL.Ireturn None) (block fin (Vlit (ZToValue 1%nat 1%Z))) Vskip
| tr_instr_Ireturn_Some :
forall r,
tr_instr fin rtrn st (RTL.Ireturn (Some r))
(Vseq (block fin (Vlit (ZToValue 1%nat 1%Z))) (block rtrn (Vvar r))) Vskip.
Inductive tr_code (c : RTL.code) (stmnts trans : PositiveMap.t stmnt)
(fin rtrn st : reg) : Prop :=
| tr_code_intro :
forall i s t n,
Maps.PTree.get n c = Some i ->
stmnts!n = Some s ->
trans!n = Some t ->
tr_instr fin rtrn st i s t ->
tr_code c stmnts trans fin rtrn st.
(** [tr_module_items start clk st rst s mis] holds if the state is correctly
translated to actual Verilog, meaning it is correctly implemented as a state
machine in Verilog. Currently it does not seem that useful because it models
the [make_module_items] nearly exactly. Therefore it might have to be changed
to make up for that. *)
Inductive tr_module_items : node -> reg -> reg -> reg -> state -> list module_item -> Prop :=
tr_module_items_intro :
forall start clk st rst s mis,
Valways_ff (Vposedge clk)
(Vcond (Vbinop Veq (Vinputvar rst) (Vlit (ZToValue 1 1)))
(nonblock st (posToExpr 32 start))
(make_statetrans st s.(st_statetrans)))
:: Valways_ff (Vposedge clk) (make_stm st s.(st_stm))
:: List.map allocate_reg (PositiveMap.elements s.(st_decl)) = mis ->
tr_module_items start clk st rst s mis.
(** [tr_module function module] Holds if the [module] is the correct translation
of the [function] that it was given. *)
Inductive tr_module : RTL.function -> module -> Prop :=
tr_module_intro :
forall f mi st rtrn fin clk rst start s0 s1 s2 s3 s4 s5 s6 i1 i2 i3 i4 i5 i6,
decl_io 1 s0 = OK fin s1 i1 ->
decl_io 32 s1 = OK rtrn s2 i2 ->
decl_io 1 s2 = OK start s3 i3 ->
decl_io 1 s3 = OK rst s4 i4 ->
decl_io 1 s4 = OK clk s5 i5 ->
decl_fresh_reg 32 s5 = OK st s6 i6 ->
tr_code f.(RTL.fn_code) s6.(st_stm)
(PositiveMap.map (statetrans_transl (fst st)) s6.(st_statetrans))
(fst fin) (fst rtrn) (fst st) ->
tr_module_items f.(RTL.fn_entrypoint) (fst clk) (fst st) (fst rst) s6 mi ->
tr_module f (mkmodule
start
rst
clk
fin
rtrn
st
(List.map set_int_size f.(RTL.fn_params))
mi).
Lemma tr_module_correct:
forall f m,
transl_module f = Errors.OK m ->
tr_module f m.
Admitted.
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