Library compcert.backend.LTL


The LTL intermediate language: abstract syntax and semantics.
LTL (``Location Transfer Language'') is the target language for register allocation and the source language for linearization.

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

Abstract syntax

LTL is close to RTL, but uses machine registers and stack slots instead of pseudo-registers. Also, the nodes of the control-flow graph are basic blocks instead of single instructions.

Definition node := positive.

Inductive instruction: Type :=
  | Lop (op: operation) (args: list mreg) (res: mreg)
  | Lload (chunk: memory_chunk) (addr: addressing) (args: list mreg) (dst: mreg)
  | Lgetstack (sl: slot) (ofs: Z) (ty: typ) (dst: mreg)
  | Lsetstack (src: mreg) (sl: slot) (ofs: Z) (ty: typ)
  | Lstore (chunk: memory_chunk) (addr: addressing) (args: list mreg) (src: mreg)
  | Lcall (sg: signature) (ros: mreg + ident)
  | Ltailcall (sg: signature) (ros: mreg + ident)
  | Lbuiltin (ef: external_function) (args: list mreg) (res: list mreg)
  | Lannot (ef: external_function) (args: list loc)
  | Lbranch (s: node)
  | Lcond (cond: condition) (args: list mreg) (s1 s2: node)
  | Ljumptable (arg: mreg) (tbl: list node)
  | Lreturn.

Definition bblock := list instruction.

Definition code: Type := PTree.t bblock.

Record function: Type := mkfunction {
  fn_sig: signature;
  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.

Operational semantics


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

Calling conventions are reflected at the level of location sets (environments mapping locations to values) by the following two functions.
call_regs caller returns the location set at function entry, as a function of the location set caller of the calling function.
  • Machine registers have the same values as in the caller.
  • Incoming stack slots (used for parameter passing) have the same values as the corresponding outgoing stack slots (used for argument passing) in the caller.
  • Local and outgoing stack slots are initialized to undefined values.

Definition call_regs (caller: locset) : locset :=
  fun (l: loc) =>
    match l with
    | R r => caller (R r)
    | S Local ofs ty => Vundef
    | S Incoming ofs ty => caller (S Outgoing ofs ty)
    | S Outgoing ofs ty => Vundef
    end.

return_regs caller callee returns the location set after a call instruction, as a function of the location set caller of the caller before the call instruction and of the location set callee of the callee at the return instruction.
  • Callee-save machine registers have the same values as in the caller before the call.
  • Caller-save machine registers have the same values as in the callee.
  • Stack slots have the same values as in the caller.

Definition return_regs (caller callee: locset) : locset :=
  fun (l: loc) =>
    match l with
    | R r =>
        if In_dec mreg_eq r destroyed_at_call
        then callee (R r)
        else caller (R r)
    | S sl ofs ty => caller (S sl ofs ty)
    end.

LTL execution states.

Inductive stackframe : Type :=
  | Stackframe:
      forall (f: function)
             (sp: val)
             (ls: locset)
             (bb: bblock),
      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} : Type :=
  | State:
      forall (stack: list stackframe)
             (f: function)
             (sp: val)
             (pc: node)
             (ls: locset)
             (m: mem),
      state
  | Block:
      forall (stack: list stackframe)
             (f: function)
             (sp: val)
             (bb: bblock)
             (ls: locset)
             (m: mem),
      state
  | Callstate:
      forall (stack: list stackframe)
             (f: fundef)
             (ls: locset)
             (m: mem),
      state
  | Returnstate:
      forall (stack: list stackframe)
             (ls: locset)
             (m: mem),
      state.

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 reglist (rs: locset) (rl: list mreg) : list val :=
  List.map (fun r => rs (R r)) rl.

Fixpoint undef_regs (rl: list mreg) (rs: locset) : locset :=
  match rl with
  | nil => rs
  | r1 :: rl => Locmap.set (R r1) Vundef (undef_regs rl rs)
  end.

Definition destroyed_by_getstack (s: slot): list mreg :=
  match s with
  | Incoming => temp_for_parent_frame :: nil
  | _ => nil
  end.

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.

parent_locset cs returns the mapping of values for locations of the caller function.
CompCertX:test-compcert-protect-stack-arg We parameterize over init_ls, the values for locations of the initial caller. For whole programs, it is Locmap.init Vundef. For non-whole programs, it will contain the values of callee-save registers as well as the arguments to the function.
Variable init_ls: locset.

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

CompCertX:test-compcert-protect-stack-arg ge is better moved here, so that init_ls can be a parameter of step before.
Variable ge: genv.

Inductive step: state -> trace -> state -> Prop :=
  | exec_start_block: forall s f sp pc rs m bb,
      (fn_code f)!pc = Some bb ->
      step (State s f sp pc rs m)
        E0 (Block s f sp bb rs m)
  | exec_Lop: forall s f sp op args res bb 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 (Block s f sp (Lop op args res :: bb) rs m)
        E0 (Block s f sp bb rs´ m)
  | exec_Lload: forall s f sp chunk addr args dst bb 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 (Block s f sp (Lload chunk addr args dst :: bb) rs m)
        E0 (Block s f sp bb rs´ m)
  | exec_Lgetstack: forall s f sp sl ofs ty dst bb rs m rs´,
      rs´ = Locmap.set (R dst) (rs (S sl ofs ty)) (undef_regs (destroyed_by_getstack sl) rs) ->
      step (Block s f sp (Lgetstack sl ofs ty dst :: bb) rs m)
        E0 (Block s f sp bb rs´ m)
  | exec_Lsetstack: forall s f sp src sl ofs ty bb rs m rs´,
      rs´ = Locmap.set (S sl ofs ty) (rs (R src)) (undef_regs (destroyed_by_setstack ty) rs) ->
      step (Block s f sp (Lsetstack src sl ofs ty :: bb) rs m)
        E0 (Block s f sp bb rs´ m)
  | exec_Lstore: forall s f sp chunk addr args src bb 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 (Block s f sp (Lstore chunk addr args src :: bb) rs m)
        E0 (Block s f sp bb rs´ )
  | exec_Lcall: forall s f sp sig ros bb rs m fd,
      find_function ge ros rs = Some fd ->
      funsig fd = sig ->
      step (Block s f sp (Lcall sig ros :: bb) rs m)
        E0 (Callstate (Stackframe f sp rs bb :: s) fd rs m)
  | exec_Ltailcall: forall s f sp sig ros bb rs m fd rs´ ,
      rs´ = return_regs (parent_locset s) rs ->
      find_function ge ros rs´ = Some fd ->
      funsig fd = sig ->
      Mem.free m sp 0 f.(fn_stacksize) = Some ->
      step (Block s f (Vptr sp Int.zero) (Ltailcall sig ros :: bb) rs m)
        E0 (Callstate s fd rs´ )
  | exec_Lbuiltin: forall s f sp ef args res bb rs m 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 (Block s f sp (Lbuiltin ef args res :: bb) rs m)
         t (Block s f sp bb rs´ )
  | exec_Lannot: forall s f sp ef args bb rs m t vl ,
      external_call´ (writable_block ge) ef ge (map rs args) m t vl ->
      forall BUILTIN_ENABLED: builtin_enabled ef,
      step (Block s f sp (Lannot ef args :: bb) rs m)
         t (Block s f sp bb rs )
  | exec_Lbranch: forall s f sp pc bb rs m,
      step (Block s f sp (Lbranch pc :: bb) rs m)
        E0 (State s f sp pc rs m)
  | exec_Lcond: forall s f sp cond args pc1 pc2 bb rs b pc rs´ m,
      eval_condition cond (reglist rs args) m = Some b ->
      pc = (if b then pc1 else pc2) ->
      rs´ = undef_regs (destroyed_by_cond cond) rs ->
      step (Block s f sp (Lcond cond args pc1 pc2 :: bb) rs m)
        E0 (State s f sp pc rs´ m)
  | exec_Ljumptable: forall s f sp arg tbl bb rs m n pc rs´,
      rs (R arg) = Vint n ->
      list_nth_z tbl (Int.unsigned n) = Some pc ->
      rs´ = undef_regs (destroyed_by_jumptable) rs ->
      step (Block s f sp (Ljumptable arg tbl :: bb) rs m)
        E0 (State s f sp pc rs´ m)
  | exec_Lreturn: forall s f sp bb rs m ,
      Mem.free m sp 0 f.(fn_stacksize) = Some ->
      step (Block s f (Vptr sp Int.zero) (Lreturn :: bb) rs m)
        E0 (Returnstate s (return_regs (parent_locset s) rs) )
  | exec_function_internal: forall s f rs m sp rs´,
      Mem.alloc m 0 f.(fn_stacksize) = (, sp) ->
      rs´ = undef_regs destroyed_at_function_entry (call_regs rs) ->
      step (Callstate s (Internal f) rs m)
        E0 (State s f (Vptr sp Int.zero) f.(fn_entrypoint) rs´ )
  | exec_function_external: forall s ef t args res rs m rs´ ,
      args = map rs (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.
      rs´ = Locmap.setlist (map R (loc_result (ef_sig ef))) res (undef_regs destroyed_at_call rs) ->
      step (Callstate s (External ef) rs m)
         t (Returnstate s rs´ )
  | exec_return: forall f sp rs1 bb s rs m,
      step (Returnstate (Stackframe f sp rs1 bb :: s) rs m)
        E0 (Block s f sp bb rs m).

End RELSEM.

Execution of a whole program boils down to invoking its main function. The result of the program is the return value of the main function, to be found in the machine register dictated by the calling conventions.

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.
Section WRITABLEBLOCKALWAYS.
Local Existing Instance writable_block_always_ops.

CompCertX:test-compcert-protect-stack-arg For whole programs, the initial locset is Locmap.init Vundef.

Operations over LTL

Computation of the possible successors of a block. This is used in particular for dataflow analyses.

Fixpoint successors_block (b: bblock) : list node :=
  match b with
  | nil => nil
  | Ltailcall _ _ :: _ => nil
  | Lbranch s :: _ => s :: nil
  | Lcond _ _ s1 s2 :: _ => s1 :: s2 :: nil
  | Ljumptable _ tbl :: _ => tbl
  | Lreturn :: _ => nil
  | instr :: => successors_block
  end.

End WITHCONFIG.