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(*
* Vericert: Verified high-level synthesis.
* Copyright (C) 2020-2021 Yann Herklotz <yann@yannherklotz.com>
*
* This program is free software: you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <https://www.gnu.org/licenses/>.
*)
Require Import compcert.backend.Registers.
Require Import compcert.common.AST.
Require Import compcert.common.Events.
Require Import compcert.common.Globalenvs.
Require Import compcert.common.Memory.
Require Import compcert.common.Smallstep.
Require Import compcert.common.Values.
Require Import compcert.lib.Coqlib.
Require Import compcert.lib.Integers.
Require Import compcert.lib.Maps.
Require Import compcert.verilog.Op.
Require Import vericert.hls.RTLBlockInstr.
Definition bblock_body : Type := list instr.
Definition code : Type := PTree.t (@bblock bblock_body).
Record function: Type := mkfunction {
fn_sig: signature;
fn_params: list reg;
fn_stacksize: Z;
fn_code: code;
fn_entrypoint: node
}.
Definition fundef := AST.fundef function.
Definition program := AST.program fundef unit.
Definition funsig (fd: fundef) :=
match fd with
| Internal f => fn_sig f
| External ef => ef_sig ef
end.
Inductive stackframe : Type :=
| Stackframe:
forall (res: reg) (**r where to store the result *)
(f: function) (**r calling function *)
(sp: val) (**r stack pointer in calling function *)
(pc: node) (**r program point in calling function *)
(rs: regset), (**r register state in calling function *)
stackframe.
Inductive state : Type :=
| State:
forall (stack: list stackframe) (**r call stack *)
(f: function) (**r current function *)
(sp: val) (**r stack pointer *)
(pc: node) (**r current program point in [c] *)
(rs: regset) (**r register state *)
(m: mem), (**r memory state *)
state
| Block:
forall (stack: list stackframe) (**r call stack *)
(f: function) (**r current function *)
(sp: val) (**r stack pointer *)
(cfi: cf_instr) (**r The control flow instruction to execute. *)
(rs: regset) (**r register state *)
(m: mem), (**r memory state *)
state
| Callstate:
forall (stack: list stackframe) (**r call stack *)
(f: fundef) (**r function to call *)
(args: list val) (**r arguments to the call *)
(m: mem), (**r memory state *)
state
| Returnstate:
forall (stack: list stackframe) (**r call stack *)
(v: val) (**r return value for the call *)
(m: mem), (**r memory state *)
state.
Definition genv := Genv.t fundef unit.
Section RELSEM.
Context (ge: genv).
Definition find_function
(ros: reg + ident) (rs: regset) : option fundef :=
match ros with
| inl r => Genv.find_funct ge rs#r
| inr symb =>
match Genv.find_symbol ge symb with
| None => None
| Some b => Genv.find_funct_ptr ge b
end
end.
Inductive step: state -> trace -> state -> Prop :=
| exec_bblock:
forall stack f sp pc rs m rs' m' bb cfi,
(fn_code f)!pc = Some (mk_bblock bb cfi) ->
step_instr_list _ ge sp (InstrState rs m) bb (InstrState rs' m') ->
step (State stack f sp pc rs m) E0 (Block stack f sp cfi rs' m')
| exec_RBcall:
forall s f sp rs m res fd ros sig args pc',
find_function ros rs = Some fd ->
funsig fd = sig ->
step (Block s f sp (RBcall sig ros args res pc') rs m)
E0 (Callstate (Stackframe res f sp pc' rs :: s) fd rs##args m)
| exec_RBtailcall:
forall s f stk rs m sig ros args fd m',
find_function ros rs = Some fd ->
funsig fd = sig ->
Mem.free m stk 0 f.(fn_stacksize) = Some m' ->
step (Block s f (Vptr stk Ptrofs.zero) (RBtailcall sig ros args) rs m)
E0 (Callstate s fd rs##args m')
| exec_RBbuiltin:
forall s f sp rs m ef args res pc' vargs t vres m',
eval_builtin_args ge (fun r => rs#r) sp m args vargs ->
external_call ef ge vargs m t vres m' ->
step (Block s f sp (RBbuiltin ef args res pc') rs m)
t (State s f sp pc' (regmap_setres res vres rs) m')
| exec_RBcond:
forall s f sp rs m cond args ifso ifnot b pc',
eval_condition cond rs##args m = Some b ->
pc' = (if b then ifso else ifnot) ->
step (Block s f sp (RBcond cond args ifso ifnot) rs m)
E0 (State s f sp pc' rs m)
| exec_RBjumptable:
forall s f sp rs m arg tbl n pc',
rs#arg = Vint n ->
list_nth_z tbl (Int.unsigned n) = Some pc' ->
step (Block s f sp (RBjumptable arg tbl) rs m)
E0 (State s f sp pc' rs m)
| exec_Ireturn:
forall s f stk rs m or m',
Mem.free m stk 0 f.(fn_stacksize) = Some m' ->
step (Block s f (Vptr stk Ptrofs.zero) (RBreturn or) rs m)
E0 (Returnstate s (regmap_optget or Vundef rs) m')
| exec_function_internal:
forall s f args m m' stk,
Mem.alloc m 0 f.(fn_stacksize) = (m', stk) ->
step (Callstate s (Internal f) args m)
E0 (State s
f
(Vptr stk Ptrofs.zero)
f.(fn_entrypoint)
(init_regs args f.(fn_params))
m')
| exec_function_external:
forall s ef args res t m m',
external_call ef ge args m t res m' ->
step (Callstate s (External ef) args m)
t (Returnstate s res m')
| exec_return:
forall res f sp pc rs s vres m,
step (Returnstate (Stackframe res f sp pc rs :: s) vres m)
E0 (State s f sp pc (rs#res <- vres) m).
End RELSEM.
Inductive initial_state (p: program): state -> Prop :=
| initial_state_intro: forall b f m0,
let ge := Genv.globalenv p in
Genv.init_mem p = Some m0 ->
Genv.find_symbol ge p.(prog_main) = Some b ->
Genv.find_funct_ptr ge b = Some f ->
funsig f = signature_main ->
initial_state p (Callstate nil f nil m0).
Inductive final_state: state -> int -> Prop :=
| final_state_intro: forall r m,
final_state (Returnstate nil (Vint r) m) r.
Definition semantics (p: program) :=
Semantics step (initial_state p) final_state (Genv.globalenv p).
(*
Inductive stackframe : Type :=
| Stackframe:
forall (res: reg) (**r where to store the result *)
(f: function) (**r calling function *)
(sp: val) (**r stack pointer in calling function *)
(pc: node) (**r program point in calling function *)
(rs: regset), (**r register state in calling function *)
stackframe.
Inductive cont : Type :=
| C
| N.
Inductive state : Type :=
| State:
forall (stack: list stackframe) (**r call stack *)
(f: function) (**r current function *)
(sp: val) (**r stack pointer *)
(pc: node) (**r current program point in [c] *)
(rs: regset) (**r register state *)
(m: mem) (**r memory state *)
(bblock: bblock) (**r bblock being executed *)
(c : cont),
state
| Callstate:
forall (stack: list stackframe) (**r call stack *)
(f: fundef) (**r function to call *)
(args: list val) (**r arguments to the call *)
(m: mem), (**r memory state *)
state
| Returnstate:
forall (stack: list stackframe) (**r call stack *)
(v: val) (**r return value for the call *)
(m: mem), (**r memory state *)
state.
Section RELSEM.
Variable ge: genv.
Definition find_function
(ros: reg + ident) (rs: regset) : option fundef :=
match ros with
| inl r => Genv.find_funct ge rs#r
| inr symb =>
match Genv.find_symbol ge symb with
| None => None
| Some b => Genv.find_funct_ptr ge b
end
end.
Inductive step : state -> trace -> state -> Prop :=
| exec_RBnop :
forall s f sp pc rs m ls ci,
step (State s f sp pc rs m (mk_bblock (RBnop :: ls) ci) C) E0
(State s f sp (Pos.succ pc) rs m (mk_bblock ls ci) C)
| exec_RBop :
forall s f sp pc rs m ls args op res ci v,
eval_operation ge sp op rs##args m = Some v ->
step (State s f sp pc rs m (mk_bblock (RBop op args res :: ls) ci) C) E0
(State s f sp (Pos.succ pc) rs m (mk_bblock ls ci) C)
| exec_RBload:
forall s f sp pc rs m chunk addr args dst a v ls ci,
eval_addressing ge sp addr rs##args = Some a ->
Mem.loadv chunk m a = Some v ->
step (State s f sp pc rs m (mk_bblock (RBload chunk addr args dst :: ls) ci) C)
E0 (State s f sp (Pos.succ pc) (rs#dst <- v) m (mk_bblock ls ci) C)
| exec_RBstore:
forall s f sp pc rs m chunk addr args src a m' ls ci,
eval_addressing ge sp addr rs##args = Some a ->
Mem.storev chunk m a rs#src = Some m' ->
step (State s f sp pc rs m (mk_bblock (RBstore chunk addr args src :: ls) ci) C)
E0 (State s f sp (Pos.succ pc) rs m' (mk_bblock ls ci) C)
| exec_RBcond:
forall s f sp pc rs m cond args ifso ifnot b pc',
eval_condition cond rs##args m = Some b ->
pc' = (if b then ifso else ifnot) ->
step (State s f sp pc rs m (mk_bblock nil (RBcond cond args ifso ifnot)) C)
E0 (State s f sp pc' rs m (mk_bblock nil (RBcond cond args ifso ifnot)) N)
.
End RELSEM.
*)
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