diff options
Diffstat (limited to 'backend/CSE2.v')
-rw-r--r-- | backend/CSE2.v | 59 |
1 files changed, 33 insertions, 26 deletions
diff --git a/backend/CSE2.v b/backend/CSE2.v index b7665097..0479dad9 100644 --- a/backend/CSE2.v +++ b/backend/CSE2.v @@ -29,13 +29,18 @@ Proof. decide equality. Defined. +Record relmap := mkrel { + var_to_sym : (PTree.t sym_val) + }. + Module RELATION. - -Definition t := (PTree.t sym_val). + +Definition t := relmap. + Definition eq (r1 r2 : t) := - forall x, (PTree.get x r1) = (PTree.get x r2). + forall x, (PTree.get x (var_to_sym r1)) = (PTree.get x (var_to_sym r2)). -Definition top : t := PTree.empty sym_val. +Definition top : t := mkrel (PTree.empty sym_val). Lemma eq_refl: forall x, eq x x. Proof. @@ -58,27 +63,27 @@ Qed. Definition sym_val_beq (x y : sym_val) := if eq_sym_val x y then true else false. -Definition beq (r1 r2 : t) := PTree.beq sym_val_beq r1 r2. +Definition beq (r1 r2 : t) := PTree.beq sym_val_beq (var_to_sym r1) (var_to_sym r2). Lemma beq_correct: forall r1 r2, beq r1 r2 = true -> eq r1 r2. Proof. unfold beq, eq. intros r1 r2 EQ x. - pose proof (PTree.beq_correct sym_val_beq r1 r2) as CORRECT. + pose proof (PTree.beq_correct sym_val_beq (var_to_sym r1) (var_to_sym r2)) as CORRECT. destruct CORRECT as [CORRECTF CORRECTB]. pose proof (CORRECTF EQ x) as EQx. clear CORRECTF CORRECTB EQ. unfold sym_val_beq in *. - destruct (r1 ! x) as [R1x | ] in *; - destruct (r2 ! x) as [R2x | ] in *; + destruct ((var_to_sym r1) ! x) as [R1x | ] in *; + destruct ((var_to_sym r2) ! x) as [R2x | ] in *; trivial; try contradiction. destruct (eq_sym_val R1x R2x) in *; congruence. Qed. Definition ge (r1 r2 : t) := forall x, - match PTree.get x r1 with + match PTree.get x (var_to_sym r1) with | None => True - | Some v => (PTree.get x r2) = Some v + | Some v => (PTree.get x (var_to_sym r2)) = Some v end. Lemma ge_refl: forall r1 r2, eq r1 r2 -> ge r1 r2. @@ -87,7 +92,7 @@ Proof. intros r1 r2 EQ x. pose proof (EQ x) as EQx. clear EQ. - destruct (r1 ! x). + destruct ((var_to_sym r1) ! x). - congruence. - trivial. Qed. @@ -98,12 +103,13 @@ Proof. intros r1 r2 r3 GE12 GE23 x. pose proof (GE12 x) as GE12x; clear GE12. pose proof (GE23 x) as GE23x; clear GE23. - destruct (r1 ! x); trivial. - destruct (r2 ! x); congruence. + destruct ((var_to_sym r1) ! x); trivial. + destruct ((var_to_sym r2) ! x); congruence. Qed. Definition lub (r1 r2 : t) := - PTree.combine + mkrel + (PTree.combine (fun ov1 ov2 => match ov1, ov2 with | (Some v1), (Some v2) => @@ -113,12 +119,12 @@ Definition lub (r1 r2 : t) := | None, _ | _, None => None end) - r1 r2. + (var_to_sym r1) (var_to_sym r2)). Lemma ge_lub_left: forall x y, ge (lub x y) x. Proof. unfold ge, lub. - intros r1 r2 x. + intros r1 r2 x. simpl. rewrite PTree.gcombine by reflexivity. destruct (_ ! _); trivial. destruct (_ ! _); trivial. @@ -128,7 +134,7 @@ Qed. Lemma ge_lub_right: forall x y, ge (lub x y) y. Proof. unfold ge, lub. - intros r1 r2 x. + intros r1 r2 x. simpl. rewrite PTree.gcombine by reflexivity. destruct (_ ! _); trivial. destruct (_ ! _); trivial. @@ -263,8 +269,8 @@ Definition kill_sym_val (dst : reg) (sv : sym_val) := end. Definition kill_reg (dst : reg) (rel : RELATION.t) := - PTree.filter1 (fun x => negb (kill_sym_val dst x)) - (PTree.remove dst rel). + mkrel (PTree.filter1 (fun x => negb (kill_sym_val dst x)) + (PTree.remove dst (var_to_sym rel))). Definition kill_sym_val_mem (sv: sym_val) := match sv with @@ -274,17 +280,18 @@ Definition kill_sym_val_mem (sv: sym_val) := end. Definition kill_mem (rel : RELATION.t) := - PTree.filter1 (fun x => negb (kill_sym_val_mem x)) rel. + mkrel + (PTree.filter1 (fun x => negb (kill_sym_val_mem x)) (var_to_sym rel)). Definition forward_move (rel : RELATION.t) (x : reg) : reg := - match rel ! x with + match (var_to_sym rel) ! x with | Some (SMove org) => org | _ => x end. Definition move (src dst : reg) (rel : RELATION.t) := - PTree.set dst (SMove (forward_move rel src)) (kill_reg dst rel). + mkrel (PTree.set dst (SMove (forward_move rel src)) (var_to_sym (kill_reg dst rel))). Definition find_op_fold op args (already : option reg) x sv := match already with @@ -300,7 +307,7 @@ Definition find_op_fold op args (already : option reg) x sv := end. Definition find_op (rel : RELATION.t) (op : operation) (args : list reg) := - PTree.fold (find_op_fold op args) rel None. + PTree.fold (find_op_fold op args) (var_to_sym rel) None. Definition find_load_fold chunk addr args (already : option reg) x sv := match already with @@ -318,12 +325,12 @@ Definition find_load_fold chunk addr args (already : option reg) x sv := end. Definition find_load (rel : RELATION.t) (chunk : memory_chunk) (addr : addressing) (args : list reg) := - PTree.fold (find_load_fold chunk addr args) rel None. + PTree.fold (find_load_fold chunk addr args) (var_to_sym rel) None. Definition oper2 (op: operation) (dst : reg) (args : list reg) (rel : RELATION.t) := let rel' := kill_reg dst rel in - PTree.set dst (SOp op (List.map (forward_move rel') args)) rel'. + mkrel (PTree.set dst (SOp op (List.map (forward_move rel') args)) (var_to_sym rel')). Definition oper1 (op: operation) (dst : reg) (args : list reg) (rel : RELATION.t) := @@ -348,7 +355,7 @@ Definition gen_oper (op: operation) (dst : reg) (args : list reg) Definition load2 (chunk: memory_chunk) (addr : addressing) (dst : reg) (args : list reg) (rel : RELATION.t) := let rel' := kill_reg dst rel in - PTree.set dst (SLoad chunk addr (List.map (forward_move rel') args)) rel'. + mkrel (PTree.set dst (SLoad chunk addr (List.map (forward_move rel') args)) (var_to_sym rel')). Definition load1 (chunk: memory_chunk) (addr : addressing) (dst : reg) (args : list reg) (rel : RELATION.t) := |