diff options
Diffstat (limited to 'src/GENERATEDIdentifiersWithoutTypesProofs.v')
| -rw-r--r-- | src/GENERATEDIdentifiersWithoutTypesProofs.v | 472 |
1 files changed, 419 insertions, 53 deletions
diff --git a/src/GENERATEDIdentifiersWithoutTypesProofs.v b/src/GENERATEDIdentifiersWithoutTypesProofs.v index 2bab688dc..7c3ec0e35 100644 --- a/src/GENERATEDIdentifiersWithoutTypesProofs.v +++ b/src/GENERATEDIdentifiersWithoutTypesProofs.v @@ -1,6 +1,7 @@ Require Import Coq.ZArith.ZArith. Require Import Coq.MSets.MSetPositive. Require Import Coq.FSets.FMapPositive. +Require Import Crypto.Util.PrimitiveSigma. Require Import Crypto.Util.MSetPositive.Facts. Require Import Crypto.Util.CPSNotations. Require Import Crypto.Util.ZRange. @@ -9,6 +10,8 @@ Require Import Crypto.Util.Tactics.DestructHead. Require Import Crypto.Util.Option. Require Import Crypto.Util.Decidable. Require Import Crypto.Util.HProp. +Require Import Crypto.Util.Equality. +Require Import Crypto.Util.Tactics.SpecializeBy. Require Import Crypto.Language. Require Import Crypto.LanguageInversion. Require Import Crypto.GENERATEDIdentifiersWithoutTypes. @@ -17,6 +20,7 @@ Require Import Crypto.Util.FixCoqMistakes. Import EqNotations. Module Compilers. Import Language.Compilers. + Import LanguageInversion.Compilers. Import GENERATEDIdentifiersWithoutTypes.Compilers. Module pattern. @@ -59,14 +63,24 @@ Module Compilers. -> P v. Proof. destruct v'; congruence. Qed. + Local Notation type_of_list := (List.fold_right (fun A B => prod A B) unit). + Fixpoint eta_type_of_list {ls} : type_of_list ls -> type_of_list ls + := match ls with + | nil => fun _ => tt + | cons x xs => fun v => (fst v, @eta_type_of_list xs (snd v)) + end. + Lemma eq_eta_type_of_list ls v + : @eta_type_of_list ls v = v. + Proof. induction ls; destruct v; cbn; reflexivity + apply f_equal; auto with nocore. Defined. + Module base. - Definition eq_subst_default_relax {t evm} : base.subst_default (base.relax t) evm = t. + Fixpoint eq_subst_default_relax {t evm} : base.subst_default (base.relax t) evm = t. Proof. - induction t; cbn; + destruct t; cbn; first [ reflexivity | apply f_equal | apply f_equal2 ]; - assumption. + auto with nocore. Defined. End base. @@ -79,6 +93,93 @@ Module Compilers. Defined. End type. + Local Lemma fast_sig_forall1_eq_ind {A T g} + (P : { f : forall a : A, T a | forall a, f a = g a } -> Type) + : (forall x : forall a, { f : T a | f = g a }, + P (exist (fun f => forall a, f a = g a) + (fun a => proj1_sig (x a)) + (fun a => proj2_sig (x a)))) + -> forall x, P x. + Proof. + intros H [x p]; refine (H (fun a => exist _ (x a) (p a))). + Defined. + + Local Lemma fast_sig_forall2_eq_ind {A B T g} + (P : { f : forall (a : A) (b : B a), T a b | forall a b, f a b = g a b } -> Type) + : (forall x : forall a b, { f : T a b | f = g a b }, + P (exist (fun f => forall a b, f a b = g a b) + (fun a b => proj1_sig (x a b)) + (fun a b => proj2_sig (x a b)))) + -> forall x, P x. + Proof. + intros H [x p]; refine (H (fun a b => exist _ (x a b) (p a b))). + Defined. + + Local Ltac my_generalize_dependent_intros v := + let k := fresh in + set (k := v) in *; clearbody k. + Ltac my_prerevert_dependent H := (* apparently this is faster *) + move H at bottom; + repeat lazymatch goal with H' : _ |- _ => tryif constr_eq H H' then fail else revert H' end. + Local Ltac generalize_proj1_sig_step := + match goal with + | [ |- context[@proj1_sig _ (fun x => forall y, _ = _) ?p] ] + => tryif is_var p then fail else my_generalize_dependent_intros p + | [ |- context[@proj1_sig _ (fun x => forall y z, _ = _) ?p] ] + => tryif is_var p then fail else my_generalize_dependent_intros p + | [ H : context[@proj1_sig _ (fun x => forall y, _ = _) ?p] |- _ ] + => tryif is_var p then fail else my_generalize_dependent_intros p + | [ H : context[@proj1_sig _ (fun x => forall y z, _ = _) ?p] |- _ ] + => tryif is_var p then fail else my_generalize_dependent_intros p + end. + Local Ltac specialize_sig_step := + match goal with + | [ H : { f : forall (a : ?A), @?T a | forall a', f a' = @?g a' } |- _ ] + => my_prerevert_dependent H; + revert H; + let P := lazymatch goal with |- forall x, @?P x => P end in + refine (@fast_sig_forall1_eq_ind A T g P _); + cbn [proj1_sig proj2_sig]; intros + | [ H : { f : forall (a : ?A) (b : @?B a), @?T a b | forall a' b', f a' b' = @?g a' b' } |- _ ] + => my_prerevert_dependent H; + revert H; + let P := lazymatch goal with |- forall x, @?P x => P end in + refine (@fast_sig_forall2_eq_ind A B T g P _); + cbn [proj1_sig proj2_sig]; intros + end. + Local Ltac rewrite_sig_step := + match goal with + | [ p : forall t idc, sig (fun y => y = _) |- _ ] + => lazymatch goal with + | [ H : context[proj1_sig (p ?t ?idc)] |- _ ] => destruct (p t idc) + | [ |- context[proj1_sig (p ?t ?idc)] ] => destruct (p t idc) + end; + subst; cbn [proj1_sig proj2_sig] in *; try clear p + | [ p : forall idc, sig (fun y => y = _) |- _ ] + => lazymatch goal with + | [ H : context[proj1_sig (p ?idc)] |- _ ] => destruct (p idc) + | [ |- context[proj1_sig (p ?idc)] ] => destruct (p idc) + end; + subst; cbn [proj1_sig proj2_sig] in *; try clear p + | [ p : sig (fun y => y = _) |- _ ] + => destruct p; subst; cbn [proj1_sig proj2_sig] in * + end. + Local Ltac clear_useless_step := + match goal with + | [ H : forall t, { f : _ | f = _ } |- _ ] => clear H + | [ H : forall t idc, { f : _ | f = _ } |- _ ] => clear H + end. + + Local Ltac do_rew_proj2_sig := + repeat first [ progress cbn [eq_rect eq_sym] in * + | progress intros + | clear_useless_step + | rewrite_sig_step + | specialize_sig_step + | generalize_proj1_sig_step ]. + + Local Notation iffT x y := ((x -> y) * (y -> x))%type. + Module Raw. Module ident. Import GENERATEDIdentifiersWithoutTypes.Compilers.pattern.Raw.ident. @@ -87,22 +188,106 @@ Module Compilers. Global Instance eq_ident_Decidable : DecidableRel (@eq ident) := dec_rel_of_bool_dec_rel ident_beq ident_bl ident_lb. + Lemma is_simple_correct0 p + : is_simple p = true + <-> (forall f1 f2, type_of p f1 = type_of p f2). + Proof. + destruct p; cbn; cbv -[Datatypes.fst Datatypes.snd projT1 projT2] in *; split; intro H; + try solve [ reflexivity | exfalso; discriminate ]. + all: repeat first [ match goal with + | [ H : nat -> ?A |- _ ] => specialize (H O) + | [ H : unit -> ?A |- _ ] => specialize (H tt) + | [ H : forall x y : PrimitiveProd.Primitive.prod _ _, _ |- _ ] => specialize (fun x1 y1 x2 y2 => H (PrimitiveProd.Primitive.pair x1 x2) (PrimitiveProd.Primitive.pair y1 y2)); cbn in H + | [ H : forall x y : Datatypes.prod _ _, _ |- _ ] => specialize (fun x1 y1 x2 y2 => H (Datatypes.pair x1 x2) (Datatypes.pair y1 y2)); cbn in H + | [ H : forall x y : PrimitiveSigma.Primitive.sigT ?P, _ |- _ ] => specialize (fun x1 y1 x2 y2 => H (PrimitiveSigma.Primitive.existT P x1 x2) (PrimitiveSigma.Primitive.existT P y1 y2)); cbn in H + | [ H : forall x y : Compilers.base.type, _ |- _ ] => specialize (fun x y => H (Compilers.base.type.type_base x) (Compilers.base.type.type_base y)) + | [ H : forall x y : Compilers.base.type.base, _ |- _ ] => specialize (H Compilers.base.type.unit Compilers.base.type.nat); try congruence; cbn in H + end + | congruence ]. + Qed. + + Lemma invert_bind_args_to_typed p f + : invert_bind_args (to_typed p f) p = Some f. + Proof. + destruct p; cbv in *; + destruct_head' (@Primitive.sigT); destruct_head'_prod; destruct_head'_unit; reflexivity. + Qed. + + Lemma fold_invert_bind_args : @invert_bind_args = @folded_invert_bind_args. + Proof. reflexivity. Qed. + + Lemma split_ident_to_ident ridc x y z + : PrimitiveSigma.Primitive.projT1 (split_ident_gen (to_ident (ident_infos_of ridc) x y z)) + = ridc. + Proof. destruct ridc; reflexivity. Defined. + + Lemma eq_indep_types_of_eq_types (ridc : ident) + (dt1 dt2 : type_of_list (dep_types (ident_infos_of ridc))) + (idt1 idt2 : type_of_list_of_kind (indep_types (ident_infos_of ridc))) + (Hty : to_type (ident_infos_of ridc) dt1 idt1 = to_type (ident_infos_of ridc) dt2 idt2) + : idt1 = idt2. + Proof. + destruct ridc; cbv in *; + destruct_head'_prod; destruct_head'_unit; try reflexivity; + type.inversion_type; reflexivity. + Qed. + + Lemma ident_transport_opt_correct P x y v + : (@ident_transport_opt P x y v <> None -> x = y) + * (forall pf : x = y, @ident_transport_opt P x y v = Some (rew pf in v)). + Proof. + cbv [ident_transport_opt]. + generalize (ident_beq_if x y), (ident_lb x y); destruct (ident_beq x y); + intros; subst; split; try congruence; intros; subst; + try intuition congruence. + eliminate_hprop_eq; reflexivity. + Qed. + + Lemma ident_transport_opt_correct' P x y v + : @ident_transport_opt P x y v <> None + -> { pf : x = y + | @ident_transport_opt P x y v = Some (rew pf in v) }. + Proof. + intro H; apply ident_transport_opt_correct in H; exists H; apply ident_transport_opt_correct. + Qed. + + Lemma ident_transport_opt_correct'' P x y v v' + : @ident_transport_opt P x y v = Some v' + -> { pf : x = y + | v' = rew pf in v }. + Proof. + intro H. + pose proof (@ident_transport_opt_correct' P x y v) as H'. + rewrite H in H'. + specialize (H' ltac:(congruence)). + destruct H'; inversion_option; subst; (exists eq_refl); reflexivity. + Qed. + Lemma to_typed_invert_bind_args_gen t idc p f : @invert_bind_args t idc p = Some f -> { pf : t = type_of p f | @to_typed p f = rew [Compilers.ident.ident] pf in idc }. Proof. - cbv [invert_bind_args type_of full_types]. - repeat first [ reflexivity - | (exists eq_refl) - | progress intros - | match goal with - | [ H : Some _ = None |- ?P ] => exact (@quick_invert_eq_option _ P _ _ H) - | [ H : None = Some _ |- ?P ] => exact (@quick_invert_eq_option _ P _ _ H) - end - | progress inversion_option - | progress subst - | break_innermost_match_step - | break_innermost_match_hyps_step ]. + rewrite fold_invert_bind_args. + cbv [folded_invert_bind_args type_of full_types to_typed] in *. + do_rew_proj2_sig. + all: repeat first [ match goal with + | [ |- context[@split_ident_gen ?t ?idc] ] + => destruct (@split_ident_gen t idc) + | [ H : context[@split_ident_gen ?t ?idc] |- _ ] + => destruct (@split_ident_gen t idc) + | [ H : Some _ = @ident_transport_opt _ _ _ _ |- _ ] => symmetry in H + | [ H : None = @ident_transport_opt _ _ _ _ |- _ ] => symmetry in H + | [ H : @ident_transport_opt ?P ?x ?y ?v = Some _ |- _ ] + => apply (@ident_transport_opt_correct'' P x y v) in H; destruct H + | [ H : @ident_transport_opt ?P ?x ?y ?v = None |- _ ] + => repeat intro; unshelve (erewrite (Datatypes.snd (ident_transport_opt_correct P x y v)) in H; inversion_option); [] + end + | progress destruct_head'_sig + | progress subst + | progress cbv [eq_rect assemble_ident] in * + | (exists eq_refl) + | reflexivity + | break_innermost_match_step ]. Qed. Lemma type_of_invert_bind_args t idc p f @@ -117,33 +302,6 @@ Module Compilers. exact (proj2_sig (@to_typed_invert_bind_args_gen t idc p f pf)). Defined. - Lemma invert_bind_args_to_typed p f - : invert_bind_args (to_typed p f) p = Some f. - Proof. - destruct p; cbn in *; - repeat first [ reflexivity - | progress destruct_head'_unit - | progress destruct_head'_prod - | progress destruct_head' (@PrimitiveSigma.Primitive.sigT) ]. - Qed. - - Lemma is_simple_correct0 p - : is_simple p = true - <-> (forall f1 f2, type_of p f1 = type_of p f2). - Proof. - destruct p; cbn; split; intro H; - try solve [ reflexivity | exfalso; discriminate ]. - all: repeat first [ match goal with - | [ H : nat -> ?A |- _ ] => specialize (H O) - | [ H : unit -> ?A |- _ ] => specialize (H tt) - | [ H : forall x y : Datatypes.prod _ _, _ |- _ ] => specialize (fun x1 y1 x2 y2 => H (Datatypes.pair x1 x2) (Datatypes.pair y1 y2)); cbn in H - | [ H : forall x y : PrimitiveSigma.Primitive.sigT ?P, _ |- _ ] => specialize (fun x1 y1 x2 y2 => H (PrimitiveSigma.Primitive.existT P x1 x2) (PrimitiveSigma.Primitive.existT P y1 y2)); cbn in H - | [ H : forall x y : Compilers.base.type, _ |- _ ] => specialize (fun x y => H (Compilers.base.type.type_base x) (Compilers.base.type.type_base y)) - | [ H : forall x y : Compilers.base.type.base, _ |- _ ] => specialize (H Compilers.base.type.unit Compilers.base.type.nat); try congruence; cbn in H - end - | congruence ]. - Qed. - Lemma is_simple_correct p : is_simple p = true <-> (forall t1 idc1 t2 idc2, @invert_bind_args t1 idc1 p <> None -> @invert_bind_args t2 idc2 p <> None -> t1 = t2). @@ -157,6 +315,64 @@ Module Compilers. apply (H _ (to_typed p f1) _ (to_typed p f2)); rewrite invert_bind_args_to_typed; congruence. } Qed. + + Lemma try_unify_split_args_Some_correct ridc1 ridc2 dt1 dt2 (*idt1 idt2*) args v + : iffT + (@try_unify_split_args ridc1 ridc2 dt1 dt2 (*idt1 idt2*) args = Some v) + { pf : existT _ ridc1 dt1 = existT _ ridc2 dt2 :> { ridc : _ & type_of_list (dep_types (preinfos (ident_infos_of ridc))) } + | (rew [fun rdt => type_of_list (indep_args _ (projT2 rdt))] pf in + (args : type_of_list (indep_args _ (projT2 (existT _ ridc1 dt1))))) + = v + (*/\ (rew [fun ridc => type_of_list_of_kind (indep_types (preinfos (ident_infos_of ridc)))] f_equal (@projT1 _ _) pf in + idt1) + = idt2*) }. + Proof. + pose proof (dep_types_dec_transparent (ident_infos_of ridc1) : DecidableRel eq). + cbv [try_unify_split_args]. + generalize (Raw.ident.ident_beq_if ridc1 ridc2). + generalize (Raw.ident.ident_lb ridc1 ridc2). + destruct (Raw.ident.ident_beq ridc1 ridc2); + [ + | split; + [ congruence + | intros; destruct_head'_sig; Sigma.inversion_sigma; subst; specialize_by reflexivity; congruence ] ]. + intros ? ?; subst. + (*pose proof (@Reflect.reflect_bool _ _ (indep_types_reflect _ idt1 idt2)) as H'. + pose proof (indep_types_reflect _ idt1 idt2) as H''.*) + repeat first [ break_innermost_match_step + | apply pair + | progress intros + | progress inversion_option + | progress subst + | progress specialize_by reflexivity + | apply conj + | progress destruct_head'_and + | progress destruct_head'_sig + | progress Sigma.inversion_sigma + | progress cbn [eq_rect eq_sym eq_rect_r Sigma.path_sigT Sigma.path_sigT_uncurried f_equal] in * + | (exists eq_refl) + | reflexivity + | progress eliminate_hprop_eq + | match goal with + | [ H : Bool.reflect _ false |- _ ] => inversion H; clear H + end + | congruence ]. + Qed. + + Lemma try_unify_split_args_None_correct ridc1 ridc2 dt1 dt2 (*idt1 idt2*) args + : @try_unify_split_args ridc1 ridc2 dt1 dt2 (*idt1 idt2*) args = None + -> forall pf : existT _ ridc1 dt1 = existT _ ridc2 dt2 :> { ridc : _ & type_of_list (dep_types (preinfos (ident_infos_of ridc))) }, + (*(rew [fun ridc => type_of_list_of_kind (indep_types (preinfos (ident_infos_of ridc)))] f_equal (@projT1 _ _) pf in + idt1) + = idt2 + ->*) False. + Proof. + intros H pf (*pf'*). + pose proof (fun v => snd (@try_unify_split_args_Some_correct ridc1 ridc2 dt1 dt2 (*idt1 idt2*) args v)) as H'. + rewrite H in H'. + specialize (H' _ (exist _ pf eq_refl(*(conj eq_refl pf')*))); cbv beta in *. + congruence. + Qed. End ident. End Raw. @@ -164,30 +380,180 @@ Module Compilers. Import GENERATEDIdentifiersWithoutTypes.Compilers.pattern.ident. Import Datatypes. (* for Some, None, option *) + Lemma fold_eta_ident_cps T t idc f : @eta_ident_cps T t idc f = proj1_sig (@pattern.eta_ident_cps_gen (fun t _ => T t) f) t idc. + Proof. reflexivity. Qed. + + Lemma fold_unify : @unify = @folded_unify. + Proof. vm_cast_no_check (eq_refl (@unify)). Qed. + + Lemma to_typed_of_typed_ident t idc evm + : (rew [Compilers.ident] type.eq_subst_default_relax in + @to_typed _ (@of_typed_ident t idc) evm (@arg_types_of_typed_ident t idc)) + = idc. + Proof. + destruct idc; + try (vm_compute; reflexivity); + cbv -[type.type_ind type.relax type.subst_default Compilers.base.type.type_ind f_equal f_equal2 base.relax base.subst_default base.eq_subst_default_relax]; + cbn [type.type_ind type.relax type.subst_default f_equal f_equal2 base.relax base.subst_default base.eq_subst_default_relax]; + repeat first [ progress subst + | progress intros + | progress cbn [f_equal f_equal2] + | reflexivity + | match goal with + | [ |- context[@base.eq_subst_default_relax ?t ?evm] ] + => generalize (base.subst_default (base.relax t) evm), (@base.eq_subst_default_relax t evm) + end ]. + Qed. + + Lemma eq_indep_types_of_eq_types {t1 t2} {idc1 : ident t1} {idc2 : ident t2} evm1 evm2 + (Hty : type.subst_default t1 evm1 = type.subst_default t2 evm2) + (pf : Primitive.projT1 (@split_types_subst_default _ idc1 evm1) + = Primitive.projT1 (@split_types_subst_default _ idc2 evm2)) + : Datatypes.snd (Primitive.projT2 (@split_types_subst_default _ idc1 evm1)) + = rew <- [fun r => full_type_of_list_of_kind (Raw.ident.indep_types (Raw.ident.preinfos (Raw.ident.ident_infos_of r)))] pf in + Datatypes.snd (Primitive.projT2 (@split_types_subst_default _ idc2 evm2)). + Proof. + pose proof (@to_type_split_types_subst_default_eq _ idc1 evm1). + pose proof (@to_type_split_types_subst_default_eq _ idc2 evm2). + generalize dependent (type.subst_default t1 evm1); + generalize dependent (type.subst_default t2 evm2); intros; subst. + cbv [split_types_subst_default] in *; cbn [Primitive.projT1 Primitive.projT2 fst snd] in *. + destruct (split_types idc1), (split_types idc2); + destruct_head'_prod; + cbn [Primitive.projT1 Primitive.projT2 fst snd] in *; + subst; cbn [eq_rect eq_rect_r eq_sym]. + eapply Raw.ident.eq_indep_types_of_eq_types; eassumption. + Qed. + Lemma eta_ident_cps_correct T t idc f : @eta_ident_cps T t idc f = f t idc. - Proof. cbv [eta_ident_cps]; break_innermost_match; reflexivity. Qed. + Proof. rewrite fold_eta_ident_cps; apply (proj2_sig (@pattern.eta_ident_cps_gen _ f)). Qed. Lemma unify_to_typed {t t' pidc idc} : forall v, @unify t t' pidc idc = Some v -> forall evm pf, - rew [Compilers.ident] pf in @to_typed t pidc evm v = idc. + rew [Compilers.ident] pf in @to_typed t pidc evm v = idc. Proof. - refine (@option_case_fast _ _ _ _). - Time destruct pidc, idc; cbv [unify to_typed]; try exact I. - Time all: break_innermost_match; try exact I. - Time all: repeat first [ reflexivity - | progress intros - | progress eliminate_hprop_eq - | progress cbn [type.subst_default base.subst_default] in * - | progress Compilers.type.inversion_type ]. + intros v H evm pf; subst t'; cbn [eq_rect]. + pose proof (@eq_indep_types_of_eq_types _ _ (@of_typed_ident _ idc) pidc evm evm type.eq_subst_default_relax) as H'. + revert v H. + set (idc' := idc) at 1; rewrite <- (@to_typed_of_typed_ident _ idc evm); subst idc'. + rewrite fold_unify. + cbv [folded_unify arg_types Raw.ident.assemble_ident]; + cbn [Primitive.projT1 Primitive.projT2]. + intros v. + Time do_rew_proj2_sig. + Time + repeat first [ progress cbn [eq_rect eq_sym] in * + | progress cbn [Primitive.projT1 Primitive.projT2 fst snd] in * + | clear_useless_step + | rewrite_sig_step + | specialize_sig_step + | generalize_proj1_sig_step + | progress cbv [to_typed Raw.ident.assemble_ident] in * + | match goal with + | [ |- context[@arg_types_of_typed_ident _ ?idc] ] + => is_var idc; + generalize dependent (@arg_types_of_typed_ident _ idc); + generalize dependent (@of_typed_ident _ idc); + clear idc; + intros + end + | progress cbv [arg_types prearg_types] in * ]. + repeat first [ progress cbn [Primitive.projT1 Primitive.projT2 fst snd] in * + | match goal with + | [ |- context[(rew [fun x : ?T => @?A x -> @?B x] ?pf in ?f) ?y] ] + => rewrite (@push_rew_fun_dep T A B _ _ pf f y) + | [ |- context[rew [fun _ : ?T => ?P] ?pf in ?f] ] + => rewrite (@Equality.transport_const T P _ _ pf f) + | [ |- context[(rew [?P] ?pf in ?x) = ?y] ] + => rewrite <- (@eq_rew_moveR _ P _ _ pf x y) + | [ |- context[rew [fun x : ?T => option (@?P x)] ?pf in Some ?v] ] + => rewrite <- (@commute_eq_rect _ P (fun x => option (P x)) (fun _ => Some) _ _ pf v) + | [ |- iffT (Raw.ident.try_unify_split_args _ (*_ _*) = Some _) _ ] + => eapply iffT_trans; [ apply Raw.ident.try_unify_split_args_Some_correct | ] + | [ H : Raw.ident.try_unify_split_args _ (*_ _*) = Some _ |- _ ] + => apply Raw.ident.try_unify_split_args_Some_correct in H + | [ |- context[to_type_split_types_subst_default_eq ?t ?i ?evm] ] + => generalize (to_type_split_types_subst_default_eq t i evm); intro + end + | progress cbv [eq_rect_r] in * + | progress cbv [split_types_subst_default] in * + | progress cbn [eq_rect] in * + | progress destruct_head'_prod + | progress subst + | match goal with + | [ |- context[existT _ (Primitive.projT1 (split_types ?x)) _ = _] ] + => destruct (split_types x); clear x + | [ H : context[existT _ (Primitive.projT1 (split_types ?x)) _ = _] |- _ ] + => destruct (split_types x); clear x + | [ |- context[@eq_trans (type.type ?base_type) ?x ?y ?z ?pf1 ?pf2] ] + => generalize (@eq_trans (type.type base_type) x y z pf1 pf2); intro + end + | rewrite <- !eq_trans_rew_distr ]. + Time + all: + repeat first [ apply pair + | progress cbn [eq_rect eq_rect_r eq_sym Sigma.path_sigT Sigma.path_sigT_uncurried f_equal] in * + | progress intros + | progress destruct_head'_sig + | progress destruct_head'_ex + | progress destruct_head'_and + | progress Sigma.inversion_sigma + | progress subst + | match goal with + | [ H : forall pf : ?x = ?x, _ |- _ ] => specialize (H eq_refl) + | [ H : lift_type_of_list_map _ ?f = _ |- _ ] + => is_var f; symmetry in H; destruct H; clear f + | [ H : context[@eq_trans (type.type ?base_type) ?x ?y ?z ?pf1 ?pf2] |- _ ] + => generalize dependent (@eq_trans (type.type base_type) x y z pf1 pf2); intros + | [ H : context[type.subst_default (type.relax _) _] |- _ ] + => rewrite type.eq_subst_default_relax in H + | [ H : ?x = ?x |- _ ] => clear H + | [ H : type.subst_default ?t ?evm = type.subst_default ?t ?evm' + |- context[lift_type_of_list_map (@subst_default_kind_of_type ?evm) (snd (Primitive.projT2 (split_types ?idc)))] ] + => let H' := fresh in + pose proof (@eq_indep_types_of_eq_types t idc idc evm evm' H eq_refl) as H'; + cbv [split_types_subst_default] in H'; + cbn [eq_rect_r eq_rect eq_sym Primitive.projT2 Primitive.projT1 fst snd] in H'; + rewrite H' in *; clear H'; + generalize dependent (type.subst_default t evm); intros; subst; clear evm + end + | rewrite <- !eq_trans_rew_distr in * + | eexists; rewrite <- !eq_trans_rew_distr, concat_pV + | match goal with + | [ H : _ = type.subst_default ?t ?evm |- _ ] + => is_var t; is_var evm; + generalize dependent (type.subst_default t evm); intros + end + | progress eliminate_hprop_eq ]. Qed. Lemma unify_of_typed_ident {t idc} : unify (@of_typed_ident t idc) idc <> None. Proof. - destruct idc; cbn; break_innermost_match; exact Some_neq_None. + rewrite fold_unify. + cbv [folded_unify]. + Time do_rew_proj2_sig. + generalize (of_typed_ident idc), (arg_types_of_typed_ident idc); intros. + repeat first [ progress rewrite ?push_rew_fun_dep, ?transport_const + | progress cbv [eq_rect_r] in * + | intro + | match goal with + | [ H : (rew [?P] ?pf in ?v) = ?v2 |- _ ] => apply (@rew_r_moveL _ P _ _ pf v v2) in H + | [ H : context[rew [fun x : ?T => option (@?P x)] ?pf in @None ?K] |- _ ] + => let H' := fresh in + pose proof (@commute_eq_rect _ (fun _ => True) (fun x => option (P x)) (fun _ _ => @None _) _ _ pf I) as H'; + setoid_rewrite <- H' in H; + clear H' + | [ H : @Raw.ident.try_unify_split_args ?a ?b ?c ?d ?e = None |- _ ] + => let H' := fresh in + pose proof (@Raw.ident.try_unify_split_args_None_correct a b c d e H) as H'; + clear H + | [ H : forall pf : _ = _, _ |- _ ] => specialize (H eq_refl) + end + | assumption ]. Qed. End ident. End pattern. |