aboutsummaryrefslogtreecommitdiffstats
path: root/backend/Conventions.v
diff options
context:
space:
mode:
authorxleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e>2008-12-30 14:48:33 +0000
committerxleroy <xleroy@fca1b0fc-160b-0410-b1d3-a4f43f01ea2e>2008-12-30 14:48:33 +0000
commit6d25b4f3fc23601b3a84b4a70aab40ba429ac4b9 (patch)
treef7adbc5ec8accc4bec3e38939bdf570a266f0e83 /backend/Conventions.v
parent1bce6b0f9f8cd614038a6e7fc21fb984724204a4 (diff)
downloadcompcert-kvx-6d25b4f3fc23601b3a84b4a70aab40ba429ac4b9.tar.gz
compcert-kvx-6d25b4f3fc23601b3a84b4a70aab40ba429ac4b9.zip
Reorganized the development, modularizing away machine-dependent parts.
Started to merge the ARM code generator. Started to add support for PowerPC/EABI. Use ocamlbuild to construct executable from Caml files. git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@930 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e
Diffstat (limited to 'backend/Conventions.v')
-rw-r--r--backend/Conventions.v805
1 files changed, 0 insertions, 805 deletions
diff --git a/backend/Conventions.v b/backend/Conventions.v
deleted file mode 100644
index b7d931f5..00000000
--- a/backend/Conventions.v
+++ /dev/null
@@ -1,805 +0,0 @@
-(* *********************************************************************)
-(* *)
-(* The Compcert verified compiler *)
-(* *)
-(* Xavier Leroy, INRIA Paris-Rocquencourt *)
-(* *)
-(* Copyright Institut National de Recherche en Informatique et en *)
-(* Automatique. All rights reserved. This file is distributed *)
-(* under the terms of the INRIA Non-Commercial License Agreement. *)
-(* *)
-(* *********************************************************************)
-
-(** Function calling conventions and other conventions regarding the use of
- machine registers and stack slots. *)
-
-Require Import Coqlib.
-Require Import AST.
-Require Import Locations.
-
-(** * Classification of machine registers *)
-
-(** Machine registers (type [mreg] in module [Locations]) are divided in
- the following groups:
-- Temporaries used for spilling, reloading, and parallel move operations.
-- Allocatable registers, that can be assigned to RTL pseudo-registers.
- These are further divided into:
--- Callee-save registers, whose value is preserved across a function call.
--- Caller-save registers that can be modified during a function call.
-
- We follow the PowerPC application binary interface (ABI) in our choice
- of callee- and caller-save registers.
-*)
-
-Definition int_caller_save_regs :=
- R3 :: R4 :: R5 :: R6 :: R7 :: R8 :: R9 :: R10 :: nil.
-
-Definition float_caller_save_regs :=
- F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 :: F8 :: F9 :: F10 :: nil.
-
-Definition int_callee_save_regs :=
- R13 :: R14 :: R15 :: R16 :: R17 :: R18 :: R19 :: R20 :: R21 :: R22 ::
- R23 :: R24 :: R25 :: R26 :: R27 :: R28 :: R29 :: R30 :: R31 :: nil.
-
-Definition float_callee_save_regs :=
- F14 :: F15 :: F16 :: F17 :: F18 :: F19 :: F20 :: F21 :: F22 ::
- F23 :: F24 :: F25 :: F26 :: F27 :: F28 :: F29 :: F30 :: F31 :: nil.
-
-Definition destroyed_at_call_regs :=
- int_caller_save_regs ++ float_caller_save_regs.
-
-Definition destroyed_at_call :=
- List.map R destroyed_at_call_regs.
-
-Definition int_temporaries := IT1 :: IT2 :: nil.
-
-Definition float_temporaries := FT1 :: FT2 :: FT3 :: nil.
-
-Definition temporaries :=
- R IT1 :: R IT2 :: R FT1 :: R FT2 :: R FT3 :: nil.
-
-(** The [index_int_callee_save] and [index_float_callee_save] associate
- a unique positive integer to callee-save registers. This integer is
- used in [Stacking] to determine where to save these registers in
- the activation record if they are used by the current function. *)
-
-Definition index_int_callee_save (r: mreg) :=
- match r with
- | R13 => 0 | R14 => 1 | R15 => 2 | R16 => 3
- | R17 => 4 | R18 => 5 | R19 => 6 | R20 => 7
- | R21 => 8 | R22 => 9 | R23 => 10 | R24 => 11
- | R25 => 12 | R26 => 13 | R27 => 14 | R28 => 15
- | R29 => 16 | R30 => 17 | R31 => 18 | _ => -1
- end.
-
-Definition index_float_callee_save (r: mreg) :=
- match r with
- | F14 => 0 | F15 => 1 | F16 => 2 | F17 => 3
- | F18 => 4 | F19 => 5 | F20 => 6 | F21 => 7
- | F22 => 8 | F23 => 9 | F24 => 10 | F25 => 11
- | F26 => 12 | F27 => 13 | F28 => 14 | F29 => 15
- | F30 => 16 | F31 => 17 | _ => -1
- end.
-
-Ltac ElimOrEq :=
- match goal with
- | |- (?x = ?y) \/ _ -> _ =>
- let H := fresh in
- (intro H; elim H; clear H;
- [intro H; rewrite <- H; clear H | ElimOrEq])
- | |- False -> _ =>
- let H := fresh in (intro H; contradiction)
- end.
-
-Ltac OrEq :=
- match goal with
- | |- (?x = ?x) \/ _ => left; reflexivity
- | |- (?x = ?y) \/ _ => right; OrEq
- | |- False => fail
- end.
-
-Ltac NotOrEq :=
- match goal with
- | |- (?x = ?y) \/ _ -> False =>
- let H := fresh in (
- intro H; elim H; clear H; [intro; discriminate | NotOrEq])
- | |- False -> False =>
- contradiction
- end.
-
-Lemma index_int_callee_save_pos:
- forall r, In r int_callee_save_regs -> index_int_callee_save r >= 0.
-Proof.
- intro r. simpl; ElimOrEq; unfold index_int_callee_save; omega.
-Qed.
-
-Lemma index_float_callee_save_pos:
- forall r, In r float_callee_save_regs -> index_float_callee_save r >= 0.
-Proof.
- intro r. simpl; ElimOrEq; unfold index_float_callee_save; omega.
-Qed.
-
-Lemma index_int_callee_save_pos2:
- forall r, index_int_callee_save r >= 0 -> In r int_callee_save_regs.
-Proof.
- destruct r; simpl; intro; omegaContradiction || OrEq.
-Qed.
-
-Lemma index_float_callee_save_pos2:
- forall r, index_float_callee_save r >= 0 -> In r float_callee_save_regs.
-Proof.
- destruct r; simpl; intro; omegaContradiction || OrEq.
-Qed.
-
-Lemma index_int_callee_save_inj:
- forall r1 r2,
- In r1 int_callee_save_regs ->
- In r2 int_callee_save_regs ->
- r1 <> r2 ->
- index_int_callee_save r1 <> index_int_callee_save r2.
-Proof.
- intros r1 r2.
- simpl; ElimOrEq; ElimOrEq; unfold index_int_callee_save;
- intros; congruence.
-Qed.
-
-Lemma index_float_callee_save_inj:
- forall r1 r2,
- In r1 float_callee_save_regs ->
- In r2 float_callee_save_regs ->
- r1 <> r2 ->
- index_float_callee_save r1 <> index_float_callee_save r2.
-Proof.
- intros r1 r2.
- simpl; ElimOrEq; ElimOrEq; unfold index_float_callee_save;
- intros; congruence.
-Qed.
-
-(** The following lemmas show that
- (temporaries, destroyed at call, integer callee-save, float callee-save)
- is a partition of the set of machine registers. *)
-
-Lemma int_float_callee_save_disjoint:
- list_disjoint int_callee_save_regs float_callee_save_regs.
-Proof.
- red; intros r1 r2. simpl; ElimOrEq; ElimOrEq; discriminate.
-Qed.
-
-Lemma register_classification:
- forall r,
- (In (R r) temporaries \/ In (R r) destroyed_at_call) \/
- (In r int_callee_save_regs \/ In r float_callee_save_regs).
-Proof.
- destruct r;
- try (left; left; simpl; OrEq);
- try (left; right; simpl; OrEq);
- try (right; left; simpl; OrEq);
- try (right; right; simpl; OrEq).
-Qed.
-
-Lemma int_callee_save_not_destroyed:
- forall r,
- In (R r) temporaries \/ In (R r) destroyed_at_call ->
- ~(In r int_callee_save_regs).
-Proof.
- intros; red; intros. elim H.
- generalize H0. simpl; ElimOrEq; NotOrEq.
- generalize H0. simpl; ElimOrEq; NotOrEq.
-Qed.
-
-Lemma float_callee_save_not_destroyed:
- forall r,
- In (R r) temporaries \/ In (R r) destroyed_at_call ->
- ~(In r float_callee_save_regs).
-Proof.
- intros; red; intros. elim H.
- generalize H0. simpl; ElimOrEq; NotOrEq.
- generalize H0. simpl; ElimOrEq; NotOrEq.
-Qed.
-
-Lemma int_callee_save_type:
- forall r, In r int_callee_save_regs -> mreg_type r = Tint.
-Proof.
- intro. simpl; ElimOrEq; reflexivity.
-Qed.
-
-Lemma float_callee_save_type:
- forall r, In r float_callee_save_regs -> mreg_type r = Tfloat.
-Proof.
- intro. simpl; ElimOrEq; reflexivity.
-Qed.
-
-Ltac NoRepet :=
- match goal with
- | |- list_norepet nil =>
- apply list_norepet_nil
- | |- list_norepet (?a :: ?b) =>
- apply list_norepet_cons; [simpl; intuition discriminate | NoRepet]
- end.
-
-Lemma int_callee_save_norepet:
- list_norepet int_callee_save_regs.
-Proof.
- unfold int_callee_save_regs; NoRepet.
-Qed.
-
-Lemma float_callee_save_norepet:
- list_norepet float_callee_save_regs.
-Proof.
- unfold float_callee_save_regs; NoRepet.
-Qed.
-
-(** * Acceptable locations for register allocation *)
-
-(** The following predicate describes the locations that can be assigned
- to an RTL pseudo-register during register allocation: a non-temporary
- machine register or a [Local] stack slot are acceptable. *)
-
-Definition loc_acceptable (l: loc) : Prop :=
- match l with
- | R r => ~(In l temporaries)
- | S (Local ofs ty) => ofs >= 0
- | S (Incoming _ _) => False
- | S (Outgoing _ _) => False
- end.
-
-Definition locs_acceptable (ll: list loc) : Prop :=
- forall l, In l ll -> loc_acceptable l.
-
-Lemma temporaries_not_acceptable:
- forall l, loc_acceptable l -> Loc.notin l temporaries.
-Proof.
- unfold loc_acceptable; destruct l.
- simpl. intuition congruence.
- destruct s; try contradiction.
- intro. simpl. tauto.
-Qed.
-Hint Resolve temporaries_not_acceptable: locs.
-
-Lemma locs_acceptable_disj_temporaries:
- forall ll, locs_acceptable ll -> Loc.disjoint ll temporaries.
-Proof.
- intros. apply Loc.notin_disjoint. intros.
- apply temporaries_not_acceptable. auto.
-Qed.
-
-Lemma loc_acceptable_noteq_diff:
- forall l1 l2,
- loc_acceptable l1 -> l1 <> l2 -> Loc.diff l1 l2.
-Proof.
- unfold loc_acceptable, Loc.diff; destruct l1; destruct l2;
- try (destruct s); try (destruct s0); intros; auto; try congruence.
- case (zeq z z0); intro.
- compare t t0; intro.
- subst z0; subst t0; tauto.
- tauto. tauto.
- contradiction. contradiction.
-Qed.
-
-Lemma loc_acceptable_notin_notin:
- forall r ll,
- loc_acceptable r ->
- ~(In r ll) -> Loc.notin r ll.
-Proof.
- induction ll; simpl; intros.
- auto.
- split. apply loc_acceptable_noteq_diff. assumption.
- apply sym_not_equal. tauto.
- apply IHll. assumption. tauto.
-Qed.
-
-(** * Function calling conventions *)
-
-(** The functions in this section determine the locations (machine registers
- and stack slots) used to communicate arguments and results between the
- caller and the callee during function calls. These locations are functions
- of the signature of the function and of the call instruction.
- Agreement between the caller and the callee on the locations to use
- is guaranteed by our dynamic semantics for Cminor and RTL, which demand
- that the signature of the call instruction is identical to that of the
- called function.
-
- Calling conventions are largely arbitrary: they must respect the properties
- proved in this section (such as no overlapping between the locations
- of function arguments), but this leaves much liberty in choosing actual
- locations. To ensure binary interoperability of code generated by our
- compiler with libraries compiled by another PowerPC compiler, we
- implement the standard conventions defined in the PowerPC application
- binary interface. *)
-
-(** ** Location of function result *)
-
-(** The result value of a function is passed back to the caller in
- registers [R3] or [F1], depending on the type of the returned value.
- We treat a function without result as a function with one integer result. *)
-
-Definition loc_result (s: signature) : mreg :=
- match s.(sig_res) with
- | None => R3
- | Some Tint => R3
- | Some Tfloat => F1
- end.
-
-(** The result location has the type stated in the signature. *)
-
-Lemma loc_result_type:
- forall sig,
- mreg_type (loc_result sig) =
- match sig.(sig_res) with None => Tint | Some ty => ty end.
-Proof.
- intros; unfold loc_result.
- destruct (sig_res sig).
- destruct t; reflexivity.
- reflexivity.
-Qed.
-
-(** The result location is acceptable. *)
-
-Lemma loc_result_acceptable:
- forall sig, loc_acceptable (R (loc_result sig)).
-Proof.
- intros. unfold loc_acceptable. red.
- unfold loc_result. destruct (sig_res sig).
- destruct t; simpl; NotOrEq.
- simpl; NotOrEq.
-Qed.
-
-(** The result location is a caller-save register. *)
-
-Lemma loc_result_caller_save:
- forall (s: signature), In (R (loc_result s)) destroyed_at_call.
-Proof.
- intros; unfold loc_result.
- destruct (sig_res s).
- destruct t; simpl; OrEq.
- simpl; OrEq.
-Qed.
-
-(** The result location is not a callee-save register. *)
-
-Lemma loc_result_not_callee_save:
- forall (s: signature),
- ~(In (loc_result s) int_callee_save_regs \/ In (loc_result s) float_callee_save_regs).
-Proof.
- intros. generalize (loc_result_caller_save s).
- generalize (int_callee_save_not_destroyed (loc_result s)).
- generalize (float_callee_save_not_destroyed (loc_result s)).
- tauto.
-Qed.
-
-(** ** Location of function arguments *)
-
-(** The PowerPC ABI states the following convention for passing arguments
- to a function:
-- The first 8 integer arguments are passed in registers [R3] to [R10].
-- The first 10 float arguments are passed in registers [F1] to [F10].
-- Each float argument passed in a float register ``consumes'' two
- integer arguments.
-- Extra arguments are passed on the stack, in [Outgoing] slots, consecutively
- assigned (1 word for an integer argument, 2 words for a float),
- starting at word offset 0.
-- Stack space is reserved (as unused [Outgoing] slots) for the arguments
- that are passed in registers.
-
-These conventions are somewhat baroque, but they are mandated by the ABI.
-*)
-
-Fixpoint loc_arguments_rec
- (tyl: list typ) (iregl: list mreg) (fregl: list mreg)
- (ofs: Z) {struct tyl} : list loc :=
- match tyl with
- | nil => nil
- | Tint :: tys =>
- match iregl with
- | nil =>
- S (Outgoing ofs Tint) :: loc_arguments_rec tys nil fregl (ofs + 1)
- | ireg :: iregs =>
- R ireg :: loc_arguments_rec tys iregs fregl ofs
- end
- | Tfloat :: tys =>
- match fregl with
- | nil =>
- S (Outgoing ofs Tfloat) :: loc_arguments_rec tys iregl nil (ofs + 2)
- | freg :: fregs =>
- R freg :: loc_arguments_rec tys (list_drop2 iregl) fregs ofs
- end
- end.
-
-Definition int_param_regs :=
- R3 :: R4 :: R5 :: R6 :: R7 :: R8 :: R9 :: R10 :: nil.
-Definition float_param_regs :=
- F1 :: F2 :: F3 :: F4 :: F5 :: F6 :: F7 :: F8 :: F9 :: F10 :: nil.
-
-(** [loc_arguments s] returns the list of locations where to store arguments
- when calling a function with signature [s]. *)
-
-Definition loc_arguments (s: signature) : list loc :=
- loc_arguments_rec s.(sig_args) int_param_regs float_param_regs 8.
-
-(** [size_arguments s] returns the number of [Outgoing] slots used
- to call a function with signature [s]. *)
-
-Fixpoint size_arguments_rec
- (tyl: list typ) (iregl: list mreg) (fregl: list mreg)
- (ofs: Z) {struct tyl} : Z :=
- match tyl with
- | nil => ofs
- | Tint :: tys =>
- match iregl with
- | nil => size_arguments_rec tys nil fregl (ofs + 1)
- | ireg :: iregs => size_arguments_rec tys iregs fregl ofs
- end
- | Tfloat :: tys =>
- match fregl with
- | nil => size_arguments_rec tys iregl nil (ofs + 2)
- | freg :: fregs => size_arguments_rec tys (list_drop2 iregl) fregs ofs
- end
- end.
-
-Definition size_arguments (s: signature) : Z :=
- size_arguments_rec s.(sig_args) int_param_regs float_param_regs 8.
-
-(** A tail-call is possible for a signature if the corresponding
- arguments are all passed in registers. *)
-
-Definition tailcall_possible (s: signature) : Prop :=
- forall l, In l (loc_arguments s) ->
- match l with R _ => True | S _ => False end.
-
-(** Argument locations are either non-temporary registers or [Outgoing]
- stack slots at nonnegative offsets. *)
-
-Definition loc_argument_acceptable (l: loc) : Prop :=
- match l with
- | R r => ~(In l temporaries)
- | S (Outgoing ofs ty) => ofs >= 0
- | _ => False
- end.
-
-Remark loc_arguments_rec_charact:
- forall tyl iregl fregl ofs l,
- In l (loc_arguments_rec tyl iregl fregl ofs) ->
- match l with
- | R r => In r iregl \/ In r fregl
- | S (Outgoing ofs' ty) => ofs' >= ofs
- | S _ => False
- end.
-Proof.
- induction tyl; simpl loc_arguments_rec; intros.
- elim H.
- destruct a.
- destruct iregl; elim H; intro.
- subst l. omega.
- generalize (IHtyl _ _ _ _ H0). destruct l; auto. destruct s; auto. omega.
- subst l. auto with coqlib.
- generalize (IHtyl _ _ _ _ H0). destruct l; auto. simpl; intuition.
- destruct fregl; elim H; intro.
- subst l. omega.
- generalize (IHtyl _ _ _ _ H0). destruct l; auto. destruct s; auto. omega.
- subst l. auto with coqlib.
- generalize (IHtyl _ _ _ _ H0). destruct l; auto.
- intros [A|B]. left; apply list_drop2_incl; auto. right; auto with coqlib.
-Qed.
-
-Lemma loc_arguments_acceptable:
- forall (s: signature) (r: loc),
- In r (loc_arguments s) -> loc_argument_acceptable r.
-Proof.
- unfold loc_arguments; intros.
- generalize (loc_arguments_rec_charact _ _ _ _ _ H).
- destruct r.
- intro H0; elim H0. simpl. unfold not. ElimOrEq; NotOrEq.
- simpl. unfold not. ElimOrEq; NotOrEq.
- destruct s0; try contradiction.
- simpl. omega.
-Qed.
-Hint Resolve loc_arguments_acceptable: locs.
-
-(** Arguments are parwise disjoint (in the sense of [Loc.norepet]). *)
-
-Remark loc_arguments_rec_notin_reg:
- forall tyl iregl fregl ofs r,
- ~(In r iregl) -> ~(In r fregl) ->
- Loc.notin (R r) (loc_arguments_rec tyl iregl fregl ofs).
-Proof.
- induction tyl; simpl; intros.
- auto.
- destruct a.
- destruct iregl; simpl. auto.
- simpl in H. split. apply sym_not_equal. tauto.
- apply IHtyl. tauto. tauto.
- destruct fregl; simpl. auto.
- simpl in H0. split. apply sym_not_equal. tauto.
- apply IHtyl.
- red; intro. apply H. apply list_drop2_incl. auto.
- tauto.
-Qed.
-
-Remark loc_arguments_rec_notin_local:
- forall tyl iregl fregl ofs ofs0 ty0,
- Loc.notin (S (Local ofs0 ty0)) (loc_arguments_rec tyl iregl fregl ofs).
-Proof.
- induction tyl; simpl; intros.
- auto.
- destruct a.
- destruct iregl; simpl; auto.
- destruct fregl; simpl; auto.
-Qed.
-
-Remark loc_arguments_rec_notin_outgoing:
- forall tyl iregl fregl ofs ofs0 ty0,
- ofs0 + typesize ty0 <= ofs ->
- Loc.notin (S (Outgoing ofs0 ty0)) (loc_arguments_rec tyl iregl fregl ofs).
-Proof.
- induction tyl; simpl; intros.
- auto.
- destruct a.
- destruct iregl; simpl.
- split. omega. eapply IHtyl. omega.
- auto.
- destruct fregl; simpl.
- split. omega. eapply IHtyl. omega.
- auto.
-Qed.
-
-Lemma loc_arguments_norepet:
- forall (s: signature), Loc.norepet (loc_arguments s).
-Proof.
- assert (forall tyl iregl fregl ofs,
- list_norepet iregl ->
- list_norepet fregl ->
- list_disjoint iregl fregl ->
- Loc.norepet (loc_arguments_rec tyl iregl fregl ofs)).
- induction tyl; simpl; intros.
- constructor.
- destruct a.
- destruct iregl; constructor.
- apply loc_arguments_rec_notin_outgoing. simpl; omega. auto.
- apply loc_arguments_rec_notin_reg. inversion H. auto.
- apply list_disjoint_notin with (m :: iregl); auto with coqlib.
- apply IHtyl. inv H; auto. auto.
- eapply list_disjoint_cons_left; eauto.
- destruct fregl; constructor.
- apply loc_arguments_rec_notin_outgoing. simpl; omega. auto.
- apply loc_arguments_rec_notin_reg.
- red; intro. apply (H1 m m). apply list_drop2_incl; auto.
- auto with coqlib. auto. inv H0; auto.
- apply IHtyl. apply list_drop2_norepet; auto.
- inv H0; auto.
- red; intros. apply H1. apply list_drop2_incl; auto. auto with coqlib.
-
- intro. unfold loc_arguments. apply H.
- unfold int_param_regs. NoRepet.
- unfold float_param_regs. NoRepet.
- red; intros x y; simpl. ElimOrEq; ElimOrEq; discriminate.
-Qed.
-
-(** The offsets of [Outgoing] arguments are below [size_arguments s]. *)
-
-Remark size_arguments_rec_above:
- forall tyl iregl fregl ofs0,
- ofs0 <= size_arguments_rec tyl iregl fregl ofs0.
-Proof.
- induction tyl; simpl; intros.
- omega.
- destruct a.
- destruct iregl. apply Zle_trans with (ofs0 + 1); auto; omega. auto.
- destruct fregl. apply Zle_trans with (ofs0 + 2); auto; omega. auto.
-Qed.
-
-Lemma size_arguments_above:
- forall s, size_arguments s >= 0.
-Proof.
- intros; unfold size_arguments. apply Zle_ge. apply Zle_trans with 8. omega.
- apply size_arguments_rec_above.
-Qed.
-
-Lemma loc_arguments_bounded:
- forall (s: signature) (ofs: Z) (ty: typ),
- In (S (Outgoing ofs ty)) (loc_arguments s) ->
- ofs + typesize ty <= size_arguments s.
-Proof.
- intros.
- assert (forall tyl iregl fregl ofs0,
- In (S (Outgoing ofs ty)) (loc_arguments_rec tyl iregl fregl ofs0) ->
- ofs + typesize ty <= size_arguments_rec tyl iregl fregl ofs0).
- induction tyl; simpl; intros.
- elim H0.
- destruct a. destruct iregl; elim H0; intro.
- inv H1. simpl. apply size_arguments_rec_above. auto.
- discriminate. auto.
- destruct fregl; elim H0; intro.
- inv H1. simpl. apply size_arguments_rec_above. auto.
- discriminate. auto.
- unfold size_arguments. eapply H0. unfold loc_arguments in H. eauto.
-Qed.
-
-(** Temporary registers do not overlap with argument locations. *)
-
-Lemma loc_arguments_not_temporaries:
- forall sig, Loc.disjoint (loc_arguments sig) temporaries.
-Proof.
- intros; red; intros x1 x2 H.
- generalize (loc_arguments_rec_charact _ _ _ _ _ H).
- destruct x1.
- intro H0; elim H0; simpl; (ElimOrEq; ElimOrEq; congruence).
- destruct s; try contradiction. intro.
- simpl; ElimOrEq; auto.
-Qed.
-Hint Resolve loc_arguments_not_temporaries: locs.
-
-(** Argument registers are caller-save. *)
-
-Lemma arguments_caller_save:
- forall sig r,
- In (R r) (loc_arguments sig) -> In (R r) destroyed_at_call.
-Proof.
- unfold loc_arguments; intros.
- elim (loc_arguments_rec_charact _ _ _ _ _ H); simpl.
- ElimOrEq; intuition.
- ElimOrEq; intuition.
-Qed.
-
-(** Callee-save registers do not overlap with argument locations. *)
-
-Lemma arguments_not_preserved:
- forall sig l,
- Loc.notin l destroyed_at_call -> loc_acceptable l ->
- Loc.notin l (loc_arguments sig).
-Proof.
- intros. unfold loc_arguments. destruct l.
- apply loc_arguments_rec_notin_reg.
- generalize (Loc.notin_not_in _ _ H). intro; red; intro.
- apply H1. generalize H2. simpl. ElimOrEq; OrEq.
- generalize (Loc.notin_not_in _ _ H). intro; red; intro.
- apply H1. generalize H2. simpl. ElimOrEq; OrEq.
- destruct s; simpl in H0; try contradiction.
- apply loc_arguments_rec_notin_local.
-Qed.
-Hint Resolve arguments_not_preserved: locs.
-
-(** Argument locations agree in number with the function signature. *)
-
-Lemma loc_arguments_length:
- forall sig,
- List.length (loc_arguments sig) = List.length sig.(sig_args).
-Proof.
- assert (forall tyl iregl fregl ofs,
- List.length (loc_arguments_rec tyl iregl fregl ofs) = List.length tyl).
- induction tyl; simpl; intros.
- auto.
- destruct a.
- destruct iregl; simpl; decEq; auto.
- destruct fregl; simpl; decEq; auto.
- intros. unfold loc_arguments. auto.
-Qed.
-
-(** Argument locations agree in types with the function signature. *)
-
-Lemma loc_arguments_type:
- forall sig, List.map Loc.type (loc_arguments sig) = sig.(sig_args).
-Proof.
- assert (forall tyl iregl fregl ofs,
- (forall r, In r iregl -> mreg_type r = Tint) ->
- (forall r, In r fregl -> mreg_type r = Tfloat) ->
- List.map Loc.type (loc_arguments_rec tyl iregl fregl ofs) = tyl).
- induction tyl; simpl; intros.
- auto.
- destruct a; [destruct iregl|destruct fregl]; simpl;
- f_equal; eauto with coqlib.
- apply IHtyl. intros. apply H. apply list_drop2_incl; auto.
- eauto with coqlib.
-
- intros. unfold loc_arguments. apply H.
- intro; simpl. ElimOrEq; reflexivity.
- intro; simpl. ElimOrEq; reflexivity.
-Qed.
-
-(** There is no partial overlap between an argument location and an
- acceptable location: they are either identical or disjoint. *)
-
-Lemma no_overlap_arguments:
- forall args sg,
- locs_acceptable args ->
- Loc.no_overlap args (loc_arguments sg).
-Proof.
- unfold Loc.no_overlap; intros.
- generalize (H r H0).
- generalize (loc_arguments_acceptable _ _ H1).
- destruct s; destruct r; simpl.
- intros. case (mreg_eq m0 m); intro. left; congruence. tauto.
- intros. right; destruct s; auto.
- intros. right. auto.
- destruct s; try tauto. destruct s0; tauto.
-Qed.
-
-(** Decide whether a tailcall is possible. *)
-
-Definition tailcall_is_possible (sg: signature) : bool :=
- let fix tcisp (l: list loc) :=
- match l with
- | nil => true
- | R _ :: l' => tcisp l'
- | S _ :: l' => false
- end
- in tcisp (loc_arguments sg).
-
-Lemma tailcall_is_possible_correct:
- forall s, tailcall_is_possible s = true -> tailcall_possible s.
-Proof.
- intro s. unfold tailcall_is_possible, tailcall_possible.
- generalize (loc_arguments s). induction l; simpl; intros.
- elim H0.
- destruct a.
- destruct H0. subst l0. auto. apply IHl. auto. auto. discriminate.
-Qed.
-
-(** ** Location of function parameters *)
-
-(** A function finds the values of its parameter in the same locations
- where its caller stored them, except that the stack-allocated arguments,
- viewed as [Outgoing] slots by the caller, are accessed via [Incoming]
- slots (at the same offsets and types) in the callee. *)
-
-Definition parameter_of_argument (l: loc) : loc :=
- match l with
- | S (Outgoing n ty) => S (Incoming n ty)
- | _ => l
- end.
-
-Definition loc_parameters (s: signature) :=
- List.map parameter_of_argument (loc_arguments s).
-
-Lemma loc_parameters_type:
- forall sig, List.map Loc.type (loc_parameters sig) = sig.(sig_args).
-Proof.
- intros. unfold loc_parameters.
- rewrite list_map_compose.
- rewrite <- loc_arguments_type.
- apply list_map_exten.
- intros. destruct x; simpl. auto.
- destruct s; reflexivity.
-Qed.
-
-Lemma loc_parameters_length:
- forall sg, List.length (loc_parameters sg) = List.length sg.(sig_args).
-Proof.
- intros. unfold loc_parameters. rewrite list_length_map.
- apply loc_arguments_length.
-Qed.
-
-Lemma loc_parameters_not_temporaries:
- forall sig, Loc.disjoint (loc_parameters sig) temporaries.
-Proof.
- intro; red; intros.
- unfold loc_parameters in H.
- elim (list_in_map_inv _ _ _ H). intros y [EQ IN].
- generalize (loc_arguments_not_temporaries sig y x2 IN H0).
- subst x1. destruct x2.
- destruct y; simpl. auto. destruct s; auto.
- byContradiction. generalize H0. simpl. NotOrEq.
-Qed.
-
-Lemma no_overlap_parameters:
- forall params sg,
- locs_acceptable params ->
- Loc.no_overlap (loc_parameters sg) params.
-Proof.
- unfold Loc.no_overlap; intros.
- unfold loc_parameters in H0.
- elim (list_in_map_inv _ _ _ H0). intros t [EQ IN].
- rewrite EQ.
- generalize (loc_arguments_acceptable _ _ IN).
- generalize (H s H1).
- destruct s; destruct t; simpl.
- intros. case (mreg_eq m0 m); intro. left; congruence. tauto.
- intros. right; destruct s; simpl; auto.
- intros; right; auto.
- destruct s; try tauto. destruct s0; try tauto.
- intros; simpl. tauto.
-Qed.
-
-(** ** Location of argument and result for dynamic memory allocation *)
-
-Definition loc_alloc_argument := R3.
-Definition loc_alloc_result := R3.