From f37a87e35850e57febba0a39ce3cb526e7886c10 Mon Sep 17 00:00:00 2001 From: xleroy Date: Fri, 28 Mar 2014 08:08:46 +0000 Subject: Revert commits r2435 and r2436 (coarser RTLtyping / finer Lineartyping): the new Lineartyping can't keep track of single floats that were spilled. git-svn-id: https://yquem.inria.fr/compcert/svn/compcert/trunk@2438 fca1b0fc-160b-0410-b1d3-a4f43f01ea2e --- common/Unityping.v | 435 ----------------------------------------------------- 1 file changed, 435 deletions(-) delete mode 100644 common/Unityping.v (limited to 'common') diff --git a/common/Unityping.v b/common/Unityping.v deleted file mode 100644 index d108c87..0000000 --- a/common/Unityping.v +++ /dev/null @@ -1,435 +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 GNU General Public License as published by *) -(* the Free Software Foundation, either version 2 of the License, or *) -(* (at your option) any later version. This file is also distributed *) -(* under the terms of the INRIA Non-Commercial License Agreement. *) -(* *) -(* *********************************************************************) - -(* A solver for unification constraints. *) - -Require Import Recdef Coqlib Maps Errors. - -Local Open Scope nat_scope. -Local Open Scope error_monad_scope. - -(** This module provides a solver for sets of unification constraints of the - following kinds: [T(x) = base-type] or [T(x) = T(y)]. - The unknowns are the types [T(x)] of every identifier [x]. *) - -(** The interface for base types. *) - -Module Type TYPE_ALGEBRA. - -Variable t: Type. -Variable eq: forall (x y: t), {x=y} + {x<>y}. -Variable default: t. - -End TYPE_ALGEBRA. - -(** The constraint solver. *) - -Module UniSolver (T: TYPE_ALGEBRA). - -(* The current set of constraints is represented by a record with two components: -- [te_typ]: a partial map from variables to types -- [te_equ]: a list of pairs [(x,y)] of variables, indicating that - the type of [x] must be equal to the type of [y]. -*) - -Definition constraint : Type := (positive * positive)%type. - -Record typenv : Type := Typenv { - te_typ: PTree.t T.t; (**r mapping var -> typ *) - te_equ: list constraint (**r additional equality constraints *) -}. - -Definition initial : typenv := {| te_typ := PTree.empty _; te_equ := nil |}. - -(** Add the constraint [T(x) = ty]. *) - -Definition set (e: typenv) (x: positive) (ty: T.t) : res typenv := - match e.(te_typ)!x with - | None => - OK {| te_typ := PTree.set x ty e.(te_typ); - te_equ := e.(te_equ) |} - | Some ty' => - if T.eq ty ty' - then OK e - else Error (MSG "bad definition/use of variable " :: POS x :: nil) - end. - -Fixpoint set_list (e: typenv) (rl: list positive) (tyl: list T.t) {struct rl}: res typenv := - match rl, tyl with - | nil, nil => OK e - | r1::rs, ty1::tys => do e1 <- set e r1 ty1; set_list e1 rs tys - | _, _ => Error (msg "arity mismatch") - end. - -(** Add the constraint [T(x) = T(y)]. - The boolean result is [true] if the types of [x] or [y] could be - made more precise. Otherwise, [te_typ] does not change and - [false] is returned. *) - -Definition move (e: typenv) (r1 r2: positive) : res (bool * typenv) := - if peq r1 r2 then OK (false, e) else - match e.(te_typ)!r1, e.(te_typ)!r2 with - | None, None => - OK (false, {| te_typ := e.(te_typ); te_equ := (r1, r2) :: e.(te_equ) |}) - | Some ty1, None => - OK (true, {| te_typ := PTree.set r2 ty1 e.(te_typ); te_equ := e.(te_equ) |}) - | None, Some ty2 => - OK (true, {| te_typ := PTree.set r1 ty2 e.(te_typ); te_equ := e.(te_equ) |}) - | Some ty1, Some ty2 => - if T.eq ty1 ty2 - then OK (false, e) - else Error(MSG "ill-typed move from " :: POS r1 :: MSG " to " :: POS r2 :: nil) - end. - -(** Solve the remaining subtyping constraints by iteration. *) - -Fixpoint solve_rec (e: typenv) (changed: bool) (q: list constraint) : res (typenv * bool) := - match q with - | nil => - OK (e, changed) - | (r1, r2) :: q' => - do (changed1, e1) <- move e r1 r2; solve_rec e1 (changed || changed1) q' - end. - -(** Measuring the state *) - -Lemma move_shape: - forall e r1 r2 changed e', - move e r1 r2 = OK (changed, e') -> - (e'.(te_equ) = e.(te_equ) \/ e'.(te_equ) = (r1, r2) :: e.(te_equ)) - /\ (changed = true -> e'.(te_equ) = e.(te_equ)). -Proof. - unfold move; intros. - destruct (peq r1 r2). inv H. auto. - destruct e.(te_typ)!r1 as [ty1|]; destruct e.(te_typ)!r2 as [ty2|]; inv H; simpl. - destruct (T.eq ty1 ty2); inv H1. auto. - auto. - auto. - split. auto. intros. discriminate. -Qed. - -Lemma length_move: - forall e r1 r2 changed e', - move e r1 r2 = OK (changed, e') -> - length e'.(te_equ) + (if changed then 1 else 0) <= S(length e.(te_equ)). -Proof. - unfold move; intros. - destruct (peq r1 r2). inv H. omega. - destruct e.(te_typ)!r1 as [ty1|]; destruct e.(te_typ)!r2 as [ty2|]; inv H; simpl. - destruct (T.eq ty1 ty2); inv H1. omega. - omega. - omega. - omega. -Qed. - -Lemma length_solve_rec: - forall q e ch e' ch', - solve_rec e ch q = OK (e', ch') -> - length e'.(te_equ) + (if ch' && negb ch then 1 else 0) <= length e.(te_equ) + length q. -Proof. - induction q; simpl; intros. -- inv H. replace (ch' && negb ch') with false. omega. destruct ch'; auto. -- destruct a as [r1 r2]; monadInv H. rename x0 into e0. rename x into ch0. - exploit IHq; eauto. intros A. - exploit length_move; eauto. intros B. - set (X := (if ch' && negb (ch || ch0) then 1 else 0)) in *. - set (Y := (if ch0 then 1 else 0)) in *. - set (Z := (if ch' && negb ch then 1 else 0)) in *. - cut (Z <= X + Y). intros. omega. - unfold X, Y, Z. destruct ch'; destruct ch; destruct ch0; simpl; auto. -Qed. - -Definition weight_typenv (e: typenv) : nat := length e.(te_equ). - - -(** Iterative solving of the remaining constraints *) - -Function solve_constraints (e: typenv) {measure weight_typenv e}: res typenv := - match solve_rec {| te_typ := e.(te_typ); te_equ := nil |} false e.(te_equ) with - | OK(e', false) => OK e (**r no more changes, fixpoint reached *) - | OK(e', true) => solve_constraints e' (**r one more iteration *) - | Error msg => Error msg - end. -Proof. - intros. exploit length_solve_rec; eauto. simpl. intros. - unfold weight_typenv. omega. -Qed. - -Definition typassign := positive -> T.t. - -Definition makeassign (e: typenv) : typassign := - fun x => match e.(te_typ)!x with Some ty => ty | None => T.default end. - -Definition solve (e: typenv) : res typassign := - do e' <- solve_constraints e; OK(makeassign e'). - -(** What it means to be a solution *) - -Definition satisf (te: typassign) (e: typenv) : Prop := - (forall x ty, e.(te_typ)!x = Some ty -> te x = ty) -/\ (forall x y, In (x, y) e.(te_equ) -> te x = te y). - -Lemma satisf_initial: forall te, satisf te initial. -Proof. - unfold initial; intros; split; simpl; intros. - rewrite PTree.gempty in H; discriminate. - contradiction. -Qed. - -(** Soundness proof *) - -Lemma set_incr: - forall te x ty e e', set e x ty = OK e' -> satisf te e' -> satisf te e. -Proof. - unfold set; intros. destruct (te_typ e)!x as [ty'|] eqn:E. -- destruct (T.eq ty ty'); inv H. auto. -- inv H. destruct H0 as [A B]; simpl in *. red; split; intros; auto. - apply A. rewrite PTree.gso by congruence. auto. -Qed. - -Hint Resolve set_incr: ty. - -Lemma set_sound: - forall te x ty e e', set e x ty = OK e' -> satisf te e' -> te x = ty. -Proof. - unfold set; intros. destruct H0 as [P Q]. - destruct (te_typ e)!x as [ty'|] eqn:E. -- destruct (T.eq ty ty'); inv H. eauto. -- inv H. simpl in P. apply P. apply PTree.gss. -Qed. - -Lemma set_list_incr: - forall te xl tyl e e', set_list e xl tyl = OK e' -> satisf te e' -> satisf te e. -Proof. - induction xl; destruct tyl; simpl; intros; monadInv H; eauto with ty. -Qed. - -Hint Resolve set_list_incr: ty. - -Lemma set_list_sound: - forall te xl tyl e e', set_list e xl tyl = OK e' -> satisf te e' -> map te xl = tyl. -Proof. - induction xl; destruct tyl; simpl; intros; monadInv H. - auto. - f_equal. eapply set_sound; eauto with ty. eauto. -Qed. - -Lemma move_incr: - forall te e r1 r2 e' changed, - move e r1 r2 = OK(changed, e') -> satisf te e' -> satisf te e. -Proof. - unfold move; intros. destruct H0 as [P Q]. - destruct (peq r1 r2). inv H; split; auto. - destruct (te_typ e)!r1 as [ty1|] eqn:E1; - destruct (te_typ e)!r2 as [ty2|] eqn:E2. -- destruct (T.eq ty1 ty2); inv H. split; auto. -- inv H; simpl in *; split; auto. intros. apply P. - rewrite PTree.gso by congruence. auto. -- inv H; simpl in *; split; auto. intros. apply P. - rewrite PTree.gso by congruence. auto. -- inv H; simpl in *; split; auto. -Qed. - -Hint Resolve move_incr: ty. - -Lemma move_sound: - forall te e r1 r2 e' changed, - move e r1 r2 = OK(changed, e') -> satisf te e' -> te r1 = te r2. -Proof. - unfold move; intros. destruct H0 as [P Q]. - destruct (peq r1 r2). congruence. - destruct (te_typ e)!r1 as [ty1|] eqn:E1; - destruct (te_typ e)!r2 as [ty2|] eqn:E2. -- destruct (T.eq ty1 ty2); inv H. erewrite ! P by eauto. auto. -- inv H; simpl in *. rewrite (P r1 ty1). rewrite (P r2 ty1). auto. - apply PTree.gss. rewrite PTree.gso by congruence. auto. -- inv H; simpl in *. rewrite (P r1 ty2). rewrite (P r2 ty2). auto. - rewrite PTree.gso by congruence. auto. apply PTree.gss. -- inv H; simpl in *. apply Q; auto. -Qed. - -Lemma solve_rec_incr: - forall te q e changed e' changed', - solve_rec e changed q = OK(e', changed') -> satisf te e' -> satisf te e. -Proof. - induction q; simpl; intros. -- inv H. auto. -- destruct a as [r1 r2]; monadInv H. eauto with ty. -Qed. - -Lemma solve_rec_sound: - forall te r1 r2 q e changed e' changed', - solve_rec e changed q = OK(e', changed') -> In (r1, r2) q -> satisf te e' -> - te r1 = te r2. -Proof. - induction q; simpl; intros. -- contradiction. -- destruct a as [r3 r4]; monadInv H. destruct H0. - + inv H. eapply move_sound; eauto. eapply solve_rec_incr; eauto. - + eapply IHq; eauto with ty. -Qed. - -Lemma move_false: - forall e r1 r2 e', - move e r1 r2 = OK(false, e') -> - te_typ e' = te_typ e /\ makeassign e r1 = makeassign e r2. -Proof. - unfold move; intros. - destruct (peq r1 r2). inv H. split; auto. - unfold makeassign; - destruct (te_typ e)!r1 as [ty1|] eqn:E1; - destruct (te_typ e)!r2 as [ty2|] eqn:E2. -- destruct (T.eq ty1 ty2); inv H. auto. -- discriminate. -- discriminate. -- inv H. split; auto. -Qed. - -Lemma solve_rec_false: - forall r1 r2 q e changed e', - solve_rec e changed q = OK(e', false) -> - changed = false /\ - (In (r1, r2) q -> makeassign e r1 = makeassign e r2). -Proof. - induction q; simpl; intros. -- inv H. tauto. -- destruct a as [r3 r4]; monadInv H. - exploit IHq; eauto. intros [P Q]. - destruct changed; try discriminate. destruct x; try discriminate. - exploit move_false; eauto. intros [U V]. - split. auto. intros [A|A]. inv A. auto. exploit Q; auto. - unfold makeassign; rewrite U; auto. -Qed. - -Lemma solve_constraints_incr: - forall te e e', solve_constraints e = OK e' -> satisf te e' -> satisf te e. -Proof. - intros te e; functional induction (solve_constraints e); intros. -- inv H. auto. -- exploit solve_rec_incr; eauto. intros [A B]. - split; auto. intros; eapply solve_rec_sound; eauto. -- discriminate. -Qed. - -Lemma solve_constraints_sound: - forall e e', solve_constraints e = OK e' -> satisf (makeassign e') e'. -Proof. - intros e0; functional induction (solve_constraints e0); intros. -- inv H. split; intros. - unfold makeassign; rewrite H. split; auto with ty. - exploit solve_rec_false. eauto. intros [A B]. eapply B; eauto. -- eauto. -- discriminate. -Qed. - -Theorem solve_sound: - forall e te, solve e = OK te -> satisf te e. -Proof. - unfold solve; intros. monadInv H. - eapply solve_constraints_incr. eauto. eapply solve_constraints_sound; eauto. -Qed. - -(** Completeness proof *) - -Lemma set_complete: - forall te e x ty, - satisf te e -> te x = ty -> exists e', set e x ty = OK e' /\ satisf te e'. -Proof. - unfold set; intros. generalize H; intros [P Q]. - destruct (te_typ e)!x as [ty1|] eqn:E. -- replace ty1 with ty. rewrite dec_eq_true. exists e; auto. - exploit P; eauto. congruence. -- econstructor; split; eauto. split; simpl; intros; auto. - rewrite PTree.gsspec in H1. destruct (peq x0 x). congruence. eauto. -Qed. - -Lemma set_list_complete: - forall te xl tyl e, - satisf te e -> map te xl = tyl -> - exists e', set_list e xl tyl = OK e' /\ satisf te e'. -Proof. - induction xl; intros; inv H0; simpl. - econstructor; eauto. - exploit (set_complete te e a (te a)); auto. intros (e1 & P & Q). - exploit (IHxl (map te xl) e1); auto. intros (e2 & U & V). - exists e2; split; auto. rewrite P; auto. -Qed. - -Lemma move_complete: - forall te e r1 r2, - satisf te e -> te r1 = te r2 -> - exists changed e', move e r1 r2 = OK(changed, e') /\ satisf te e'. -Proof. - unfold move; intros. elim H; intros P Q. - assert (Q': forall x y, In (x, y) ((r1, r2) :: te_equ e) -> te x = te y). - { intros. destruct H1; auto. congruence. } - destruct (peq r1 r2). econstructor; econstructor; eauto. - destruct (te_typ e)!r1 as [ty1|] eqn:E1; - destruct (te_typ e)!r2 as [ty2|] eqn:E2. -- replace ty2 with ty1. rewrite dec_eq_true. econstructor; econstructor; eauto. - exploit (P r1); eauto. exploit (P r2); eauto. congruence. -- econstructor; econstructor; split; eauto. - split; simpl; intros; auto. rewrite PTree.gsspec in H1. destruct (peq x r2). - inv H1. rewrite <- H0. eauto. - eauto. -- econstructor; econstructor; split; eauto. - split; simpl; intros; auto. rewrite PTree.gsspec in H1. destruct (peq x r1). - inv H1. rewrite H0. eauto. - eauto. -- econstructor; econstructor; split; eauto. - split; eauto. -Qed. - -Lemma solve_rec_complete: - forall te q e changed, - satisf te e -> - (forall r1 r2, In (r1, r2) q -> te r1 = te r2) -> - exists e' changed', solve_rec e changed q = OK(e', changed') /\ satisf te e'. -Proof. - induction q; simpl; intros. -- econstructor; econstructor; eauto. -- destruct a as [r1 r2]. - exploit (move_complete te e r1 r2); auto. intros (changed1 & e1 & A & B). - exploit (IHq e1 (changed || changed1)); auto. intros (e' & changed' & C & D). - exists e'; exists changed'. rewrite A; simpl; rewrite C; auto. -Qed. - -Lemma solve_constraints_complete: - forall te e, satisf te e -> exists e', solve_constraints e = OK e' /\ satisf te e'. -Proof. - intros te e. functional induction (solve_constraints e); intros. -- exists e; auto. -- exploit (solve_rec_complete te (te_equ e) {| te_typ := te_typ e; te_equ := nil |} false). - destruct H; split; auto. simpl; tauto. - destruct H; auto. - intros (e1 & changed1 & P & Q). - apply IHr. congruence. -- exploit (solve_rec_complete te (te_equ e) {| te_typ := te_typ e; te_equ := nil |} false). - destruct H; split; auto. simpl; tauto. - destruct H; auto. - intros (e1 & changed1 & P & Q). - congruence. -Qed. - -Lemma solve_complete: - forall te e, satisf te e -> exists te', solve e = OK te'. -Proof. - intros. unfold solve. - destruct (solve_constraints_complete te e H) as (e' & P & Q). - econstructor. rewrite P. simpl. eauto. -Qed. - -End UniSolver. - -- cgit v1.2.3