Library compcert.backend.Linear


The Linear intermediate language: abstract syntax and semantcs
The Linear language is a variant of LTL where control-flow is not expressed as a graph of basic blocks, but as a linear list of instructions with explicit labels and ``goto'' instructions.

Require Import Coqlib.
Require Import AST.
Require Import Integers.
Require Import Values.
Require Import Memory.
Require Import Events.
Require Import Globalenvs.
Require Import Smallstep.
Require Import Op.
Require Import Locations.
Require Import LTL.
Require Import Conventions.

Abstract syntax


Definition label := positive.

Inductive instruction: Type :=
  | Lgetstack: slot -> Z -> typ -> mreg -> instruction
  | Lsetstack: mreg -> slot -> Z -> typ -> instruction
  | Lop: operation -> list mreg -> mreg -> instruction
  | Lload: memory_chunk -> addressing -> list mreg -> mreg -> instruction
  | Lstore: memory_chunk -> addressing -> list mreg -> mreg -> instruction
  | Lcall: signature -> mreg + ident -> instruction
  | Ltailcall: signature -> mreg + ident -> instruction
  | Lbuiltin: external_function -> list mreg -> list mreg -> instruction
  | Lannot: external_function -> list loc -> instruction
  | Llabel: label -> instruction
  | Lgoto: label -> instruction
  | Lcond: condition -> list mreg -> label -> instruction
  | Ljumptable: mreg -> list label -> instruction
  | Lreturn: instruction.

Definition code: Type := list instruction.

Record function: Type := mkfunction {
  fn_sig: signature;
  fn_stacksize: Z;
  fn_code: code
}.

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.

Definition genv := Genv.t fundef unit.
Definition locset := Locmap.t.

Operational semantics

Looking up labels in the instruction list.

Definition is_label (lbl: label) (instr: instruction) : bool :=
  match instr with
  | Llabel lbl´ => if peq lbl lbl´ then true else false
  | _ => false
  end.

Lemma is_label_correct:
  forall lbl instr,
  if is_label lbl instr then instr = Llabel lbl else instr <> Llabel lbl.
Proof.
  intros. destruct instr; simpl; try discriminate.
  case (peq lbl l); intro; congruence.
Qed.

find_label lbl c returns a list of instruction, suffix of the code c, that immediately follows the Llabel lbl pseudo-instruction. If the label lbl is multiply-defined, the first occurrence is retained. If the label lbl is not defined, None is returned.

Fixpoint find_label (lbl: label) (c: code) {struct c} : option code :=
  match c with
  | nil => None
  | i1 :: il => if is_label lbl i1 then Some il else find_label lbl il
  end.

CompCertX:test-compcert-param-memory We create section WITHMEM and associated contexts to parameterize the proof over the memory model. CompCertX:test-compcert-param-extcall Actually, we also need to parameterize over external functions. To this end, we created a CompilerConfiguration class (cf. Events) which is designed to be the single class on which the whole CompCert is to be parameterized. It includes all operations and properties on which CompCert depends: memory model, semantics of external functions and their preservation through compilation.
Section WITHCONFIG.
Context `{compiler_config: CompilerConfiguration}.

Section RELSEM.

CompCertX:test-compcert-protect-stack-arg We also parameterize over a way to mark blocks writable.
Context `{writable_block_ops: WritableBlockOps}.

Definition find_function (ge: genv) (ros: mreg + ident) (rs: locset) : option fundef :=
  match ros with
  | inl r => Genv.find_funct ge (rs (R r))
  | inr symb =>
      match Genv.find_symbol ge symb with
      | None => None
      | Some b => Genv.find_funct_ptr ge b
      end
  end.

Linear execution states.

Inductive stackframe: Type :=
  | Stackframe:
      forall (f: function)
             (sp: val)
             (rs: locset)
             (c: code),
      stackframe.

CompCertX:test-compcert-param-memory The state now depends on the type mem for memory states, which is an implicit argument. To have Coq guess the right one, we make state also depend on memory operations.
Inductive state `{memory_model_ops: Mem.MemoryModelOps mem} : Type :=
  | State:
      forall (stack: list stackframe)
             (f: function)
             (sp: val)
             (c: code)
             (rs: locset)
             (m: mem),
      state
  | Callstate:
      forall (stack: list stackframe)
             (f: fundef)
             (rs: locset)
             (m: mem),
      state
  | Returnstate:
      forall (stack: list stackframe)
             (rs: locset)
             (m: mem),
      state.

parent_locset cs returns the mapping of values for locations of the caller function.
CompCertX:test-compcert-protect-stack-arg The initial location set of the caller is now a parameter of the semantics. For whole programs, it is Locmap.init Vundef (there is no "caller of main").

Variable init_rs: locset.

Definition parent_locset (stack: list stackframe) : locset :=
  match stack with
  | nil => init_rs
  | Stackframe f sp ls c :: stack´ => ls
  end.

CompCertX:test-compcert-protect-stack-arg Parameter ge is better moved here, to allow step to be parameterized on init_rs first.

Variable ge: genv.

Inductive step: state -> trace -> state -> Prop :=
  | exec_Lgetstack:
      forall s f sp sl ofs ty dst b rs m rs´,
      rs´ = Locmap.set (R dst) (rs (S sl ofs ty)) (undef_regs (destroyed_by_getstack sl) rs) ->
      step (State s f sp (Lgetstack sl ofs ty dst :: b) rs m)
        E0 (State s f sp b rs´ m)
  | exec_Lsetstack:
      forall s f sp src sl ofs ty b rs m rs´,
      rs´ = Locmap.set (S sl ofs ty) (rs (R src)) (undef_regs (destroyed_by_setstack ty) rs) ->
      step (State s f sp (Lsetstack src sl ofs ty :: b) rs m)
        E0 (State s f sp b rs´ m)
  | exec_Lop:
      forall s f sp op args res b rs m v rs´,
      eval_operation ge sp op (reglist rs args) m = Some v ->
      rs´ = Locmap.set (R res) v (undef_regs (destroyed_by_op op) rs) ->
      step (State s f sp (Lop op args res :: b) rs m)
        E0 (State s f sp b rs´ m)
  | exec_Lload:
      forall s f sp chunk addr args dst b rs m a v rs´,
      eval_addressing ge sp addr (reglist rs args) = Some a ->
      Mem.loadv chunk m a = Some v ->
      rs´ = Locmap.set (R dst) v (undef_regs (destroyed_by_load chunk addr) rs) ->
      step (State s f sp (Lload chunk addr args dst :: b) rs m)
        E0 (State s f sp b rs´ m)
  | exec_Lstore:
      forall s f sp chunk addr args src b rs m a rs´,
      eval_addressing ge sp addr (reglist rs args) = Some a ->
      Mem.storev chunk m a (rs (R src)) = Some ->
      rs´ = undef_regs (destroyed_by_store chunk addr) rs ->
      forall WRITABLE: forall b o, a = Vptr b o -> writable_block ge b,
      step (State s f sp (Lstore chunk addr args src :: b) rs m)
        E0 (State s f sp b rs´ )
  | exec_Lcall:
      forall s f sp sig ros b rs m ,
      find_function ge ros rs = Some ->
      sig = funsig ->
      step (State s f sp (Lcall sig ros :: b) rs m)
        E0 (Callstate (Stackframe f sp rs b:: s) rs m)
  | exec_Ltailcall:
      forall s f stk sig ros b rs m rs´ ,
      rs´ = return_regs (parent_locset s) rs ->
      find_function ge ros rs´ = Some ->
      sig = funsig ->
      Mem.free m stk 0 f.(fn_stacksize) = Some ->
      step (State s f (Vptr stk Int.zero) (Ltailcall sig ros :: b) rs m)
        E0 (Callstate s rs´ )
  | exec_Lbuiltin:
      forall s f sp rs m ef args res b t vl rs´ ,
      external_call´ (writable_block ge) ef ge (reglist rs args) m t vl ->
      rs´ = Locmap.setlist (map R res) vl (undef_regs (destroyed_by_builtin ef) rs) ->
CompCertX:test-compcert-disable-extcall-as-builtin We may need to disallow the use of external function calls (EF_external) as builtins. This is already the case in assembly generation (PrintAsm.ml), but not in the semantics of languages, which we propose to fix through providing a switch in the compiler configuration, hence the CompilerConfigOps class, and this new clause in the operational semantics.
      forall BUILTIN_ENABLED: builtin_enabled ef,
      step (State s f sp (Lbuiltin ef args res :: b) rs m)
         t (State s f sp b rs´ )
  | exec_Lannot:
      forall s f sp rs m ef args b t v ,
      external_call´ (writable_block ge) ef ge (map rs args) m t v ->
      forall BUILTIN_ENABLED: builtin_enabled ef,
      step (State s f sp (Lannot ef args :: b) rs m)
         t (State s f sp b rs )
  | exec_Llabel:
      forall s f sp lbl b rs m,
      step (State s f sp (Llabel lbl :: b) rs m)
        E0 (State s f sp b rs m)
  | exec_Lgoto:
      forall s f sp lbl b rs m ,
      find_label lbl f.(fn_code) = Some ->
      step (State s f sp (Lgoto lbl :: b) rs m)
        E0 (State s f sp rs m)
  | exec_Lcond_true:
      forall s f sp cond args lbl b rs m rs´ ,
      eval_condition cond (reglist rs args) m = Some true ->
      rs´ = undef_regs (destroyed_by_cond cond) rs ->
      find_label lbl f.(fn_code) = Some ->
      step (State s f sp (Lcond cond args lbl :: b) rs m)
        E0 (State s f sp rs´ m)
  | exec_Lcond_false:
      forall s f sp cond args lbl b rs m rs´,
      eval_condition cond (reglist rs args) m = Some false ->
      rs´ = undef_regs (destroyed_by_cond cond) rs ->
      step (State s f sp (Lcond cond args lbl :: b) rs m)
        E0 (State s f sp b rs´ m)
  | exec_Ljumptable:
      forall s f sp arg tbl b rs m n lbl rs´,
      rs (R arg) = Vint n ->
      list_nth_z tbl (Int.unsigned n) = Some lbl ->
      find_label lbl f.(fn_code) = Some ->
      rs´ = undef_regs (destroyed_by_jumptable) rs ->
      step (State s f sp (Ljumptable arg tbl :: b) rs m)
        E0 (State s f sp rs´ m)
  | exec_Lreturn:
      forall s f stk b rs m ,
      Mem.free m stk 0 f.(fn_stacksize) = Some ->
      step (State s f (Vptr stk Int.zero) (Lreturn :: b) rs m)
        E0 (Returnstate s (return_regs (parent_locset s) rs) )
  | exec_function_internal:
      forall s f rs m rs´ stk,
      Mem.alloc m 0 f.(fn_stacksize) = (, stk) ->
      rs´ = undef_regs destroyed_at_function_entry (call_regs rs) ->
      step (Callstate s (Internal f) rs m)
        E0 (State s f (Vptr stk Int.zero) f.(fn_code) rs´ )
  | exec_function_external:
      forall s ef args res rs1 rs2 m t ,
      args = map rs1 (loc_arguments (ef_sig ef)) ->
      external_call´ (writable_block ge) ef ge args m t res ->
      
CompCertX:test-compcert-undef-destroyed-by-call We erase non-callee-save registers.
      rs2 = Locmap.setlist (map R (loc_result (ef_sig ef))) res (undef_regs destroyed_at_call rs1) ->
      step (Callstate s (External ef) rs1 m)
         t (Returnstate s rs2 )
  | exec_return:
      forall s f sp rs0 c rs m,
      step (Returnstate (Stackframe f sp rs0 c :: s) rs m)
        E0 (State s f sp c rs 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 (Locmap.init Vundef) m0).

Inductive final_state: state -> int -> Prop :=
  | final_state_intro: forall rs m r retcode,
      loc_result signature_main = r :: nil ->
      rs (R r) = Vint retcode ->
      final_state (Returnstate nil rs m) retcode.

CompCertX:test-compcert-protect-stack-arg For whole programs, all blocks are writable.
Local Existing Instance writable_block_always_ops.

Definition semantics (p: program) :=
  Semantics (step (Locmap.init Vundef)) (initial_state p) final_state (Genv.globalenv p).

End WITHCONFIG.