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Diffstat (limited to 'src/Compilers/LinearizeWf.v')
| -rw-r--r-- | src/Compilers/LinearizeWf.v | 176 |
1 files changed, 176 insertions, 0 deletions
diff --git a/src/Compilers/LinearizeWf.v b/src/Compilers/LinearizeWf.v new file mode 100644 index 000000000..073137fd4 --- /dev/null +++ b/src/Compilers/LinearizeWf.v @@ -0,0 +1,176 @@ +(** * Linearize: Place all and only operations in let binders *) +Require Import Crypto.Compilers.Syntax. +Require Import Crypto.Compilers.Wf. +Require Import Crypto.Compilers.WfProofs. +Require Import Crypto.Compilers.Linearize. +Require Import (*Crypto.Util.Tactics*) Crypto.Util.Sigma. + +Local Open Scope ctype_scope. +Section language. + Context {base_type_code : Type} + {op : flat_type base_type_code -> flat_type base_type_code -> Type}. + + Local Notation flat_type := (flat_type base_type_code). + Local Notation type := (type base_type_code). + Local Notation Tbase := (@Tbase base_type_code). + Local Notation exprf := (@exprf base_type_code op). + Local Notation expr := (@expr base_type_code op). + Local Notation Expr := (@Expr base_type_code op). + Local Notation wff := (@wff base_type_code op). + Local Notation wf := (@wf base_type_code op). + + Section with_var. + Context {var1 var2 : base_type_code -> Type}. + + Local Ltac t_fin_step tac := + match goal with + | _ => assumption + | _ => progress simpl in * + | _ => progress subst + | _ => progress inversion_sigma + | _ => setoid_rewrite List.in_app_iff + | [ H : context[List.In _ (_ ++ _)] |- _ ] => setoid_rewrite List.in_app_iff in H + | _ => progress intros + | _ => solve [ eauto ] + | _ => solve [ intuition (subst; eauto) ] + | [ H : forall (x : prod _ _) (y : prod _ _), _ |- _ ] => specialize (fun x x' y y' => H (x, x') (y, y')) + | _ => rewrite !List.app_assoc + | [ H : _ \/ _ |- _ ] => destruct H + | [ H : _ |- _ ] => apply H + | _ => eapply wff_in_impl_Proper; [ solve [ eauto ] | ] + | _ => progress tac + | [ |- wff _ _ _ ] => constructor + | [ |- wf _ _ _ ] => constructor + end. + Local Ltac t_fin tac := repeat t_fin_step tac. + + Local Hint Constructors Wf.wff. + Local Hint Resolve List.in_app_or List.in_or_app. + + Local Ltac small_inversion_helper wf G0 e2 := + let t0 := match type of wf with wff (t:=?t0) _ _ _ => t0 end in + let e1 := match goal with + | |- context[wff G0 (under_letsf ?e1 _) (under_letsf e2 _)] => e1 + end in + pattern G0, t0, e1, e2; + lazymatch goal with + | [ |- ?retP _ _ _ _ ] + => first [ refine (match wf in @Wf.wff _ _ _ _ G t v1 v2 + return match v1 return Prop with + | TT => retP G t v1 v2 + | _ => forall P : Prop, P -> P + end with + | WfTT _ => _ + | _ => fun _ p => p + end) + | refine (match wf in @Wf.wff _ _ _ _ G t v1 v2 + return match v1 return Prop with + | Var _ _ => retP G t v1 v2 + | _ => forall P : Prop, P -> P + end with + | WfVar _ _ _ _ _ => _ + | _ => fun _ p => p + end) + | refine (match wf in @Wf.wff _ _ _ _ G t v1 v2 + return match v1 return Prop with + | Op _ _ _ _ => retP G t v1 v2 + | _ => forall P : Prop, P -> P + end with + | WfOp _ _ _ _ _ _ _ => _ + | _ => fun _ p => p + end) + | refine (match wf in @Wf.wff _ _ _ _ G t v1 v2 + return match v1 return Prop with + | LetIn _ _ _ _ => retP G t v1 v2 + | _ => forall P : Prop, P -> P + end with + | WfLetIn _ _ _ _ _ _ _ _ _ => _ + | _ => fun _ p => p + end) + | refine (match wf in @Wf.wff _ _ _ _ G t v1 v2 + return match v1 return Prop with + | Pair _ _ _ _ => retP G t v1 v2 + | _ => forall P : Prop, P -> P + end with + | WfPair _ _ _ _ _ _ _ _ _ => _ + | _ => fun _ p => p + end) ] + end. + Fixpoint wff_under_letsf G {t} e1 e2 {tC} eC1 eC2 + (wf : @wff var1 var2 G t e1 e2) + (H : forall (x1 : interp_flat_type var1 t) (x2 : interp_flat_type var2 t), + wff (flatten_binding_list x1 x2 ++ G) (eC1 x1) (eC2 x2)) + {struct e1} + : @wff var1 var2 G tC (under_letsf e1 eC1) (under_letsf e2 eC2). + Proof using Type. + revert H. + set (e1v := e1) in *. + destruct e1 as [ | | ? ? ? args | tx ex tC0 eC0 | ? ex ? ey ]; + [ clear wff_under_letsf + | clear wff_under_letsf + | clear wff_under_letsf + | generalize (fun G => match e1v return match e1v with LetIn _ _ _ _ => _ | _ => _ end with + | LetIn _ ex _ eC => wff_under_letsf G _ ex + | _ => I + end); + generalize (fun G => match e1v return match e1v with + | LetIn tx0 _ tC1 e0 => (* 8.4's type inferencer is broken, so we copy/paste the term from 8.5. This entire clause could just be [_], if Coq 8.4 worked *) + forall (x : @interp_flat_type base_type_code var1 tx0) (e3 : exprf tC1) + (tC2 : flat_type) (eC3 : @interp_flat_type base_type_code var1 tC1 -> exprf tC2) + (eC4 : @interp_flat_type base_type_code var2 tC1 -> exprf tC2), + wff G (e0 x) e3 -> + (forall (x1 : @interp_flat_type base_type_code var1 tC1) + (x2 : @interp_flat_type base_type_code var2 tC1), + wff (@flatten_binding_list base_type_code var1 var2 tC1 x1 x2 ++ G) (eC3 x1) (eC4 x2)) -> + wff G (@under_letsf base_type_code op var1 tC1 (e0 x) tC2 eC3) + (@under_letsf base_type_code op var2 tC1 e3 tC2 eC4) + | _ => _ end with + | LetIn _ ex tC' eC => fun x => wff_under_letsf G tC' (eC x) + | _ => I + end); + clear wff_under_letsf + | generalize (fun G => match e1v return match e1v with Pair _ _ _ _ => _ | _ => _ end with + | Pair _ ex _ ey => wff_under_letsf G _ ex + | _ => I + end); + generalize (fun G => match e1v return match e1v with Pair _ _ _ _ => _ | _ => _ end with + | Pair _ ex _ ey => wff_under_letsf G _ ey + | _ => I + end); + clear wff_under_letsf ]; + revert eC1 eC2; + (* alas, Coq's refiner isn't smart enough to figure out these small inversions for us *) + small_inversion_helper wf G e2; + t_fin idtac. + Qed. + + Local Hint Resolve wff_under_letsf. + Local Hint Constructors or. + Local Hint Extern 1 => progress unfold List.In in *. + Local Hint Resolve wff_in_impl_Proper. + Local Hint Resolve wff_SmartVarf. + + Lemma wff_linearizef G {t} e1 e2 + : @wff var1 var2 G t e1 e2 + -> @wff var1 var2 G t (linearizef e1) (linearizef e2). + Proof using Type. + induction 1; t_fin ltac:(apply wff_under_letsf). + Qed. + + Local Hint Resolve wff_linearizef. + + Lemma wf_linearize {t} e1 e2 + : @wf var1 var2 t e1 e2 + -> @wf var1 var2 t (linearize e1) (linearize e2). + Proof using Type. + destruct 1; constructor; auto. + Qed. + End with_var. + + Lemma Wf_Linearize {t} (e : Expr t) : Wf e -> Wf (Linearize e). + Proof using Type. + intros wf var1 var2; apply wf_linearize, wf. + Qed. +End language. + +Hint Resolve Wf_Linearize : wf. |