diff options
Diffstat (limited to 'src/GENERATEDIdentifiersWithoutTypes.v')
| -rw-r--r-- | src/GENERATEDIdentifiersWithoutTypes.v | 677 |
1 files changed, 412 insertions, 265 deletions
diff --git a/src/GENERATEDIdentifiersWithoutTypes.v b/src/GENERATEDIdentifiersWithoutTypes.v index a7763c0c1..111b88bef 100644 --- a/src/GENERATEDIdentifiersWithoutTypes.v +++ b/src/GENERATEDIdentifiersWithoutTypes.v @@ -1,5 +1,4 @@ Require Import Coq.ZArith.ZArith. -Require Import Coq.Logic.JMeq. Require Import Coq.FSets.FMapPositive. Require Import Coq.MSets.MSetPositive. Require Import Coq.Lists.List. @@ -18,6 +17,7 @@ Require Crypto.Util.Tuple. Import ListNotations. Local Open Scope list_scope. Import PrimitiveSigma.Primitive. +Import EqNotations. Module Compilers. Set Boolean Equality Schemes. Set Decidable Equality Schemes. @@ -66,8 +66,8 @@ Module Compilers. | nil => fun x => x | T :: Ts => fun v_vs - => (F T (Datatypes.fst v_vs), - @lift_type_of_list_map A Ts P1 P2 F (Datatypes.snd v_vs)) + => (F T (fst v_vs), + @lift_type_of_list_map A Ts P1 P2 F (snd v_vs)) end. Module pattern. @@ -227,10 +227,28 @@ Module Compilers. | _ => constr_fail_with ltac:(fun _ => fail 1 "Could not find" ctor "from" from_all_idents "(index" n ") in" to_all_idents "(failed to eliminate dependency on dummy default argument in" v ")") end in v. + + Ltac make_ident_index ty all_idents := + let all_idents := (eval hnf in all_idents) in + let v := (eval cbv [id] in + (ltac:(intros; + let idc := lazymatch goal with idc : _ |- _ => idc end in + let idc' := fresh "idc'" in + pose idc as idc'; + destruct idc; + let idc := (eval cbv [idc'] in idc') in + let idc := head idc in + let n := get_ctor_number' idc all_idents in + exact n) + : ty)) in + refine v. End Tactics. Definition all_idents : list { T : Type & T } := ltac:(make_all_idents). + Definition ident_index : forall t, ident t -> nat + := ltac:(make_ident_index (forall t, ident t -> nat) all_idents). + Definition eta_ident_cps_gen {T : forall t, Compilers.ident.ident t -> Type} (f : forall t idc, T t idc) @@ -246,24 +264,33 @@ Module Compilers. Definition eta_ident_cps_gen2 {T0 : forall t, Compilers.ident.ident t -> Type} (f0 : forall t idc, T0 t idc) - {T1 : forall t (idc : Compilers.ident.ident t), T0 t idc -> Type} + {T1 : forall t idc, T0 t idc -> Type} (f1 : forall t idc, T1 t idc (f0 t idc)) - : forall t idc, T1 t idc (proj1_sig (@eta_ident_cps_gen T0 f0) t idc). - Proof. intros t idc; cbv [proj1_sig eta_ident_cps_gen]; destruct idc; exact (f1 _ _). Defined. + : { f' : forall t idc, T1 t idc (proj1_sig (@eta_ident_cps_gen T0 f0) t idc) + | forall t idc, + f' t idc = rew [T1 t idc] (eq_sym (proj2_sig (@eta_ident_cps_gen T0 f0) t idc)) in f1 t idc }. + Proof. apply eta_ident_cps_gen. Defined. Definition eta_ident_cps_gen3 {T0 : forall t, Compilers.ident.ident t -> Type} (f0 : forall t idc, T0 t idc) - {T1 : forall t (idc : Compilers.ident.ident t), T0 t idc -> Type} + {T1 : forall t idc, T0 t idc -> Type} (f1 : forall t idc, T1 t idc (f0 t idc)) {T2 : forall t idc x, T1 t idc x -> Type} (f2 : forall t idc, T2 t idc (f0 t idc) (f1 t idc)) - : forall t idc, T2 t idc (proj1_sig (@eta_ident_cps_gen T0 f0) t idc) (@eta_ident_cps_gen2 T0 f0 T1 f1 t idc). - Proof. intros t idc; cbv [proj1_sig eta_ident_cps_gen eta_ident_cps_gen2]; destruct idc; exact (f2 _ _). Defined. + : { f' : forall t idc, T2 t idc (proj1_sig (@eta_ident_cps_gen T0 f0) t idc) (proj1_sig (@eta_ident_cps_gen2 T0 f0 T1 f1) t idc) + | forall t idc, + f' t idc + = rew [T2 t idc _] (eq_sym (proj2_sig (@eta_ident_cps_gen2 T0 f0 T1 f1) t idc)) in + match eq_sym (proj2_sig (@eta_ident_cps_gen _ f0) t idc) as p return T2 t idc _ (rew [T1 t idc] p in f1 t idc) with + | eq_refl => f2 t idc + end }. + Proof. apply eta_ident_cps_gen. Defined. Module Raw. Module ident. Local Unset Decidable Equality Schemes. + Local Unset Boolean Equality Schemes. Module MakeIdent. Import Compilers.ident. Ltac map_projT2 tac ls := @@ -401,6 +428,23 @@ Module Compilers. Definition all_idents : list ident := ltac:(make_all_idents). + Definition ident_index : ident -> nat + := ltac:(let idc := fresh "idc" in + let idc' := fresh "idc'" in + let v := (eval cbv [id] in + (ltac:(intro idc; + pose idc as idc'; + destruct idc; + let idc := (eval cbv [idc'] in idc') in + let all_idents := (eval cbv [all_idents] in all_idents) in + let n := get_ctor_number' idc all_idents in + exact n) + : ident -> nat)) in + refine v). + + Lemma ident_index_idempotent idc : List.nth_error all_idents (ident_index idc) = Some idc. + Proof. destruct idc; vm_compute; reflexivity. Defined. + Definition eta_ident_cps_gen {T : ident -> Type} (f : forall idc, T idc) @@ -412,8 +456,10 @@ Module Compilers. (f0 : forall idc, T0 idc) {T1 : forall idc, T0 idc -> Type} (f1 : forall idc, T1 idc (f0 idc)) - : forall idc, T1 idc (proj1_sig (@eta_ident_cps_gen T0 f0) idc). - Proof. intros idc; cbv [proj1_sig eta_ident_cps_gen]; destruct idc; exact (f1 _). Defined. + : { f' : forall idc, T1 idc (proj1_sig (@eta_ident_cps_gen T0 f0) idc) + | forall idc, + f' idc = rew [T1 idc] (eq_sym (proj2_sig (@eta_ident_cps_gen T0 f0) idc)) in f1 idc }. + Proof. apply eta_ident_cps_gen. Defined. Definition eta_ident_cps_gen3 {T0 : ident -> Type} @@ -422,29 +468,85 @@ Module Compilers. (f1 : forall idc, T1 idc (f0 idc)) {T2 : forall idc x, T1 idc x -> Type} (f2 : forall idc, T2 idc (f0 idc) (f1 idc)) - : forall idc, T2 idc (proj1_sig (@eta_ident_cps_gen T0 f0) idc) (@eta_ident_cps_gen2 T0 f0 T1 f1 idc). - Proof. intros idc; cbv [proj1_sig eta_ident_cps_gen eta_ident_cps_gen2]; destruct idc; exact (f2 _). Defined. + : { f' : forall idc, T2 idc (proj1_sig (@eta_ident_cps_gen T0 f0) idc) (proj1_sig (@eta_ident_cps_gen2 T0 f0 T1 f1) idc) + | forall idc, + f' idc + = rew [T2 idc _] (eq_sym (proj2_sig (@eta_ident_cps_gen2 T0 f0 T1 f1) idc)) in + match eq_sym (proj2_sig (@eta_ident_cps_gen _ f0) idc) as p return T2 idc _ (rew [T1 idc] p in f1 idc) with + | eq_refl => f2 idc + end }. + Proof. apply eta_ident_cps_gen. Defined. + + Definition ident_beq : ident -> ident -> bool + := fun idc1 idc2 + => proj1_sig + (eta_ident_cps_gen + (fun idc1 + => proj1_sig + (eta_ident_cps_gen + (fun idc2 + => Nat.eqb (ident_index idc1) (ident_index idc2))) + idc2)) + idc1. + + Ltac rew_proj2_sig := + repeat match goal with + | [ |- context[@proj1_sig _ (fun _ => forall x, _ = _) ?p] ] + => rewrite !(proj2_sig p) + | [ |- context[@proj1_sig _ (fun _ => forall x y, _ = _) ?p] ] + => rewrite !(proj2_sig p) + end. + + Definition nat_eqb_refl_transparent (x : nat) : Nat.eqb x x = true. + Proof. induction x; cbn; constructor + assumption. Defined. Definition ident_lb (x y : ident) : x = y -> ident_beq x y = true. - Proof. intro H; subst y; destruct x; reflexivity. Defined. - Definition ident_beq_if (x y : ident) : if ident_beq x y then x = y else True. - Proof. destruct x, y; cbv; constructor. Defined. + Proof. + intro H; subst y; cbv [ident_beq]; + rew_proj2_sig; apply nat_eqb_refl_transparent. + Defined. + + Lemma ident_index_inj idc1 idc2 : ident_index idc1 = ident_index idc2 -> idc1 = idc2. + Proof. + intro H. + pose proof (ident_index_idempotent idc1) as H1. + pose proof (ident_index_idempotent idc2) as H2. + rewrite H in H1; rewrite H1 in H2. + set (sidc1 := Some idc1) in *. + set (sidc2 := Some idc2) in *. + change (match sidc1, sidc2 with Some idc1, Some idc2 => idc1 = idc2 | _, _ => True end). + clearbody sidc2; subst sidc2 sidc1; reflexivity. + Defined. + + Definition nat_eqb_bl_transparent (x y : nat) : Nat.eqb x y = true -> x = y. + Proof. + revert y; induction x, y; cbn; intro; try apply f_equal; auto using eq_refl with nocore; + exfalso; apply Bool.diff_false_true; assumption. + Defined. + Definition ident_bl (x y : ident) : ident_beq x y = true -> x = y. Proof. - generalize (ident_beq_if x y); destruct (ident_beq x y); intros; - first [ assumption | exfalso; apply Bool.diff_false_true; assumption ]. + cbv [ident_beq]; rew_proj2_sig; intro H. + apply nat_eqb_bl_transparent in H. + apply ident_index_inj in H. + exact H. + Defined. + + Definition ident_beq_if (x y : ident) : if ident_beq x y then x = y else True. + Proof. + generalize (ident_beq x y), (ident_bl x y). + intros b H; destruct b; exact I + auto using eq_refl with nocore. Defined. Definition ident_transport_opt (P : ident -> Type) {x y : ident} : P x -> Datatypes.option (P y) - := Eval cbv [ident_beq ident_beq_if] in - fun v - => (if ident_beq x y as b return (if b then x = y else True) -> _ - then fun pf => Datatypes.Some - match pf in (_ = y) return P y with - | eq_refl => v - end - else fun _ => Datatypes.None) - (@ident_beq_if x y). + := fun v + => (if ident_beq x y as b return (if b then x = y else True) -> _ + then fun pf => Datatypes.Some + match pf in (_ = y) return P y with + | eq_refl => v + end + else fun _ => Datatypes.None) + (@ident_beq_if x y). Inductive kind_of_type := GallinaType (_ : Type) | BaseBaseType | BaseType. Definition Type_of_kind_of_type (T : kind_of_type) @@ -472,7 +574,10 @@ Module Compilers. dep_types_dec_transparent : forall x y : type_of_list (dep_types preinfos), {x = y} + {x <> y}; indep_args_beq : _; indep_args_reflect - : forall x, reflect_rel (@eq (type_of_list (indep_args preinfos x))) (indep_args_beq x) + : forall x, reflect_rel (@eq (type_of_list (indep_args preinfos x))) (indep_args_beq x); + indep_types_beq : _; + indep_types_reflect + : reflect_rel (@eq (type_of_list_of_kind (indep_types preinfos))) indep_types_beq; }. Definition ident_args (pi : preident_infos) @@ -481,25 +586,10 @@ Module Compilers. Definition assemble_ident {pi} (args : ident_args pi) := to_ident pi (projT1 args) (Datatypes.fst (projT2 args)) (Datatypes.snd (projT2 args)). - Ltac build_ident_to_cident := - let v - := (eval cbv [proj1_sig eta_ident_cps_gen List.find List.combine all_idents pattern.all_idents ident_beq] in - (fun default - => proj1_sig - (@eta_ident_cps_gen - (fun _ => { T : Type & T }) - (fun idc - => match List.find - (fun '(idc', v) => ident_beq idc idc') - (List.combine all_idents pattern.all_idents) with - | Datatypes.Some (_, v) => v - | Datatypes.None => default - end)))) in - let v := strip_default v in - v. - Ltac make_ident_to_cident := let v := build_ident_to_cident in refine v. - - Definition ident_to_cident : ident -> { T : Type & T } := ltac:(make_ident_to_cident). + Definition ident_to_cident : ident -> { T : Type & T } + := proj1_sig + (eta_ident_cps_gen + (fun idc => List.nth_default (@existT Type _ True I) pattern.all_idents (ident_index idc))). Ltac fun_to_curried_ident_infos f := let type_to_kind T @@ -555,12 +645,13 @@ Module Compilers. | T => ltac:(destruct idc; let T := (eval cbv [T ident_to_cident projT2] in (projT2 T)) in + let T := (eval cbv in T) in let v := fun_to_curried_ident_infos T in let v := (eval cbv [type_of_list List.map Type_of_kind_of_type] in v) in let c := constr:(@Build_ident_infos v) in let T := type of c in let T := (eval cbv [dep_types indep_types indep_args type_of_list List.map Type_of_kind_of_type] in T) in - refine ((c : T) _ _ _); + refine ((c : T) _ _ _ _ _); repeat decide equality) end) in let v := (eval cbv [dep_types indep_types indep_args type_of_list preinfos List.map Type_of_kind_of_type Datatypes.prod_rect base.type.base_rect unit_rect sumbool_rect prod_rec unit_rec sumbool_rec base.type.base_rec eq_ind_r eq_ind eq_sym eq_rec eq_rect] in v) in @@ -608,76 +699,99 @@ Module Compilers. (exists ridc); cbv [ident_infos_of ident_args type_of_list indep_args dep_types indep_types preinfos assemble_ident to_ident List.map Type_of_kind_of_type]; unshelve (eexists; refine_sigT_and_pair; try constructor); - repeat esplit) + cbv [to_type Datatypes.fst]; + try solve [ repeat unshelve esplit ]) : { ridc : ident & { args : ident_args (ident_infos_of ridc) - | JMeq idc (assemble_ident args) } })) in + | { pf : _ = _ + | idc = rew [Compilers.ident.ident] pf in assemble_ident args } } })) in v. Ltac make_split_ident_gen := let v := build_split_ident_gen in refine v. Definition split_ident_gen : forall {t} (idc : Compilers.ident.ident t), { ridc : ident & { args : ident_args (ident_infos_of ridc) - | JMeq idc (assemble_ident args) } } + | { pf : _ = _ + | idc = rew [Compilers.ident.ident] pf in assemble_ident args } } } := ltac:(make_split_ident_gen). - Ltac do_reduce v := - let v := (eval cbv [proj1_sig eta_ident_cps_gen eta_ident_cps_gen2 eta_ident_cps_gen3 ident_args ident_infos_of type_of_list dep_types indep_types indep_args preinfos to_type ident_transport_opt split_ident_gen pattern.eta_ident_cps_gen to_ident to_type List.map Type_of_kind_of_type] in v) in - v. - + Definition prefull_types : ident -> Type + := fun idc => ident_args (ident_infos_of idc). Definition full_types : ident -> Type - := ltac:(let v := do_reduce - (proj1_sig - (eta_ident_cps_gen - (fun idc - => ident_args (ident_infos_of idc)))) in - refine v). + := proj1_sig (eta_ident_cps_gen prefull_types). Definition is_simple : ident -> bool - := ltac:(let v := do_reduce - (proj1_sig - (eta_ident_cps_gen - (fun idc - => let ii := ident_infos_of idc in - match dep_types ii, indep_types ii return _ with (* COQBUG(https://github.com/coq/coq/issues/9955) *) - | [], [] => true - | _, _ => false - end))) in - refine v). + := fun idc + => let ii := ident_infos_of idc in + match dep_types ii, indep_types ii return _ with (* COQBUG(https://github.com/coq/coq/issues/9955) *) + | [], [] => true + | _, _ => false + end. Definition type_of : forall (pidc : ident), full_types pidc -> Compilers.type Compilers.base.type - := ltac:(let v := do_reduce - (@eta_ident_cps_gen2 - _ (fun idc => ident_args (ident_infos_of idc)) - (fun pidc full_types_pidc - => full_types_pidc -> Compilers.type Compilers.base.type) - (fun pidc args - => to_type (ident_infos_of pidc) (projT1 args) (Datatypes.fst (projT2 args)))) in - refine v). + := proj1_sig + (@eta_ident_cps_gen2 + _ prefull_types + (fun pidc full_types_pidc => full_types_pidc -> Compilers.type Compilers.base.type) + (fun pidc args + => to_type (ident_infos_of pidc) (projT1 args) (Datatypes.fst (projT2 args)))). + + Definition folded_invert_bind_args : forall {t} (idc : Compilers.ident.ident t) (pidc : ident), Datatypes.option (full_types pidc) + := fun t idc pidc + => proj1_sig + (pattern.eta_ident_cps_gen + (fun t idc + => proj1_sig + (@eta_ident_cps_gen2 + _ prefull_types + (fun pidc full_types_pidc => Datatypes.option full_types_pidc) + (fun pidc + => let '(existT ridc (exist args _)) := split_ident_gen idc in + ident_transport_opt + (fun idc => ident_args (ident_infos_of idc)) + args)) + pidc)) + t idc. Definition invert_bind_args : forall {t} (idc : Compilers.ident.ident t) (pidc : ident), Datatypes.option (full_types pidc) - := ltac:(let v := do_reduce - (fun t idc pidc - => proj1_sig - (pattern.eta_ident_cps_gen - (fun t idc - => @eta_ident_cps_gen2 - _ (fun idc => ident_args (ident_infos_of idc)) - (fun pidc full_types_pidc => Datatypes.option full_types_pidc) - (fun pidc - => let '(existT ridc (exist args _)) := split_ident_gen idc in - ident_transport_opt - (fun idc => ident_args (ident_infos_of idc)) - args) - pidc)) - t idc) in + := ltac:(let v := (eval cbv [folded_invert_bind_args] in (@folded_invert_bind_args)) in + let v := (eval cbv [pattern.eta_ident_cps_gen proj1_sig eta_ident_cps_gen2 eta_ident_cps_gen proj1_sig proj2_sig eq_rect eq_sym split_ident_gen projT2 ident_transport_opt ident_beq ident_index Nat.eqb ident_beq_if ident_bl eq_ind_r eq_ind nat_eqb_bl_transparent nat_ind ident_index_inj ident_index_idempotent f_equal] in v) in refine v). + Definition to_typed : forall (pidc : ident) (args : full_types pidc), Compilers.ident.ident (type_of pidc args) - := ltac:(let v := do_reduce - (@eta_ident_cps_gen3 - _ (fun idc => ident_args (ident_infos_of idc)) - (fun pidc full_types_pidc => full_types_pidc -> Compilers.type Compilers.base.type) - (fun pidc args => to_type (ident_infos_of pidc) (projT1 args) (Datatypes.fst (projT2 args))) - (fun pidc full_types_pidc type_of_pidc => forall args : full_types_pidc, Compilers.ident.ident (type_of_pidc args)) - (fun pidc args - => to_ident _ _ _ (Datatypes.snd (projT2 args)))) in - refine v). + := proj1_sig + (@eta_ident_cps_gen3 + _ prefull_types + (fun pidc full_types_pidc => full_types_pidc -> Compilers.type Compilers.base.type) + (fun pidc args => to_type (ident_infos_of pidc) (projT1 args) (Datatypes.fst (projT2 args))) + (fun pidc full_types_pidc type_of_pidc => forall args : full_types_pidc, Compilers.ident.ident (type_of_pidc args)) + (fun pidc args + => to_ident _ _ _ (Datatypes.snd (projT2 args)))). + + Definition try_unify_split_args {ridc1 ridc2 : ident} + : forall {dt1 : type_of_list (dep_types (preinfos (ident_infos_of ridc1)))} + {dt2 : type_of_list (dep_types (preinfos (ident_infos_of ridc2)))} + (*(idt1 : type_of_list_of_kind (indep_types (preinfos (ident_infos_of ridc1)))) + (idt2 : type_of_list_of_kind (indep_types (preinfos (ident_infos_of ridc2))))*), + type_of_list (indep_args _ dt1) -> Datatypes.option (type_of_list (indep_args _ dt2)) + := (if ident_beq ridc1 ridc2 as b return (if b then ridc1 = ridc2 else True) -> _ + then fun pf + => match pf in (_ = ridc2) return forall (dt1 : type_of_list (dep_types (preinfos (ident_infos_of ridc1)))) + (dt2 : type_of_list (dep_types (preinfos (ident_infos_of ridc2)))) + (*(idt1 : type_of_list_of_kind (indep_types (preinfos (ident_infos_of ridc1)))) + (idt2 : type_of_list_of_kind (indep_types (preinfos (ident_infos_of ridc2))))*), + type_of_list (indep_args _ dt1) -> Datatypes.option (type_of_list (indep_args _ dt2)) with + | eq_refl + => fun dt1 dt2 (*idt1 idt2*) + => match dep_types_dec_transparent _ dt1 dt2 with + | left pf + => match pf in (_ = dt2) return type_of_list (indep_args _ dt1) -> Datatypes.option (type_of_list (indep_args _ dt2)) with + | eq_refl + => (*if indep_types_beq _ idt1 idt2 + then*) Datatypes.Some + (*else fun _ => Datatypes.None*) + end + | right _ => fun _ => Datatypes.None + end + end + else fun _ _ _ _ (*_ _*) => Datatypes.None) + (ident_beq_if ridc1 ridc2). End ident. Notation ident := ident.ident. End Raw. @@ -861,18 +975,26 @@ Module Compilers. (f0 : forall t idc, T0 t idc) {T1 : forall t (idc : ident t), T0 t idc -> Type} (f1 : forall t idc, T1 t idc (f0 t idc)) - : forall t idc, T1 t idc (proj1_sig (@eta_ident_cps_gen T0 f0) t idc). - Proof. intros t idc; cbv [proj1_sig eta_ident_cps_gen]; destruct idc; exact (f1 _ _). Defined. + : { f' : forall t idc, T1 t idc (proj1_sig (@eta_ident_cps_gen T0 f0) t idc) + | forall t idc, + f' t idc = rew [T1 t idc] (eq_sym (proj2_sig (@eta_ident_cps_gen T0 f0) t idc)) in f1 t idc }. + Proof. apply eta_ident_cps_gen. Defined. Definition eta_ident_cps_gen3 {T0 : forall t, ident t -> Type} (f0 : forall t idc, T0 t idc) - {T1 : forall t (idc : ident t), T0 t idc -> Type} + {T1 : forall t idc, T0 t idc -> Type} (f1 : forall t idc, T1 t idc (f0 t idc)) {T2 : forall t idc x, T1 t idc x -> Type} (f2 : forall t idc, T2 t idc (f0 t idc) (f1 t idc)) - : forall t idc, T2 t idc (proj1_sig (@eta_ident_cps_gen T0 f0) t idc) (@eta_ident_cps_gen2 T0 f0 T1 f1 t idc). - Proof. intros t idc; cbv [proj1_sig eta_ident_cps_gen eta_ident_cps_gen2]; destruct idc; exact (f2 _ _). Defined. + : { f' : forall t idc, T2 t idc (proj1_sig (@eta_ident_cps_gen T0 f0) t idc) (proj1_sig (@eta_ident_cps_gen2 T0 f0 T1 f1) t idc) + | forall t idc, + f' t idc + = rew [T2 t idc _] (eq_sym (proj2_sig (@eta_ident_cps_gen2 T0 f0 T1 f1) t idc)) in + match eq_sym (proj2_sig (@eta_ident_cps_gen _ f0) t idc) as p return T2 t idc _ (rew [T1 t idc] p in f1 t idc) with + | eq_refl => f2 t idc + end }. + Proof. apply eta_ident_cps_gen. Defined. Definition Type_of_kind_of_type (T : Raw.ident.kind_of_type) := match T with @@ -881,6 +1003,9 @@ Module Compilers. | Raw.ident.BaseType => pattern.base.type.type end. + Notation full_type_of_list_of_kind ls + := (type_of_list (List.map Raw.ident.Type_of_kind_of_type ls)). + Notation type_of_list_of_kind ls := (type_of_list (List.map Type_of_kind_of_type ls)). @@ -980,176 +1105,198 @@ Module Compilers. { t : _ & { idc : ident t | @split_types _ idc = existT _ ridc (dt, idt) } } := ltac:(make_add_types_from_raw_sig (@split_types)). + + Definition split_types_subst_default : forall {t} (idc : ident t) (evm : EvarMap), { ridc : Raw.ident & type_of_list (dep_types (preinfos (ident_infos_of ridc))) * full_type_of_list_of_kind (indep_types (preinfos (ident_infos_of ridc))) }%type + := fun t idc evm + => let res := @split_types t idc in + existT _ (projT1 res) (Datatypes.fst (projT2 res), + lift_type_of_list_map (@subst_default_kind_of_type evm) (Datatypes.snd (projT2 res))). + + Lemma to_type_split_types_subst_default_eq t idc evm + : Raw.ident.to_type + (preinfos (ident_infos_of (projT1 (@split_types_subst_default t idc evm)))) + (Datatypes.fst (projT2 (split_types_subst_default idc evm))) + (Datatypes.snd (projT2 (split_types_subst_default idc evm))) + = type.subst_default t evm. + Proof. + destruct idc; cbv -[type.subst_default base.subst_default]; + cbn [type.subst_default base.subst_default]; reflexivity. + Defined. + + Lemma projT1_add_types_from_raw_sig_eq t idc + : projT1 + (add_types_from_raw_sig + (projT1 (Raw.ident.split_ident_gen idc)) + (projT1 (proj1_sig (projT2 (Raw.ident.split_ident_gen idc)))) + (lift_type_of_list_map + (@relax_kind_of_type) + (Datatypes.fst (projT2 (proj1_sig (projT2 (@Raw.ident.split_ident_gen t idc))))))) + = type.relax t. + Proof. + destruct idc; cbv -[type.relax base.relax]; + cbn [type.relax base.relax]; reflexivity. + Defined. + Definition prearg_types : forall {t} (idc : ident t), list Type := (fun t idc => let st := @split_types t idc in let pi := preinfos (ident_infos_of (projT1 st)) in indep_args pi (Datatypes.fst (projT2 st))). - Definition try_unify_split_args {ridc1 ridc2 : Raw.ident.ident} - : forall {dt1 : type_of_list (dep_types (preinfos (ident_infos_of ridc1)))} - {dt2 : type_of_list (dep_types (preinfos (ident_infos_of ridc2)))}, - type_of_list (indep_args _ dt1) -> Datatypes.option (type_of_list (indep_args _ dt2)) - := (if Raw.ident.ident_beq ridc1 ridc2 as b return (if b then ridc1 = ridc2 else True) -> _ - then fun pf - => match pf in (_ = ridc2) return forall (dt1 : type_of_list (dep_types (preinfos (ident_infos_of ridc1)))) - (dt2 : type_of_list (dep_types (preinfos (ident_infos_of ridc2)))), - type_of_list (indep_args _ dt1) -> Datatypes.option (type_of_list (indep_args _ dt2)) with - | eq_refl - => fun dt1 dt2 - => match Raw.ident.dep_types_dec_transparent _ dt1 dt2 with - | left pf - => match pf in (_ = dt2) return type_of_list (indep_args _ dt1) -> Datatypes.option (type_of_list (indep_args _ dt2)) with - | eq_refl => Datatypes.Some - end - | right _ => fun _ => Datatypes.None - end - end - else fun _ _ _ _ => Datatypes.None) - (Raw.ident.ident_beq_if ridc1 ridc2). - - Ltac do_reduce v := - let v := (eval cbv [proj1_sig pattern.eta_ident_cps_gen pattern.eta_ident_cps_gen2 eta_ident_cps_gen eta_ident_cps_gen2 eta_ident_cps_gen3 eta_ident_cps_gen_expand_literal pattern.eta_ident_cps_gen_expand_literal split_types projT1 projT2 preinfos dep_types indep_types ident_infos_of split_types add_types_from_raw_sig type_of_list List.map List.app Type_of_kind_of_type indep_args lift_type_of_list_map relax_kind_of_type subst_default_kind_of_type Raw.ident.assemble_ident Raw.ident.to_type prearg_types Raw.ident.Type_of_kind_of_type Raw.ident.to_ident Raw.ident.indep_args_beq Raw.ident.split_ident_gen Raw.ident.dep_types_dec_transparent try_unify_split_args Raw.ident.ident_beq_if Raw.ident.dep_types_dec_transparent Raw.ident.ident_beq] in v) in - let v := (eval cbn [Datatypes.fst Datatypes.snd] in v) in - v. - Definition strip_types : forall {t} (idc : ident t), Raw.ident - := ltac:(let v := do_reduce - (proj1_sig - (eta_ident_cps_gen - (fun t idc => projT1 (@split_types t idc)))) in - refine v). + := proj1_sig + (eta_ident_cps_gen + (fun t idc => projT1 (@split_types t idc))). Definition arg_types : forall {t} (idc : ident t), list Type - := ltac:(let v := (eval cbv [prearg_types] in (@prearg_types)) in - let v := do_reduce - (proj1_sig - (eta_ident_cps_gen - v)) in - refine v). - Definition to_typed : forall {t} (idc : ident t) (evm : EvarMap), type_of_list (arg_types idc) -> Compilers.ident.ident (pattern.type.subst_default t evm) - := ltac:(let v := constr: - (fun t (idc : ident t) (evm : EvarMap) - => @eta_ident_cps_gen2 - _ (@prearg_types) - (fun t idc arg_types_idc - => forall args : type_of_list arg_types_idc, - Compilers.ident.ident - (let st := @split_types _ idc in - let pi := preinfos (ident_infos_of (projT1 st)) in - Raw.ident.to_type - pi - (Datatypes.fst (projT2 st)) - (lift_type_of_list_map - (@subst_default_kind_of_type evm) - (Datatypes.snd (projT2 st))))) - (fun t idc args - => let st := @split_types _ idc in - (@Raw.ident.assemble_ident - (preinfos (ident_infos_of (projT1 (@split_types _ idc)))) - (existT - _ (Datatypes.fst (projT2 st)) - (lift_type_of_list_map (@subst_default_kind_of_type evm) (Datatypes.snd (projT2 st)), args)))) - t idc) in - let V' := fresh "V'" in - let v := constr:( - (fun t (idc : ident t) (evm : EvarMap) - => match v t idc evm return type_of_list (@arg_types _ idc) -> Compilers.ident.ident (pattern.type.subst_default t evm) with - | V' - => ltac:(destruct idc; - let v := (eval cbv [V'] in V') in - clear V'; - let v := do_reduce v in - refine v) - end)) in - let v := (eval cbv [id] in v) in - refine v). + := proj1_sig (eta_ident_cps_gen (@prearg_types)). + + Definition arg_types_unfolded : forall {t} (idc : ident t), list Type + := Eval cbv -[base.interp] in @arg_types. + + Definition to_typed : forall {t} (idc : ident t) (evm : EvarMap), type_of_list (arg_types idc) -> Compilers.ident.ident (type.subst_default t evm) + := fun t (idc : ident t) (evm : EvarMap) + => proj1_sig + (@eta_ident_cps_gen2 + _ (@prearg_types) + (fun t idc arg_types_idc + => forall args : type_of_list arg_types_idc, + Compilers.ident.ident (type.subst_default t evm) + (*let st := @split_types _ idc in + let pi := preinfos (ident_infos_of (projT1 st)) in + Raw.ident.to_type + pi + (Datatypes.fst (projT2 st)) + (lift_type_of_list_map + (@subst_default_kind_of_type evm) + (Datatypes.snd (projT2 st)))*)) + (fun t idc args + => rew [Compilers.ident.ident] to_type_split_types_subst_default_eq t idc evm in + let st := @split_types_subst_default _ idc evm in + (@Raw.ident.assemble_ident + (preinfos (ident_infos_of (projT1 (@split_types_subst_default _ idc evm)))) + (existT + _ (Datatypes.fst (projT2 st)) + (Datatypes.snd (projT2 st), args))))) + t idc. + + Definition to_typed_unfolded : forall {t} (idc : ident t) (evm : EvarMap), type_of_list (arg_types_unfolded idc) -> Compilers.ident.ident (type.subst_default t evm) + := ltac:(let v := (eval cbv -[type.subst_default base.subst_default arg_types_unfolded type_of_list base.base_interp Datatypes.fst Datatypes.snd] in + (fun t (idc : ident t) (evm : EvarMap) + => proj1_sig + (@eta_ident_cps_gen + (fun t idc => type_of_list (arg_types_unfolded idc) -> Compilers.ident.ident (type.subst_default t evm)) + (fun t idc => @to_typed t idc evm)) + t idc)) in + let v := (eval cbn [Datatypes.fst Datatypes.snd type_of_list] in v) in + exact v). + Definition type_of_list_arg_types_beq : forall t idc, type_of_list (@arg_types t idc) -> type_of_list (@arg_types t idc) -> bool - := ltac:(let v := do_reduce - (@eta_ident_cps_gen2 - _ (@prearg_types) - (fun t idc arg_types_idc => type_of_list arg_types_idc -> type_of_list arg_types_idc -> bool) - (fun t idc - => Raw.ident.indep_args_beq _ _)) in - refine v). + := proj1_sig + (@eta_ident_cps_gen2 + _ (@prearg_types) + (fun t idc arg_types_idc => type_of_list arg_types_idc -> type_of_list arg_types_idc -> bool) + (fun t idc + => Raw.ident.indep_args_beq _ _)). + + Definition type_of_list_arg_types_beq_unfolded : forall t idc, type_of_list (@arg_types_unfolded t idc) -> type_of_list (@arg_types_unfolded t idc) -> bool + := Eval cbv -[Prod.prod_beq arg_types_unfolded type_of_list base.interp_beq base.base_interp_beq Z.eqb base.base_interp ZRange.zrange_beq] in + proj1_sig + (@eta_ident_cps_gen + (fun t idc => type_of_list (@arg_types_unfolded t idc) -> type_of_list (@arg_types_unfolded t idc) -> bool) + (@type_of_list_arg_types_beq)). + Definition reflect_type_of_list_arg_types_beq : forall {t idc}, reflect_rel (@eq (type_of_list (@arg_types t idc))) (@type_of_list_arg_types_beq t idc) - := @eta_ident_cps_gen3 - _ (@prearg_types) - (fun t idc arg_types_idc => type_of_list arg_types_idc -> type_of_list arg_types_idc -> bool) - (fun t idc => Raw.ident.indep_args_beq _ _) - (fun t idc arg_types_idc beq => reflect_rel (@eq (type_of_list arg_types_idc)) beq) - (fun t idc => Raw.ident.indep_args_reflect _ _). - Definition preof_typed_ident - := (fun t (idc : Compilers.ident.ident t) - => proj1_sig + := proj1_sig + (@eta_ident_cps_gen3 + _ (@prearg_types) + (fun t idc arg_types_idc => type_of_list arg_types_idc -> type_of_list arg_types_idc -> bool) + (fun t idc => Raw.ident.indep_args_beq _ _) + (fun t idc arg_types_idc beq => reflect_rel (@eq (type_of_list arg_types_idc)) beq) + (fun t idc => Raw.ident.indep_args_reflect _ _)). + + Definition preof_typed_ident_sig : forall {t} (idc : Compilers.ident.ident t), _ + := fun t idc + => add_types_from_raw_sig + (projT1 (Raw.ident.split_ident_gen idc)) + (projT1 (proj1_sig (projT2 (Raw.ident.split_ident_gen idc)))) + (lift_type_of_list_map + (@relax_kind_of_type) + (Datatypes.fst (projT2 (proj1_sig (projT2 (Raw.ident.split_ident_gen idc)))))). + Definition preof_typed_ident : forall {t} (idc : Compilers.ident.ident t), ident (type.relax t) + := fun t idc + => rew [ident] projT1_add_types_from_raw_sig_eq t idc in + proj1_sig (projT2 - (add_types_from_raw_sig - (projT1 (Raw.ident.split_ident_gen idc)) - (projT1 (proj1_sig (projT2 (Raw.ident.split_ident_gen idc)))) - (lift_type_of_list_map - (@relax_kind_of_type) - (Datatypes.fst (projT2 (proj1_sig (projT2 (Raw.ident.split_ident_gen idc))))))))). + (@preof_typed_ident_sig t idc)). Definition of_typed_ident : forall {t} (idc : Compilers.ident.ident t), ident (type.relax t) - := ltac:(let v := (eval cbv [preof_typed_ident] in + := proj1_sig (pattern.eta_ident_cps_gen (@preof_typed_ident)). + + Definition of_typed_ident_unfolded : forall {t} (idc : Compilers.ident.ident t), ident (type.relax t) + := ltac:(let v := (eval cbv -[type.relax base.relax] in @of_typed_ident) in + let v := (eval cbn [type.relax base.relax] in v) in + exact v). + + Definition arg_types_of_typed_ident : forall {t} (idc : Compilers.ident.ident t), type_of_list (arg_types (of_typed_ident idc)). + Proof. + refine (proj1_sig + (@pattern.eta_ident_cps_gen2 + _ (@preof_typed_ident) + (fun t idc of_typed_ident_idc => type_of_list (arg_types of_typed_ident_idc)) + (fun t idc + => match projT1_add_types_from_raw_sig_eq t idc as H' + return type_of_list (arg_types (rew [ident] H' in proj1_sig (projT2 (@preof_typed_ident_sig _ idc)))) + with + | eq_refl + => rew <- [type_of_list] + (proj2_sig (eta_ident_cps_gen (@prearg_types)) + (projT1 (preof_typed_ident_sig idc)) + (proj1_sig (projT2 (preof_typed_ident_sig idc)))) in + rew <- [fun k' => type_of_list (indep_args (preinfos (ident_infos_of (projT1 k'))) (Datatypes.fst (projT2 k')))] + (proj2_sig (projT2 (@preof_typed_ident_sig t idc))) in + _ + end))). + refine (let st := Raw.ident.split_ident_gen idc in + let args := proj1_sig (projT2 st) in + Datatypes.snd (projT2 args)). + Defined. + + Definition arg_types_of_typed_ident_unfolded : forall {t} (idc : Compilers.ident.ident t), type_of_list (arg_types_unfolded (of_typed_ident_unfolded idc)) + := ltac:(let v := (eval cbv -[type.relax base.relax type_of_list of_typed_ident arg_types_unfolded of_typed_ident_unfolded base.base_interp] in (proj1_sig - (pattern.eta_ident_cps_gen - preof_typed_ident))) in - let V' := fresh "V'" in - let v := constr:( - (fun t (idc : Compilers.ident.ident t) - => match v t idc return ident (type.relax t) with - | V' - => ltac:(destruct idc; - let v := (eval cbv [V'] in V') in - clear V'; - let v := do_reduce v in - refine v) - end)) in - let v := (eval cbv [id] in v) in - refine v). - Definition arg_types_of_typed_ident : forall {t} (idc : Compilers.ident.ident t), type_of_list (arg_types (of_typed_ident idc)) - := ltac:(let v := constr:(fun t (idc : Compilers.ident.ident t) - => let st := Raw.ident.split_ident_gen idc in - let args := proj1_sig (projT2 st) in - Datatypes.snd (projT2 args)) in - let V' := fresh "V'" in - let v := constr:( - (fun t (idc : Compilers.ident.ident t) - => match v t idc return type_of_list (arg_types (of_typed_ident idc)) with - | V' - => ltac:(destruct idc; - let v := (eval cbv [V'] in V') in - clear V'; - let v := do_reduce v in - refine v) - end)) in - let v := (eval cbv [id] in v) in - refine v). - - Definition unify : forall {t t'} (pidc : ident t) (idc : Compilers.ident.ident t'), Datatypes.option (type_of_list (@arg_types t pidc)) - := ltac:(let v := constr:(fun t t' (pidc : ident t) (idc : Compilers.ident.ident t') - => proj1_sig - (eta_ident_cps_gen_expand_literal - (fun t pidc - => proj1_sig - (pattern.eta_ident_cps_gen_expand_literal - (fun t' idc - => @eta_ident_cps_gen2 - _ (@prearg_types) - (fun _ idc arg_types_idc => type_of_list arg_types_idc -> Datatypes.option (type_of_list (@arg_types t pidc))) - (fun t idc - => @eta_ident_cps_gen2 - _ (@prearg_types) - (fun _ pidc arg_types_pidc => type_of_list (@prearg_types _ idc) -> Datatypes.option (type_of_list arg_types_pidc)) - (fun t' pidc - => try_unify_split_args) - _ pidc) - _ (of_typed_ident idc) (@arg_types_of_typed_ident _ idc))) - _ idc)) - _ pidc) in - let v := (eval cbv [of_typed_ident arg_types_of_typed_ident] in v) in - let v := (eval cbv [pattern.eta_ident_cps_gen_expand_literal proj1_sig eta_ident_cps_gen_expand_literal eta_ident_cps_gen2 split_types projT1 projT2 try_unify_split_args Raw.ident.ident_beq_if Raw.ident.dep_types_dec_transparent Raw.ident.ident_beq Raw.ident.dep_types_dec_transparent ident_infos_of Datatypes.fst Datatypes.snd] in v) in - refine v). - + (@pattern.eta_ident_cps_gen + (fun t idc => type_of_list (arg_types_unfolded (of_typed_ident_unfolded idc))) + (@arg_types_of_typed_ident)))) in + exact v). + + Definition folded_unify : forall {t t'} (pidc : ident t) (idc : Compilers.ident.ident t') (*evm : EvarMap*), Datatypes.option (type_of_list (@arg_types t pidc)) + := fun t t' (pidc : ident t) (idc : Compilers.ident.ident t') (*evm : EvarMap*) + => proj1_sig + (eta_ident_cps_gen_expand_literal + (fun t pidc + => proj1_sig + (pattern.eta_ident_cps_gen_expand_literal + (fun t' idc + => proj1_sig + (@eta_ident_cps_gen2 + _ (@prearg_types) + (fun _ idc arg_types_idc => type_of_list arg_types_idc -> Datatypes.option (type_of_list (@arg_types t pidc))) + (fun t idc + => proj1_sig + (@eta_ident_cps_gen2 + _ (@prearg_types) + (fun _ pidc arg_types_pidc => type_of_list (@prearg_types _ idc) -> Datatypes.option (type_of_list arg_types_pidc)) + (fun t' pidc idc_indep_args + => Raw.ident.try_unify_split_args + (*(Datatypes.snd (projT2 (@split_types_subst_default _ idc evm))) + (Datatypes.snd (projT2 (@split_types_subst_default _ pidc evm)))*) + idc_indep_args)) + _ pidc)) + _ (of_typed_ident idc) (@arg_types_of_typed_ident _ idc))) + _ idc)) + _ pidc. + + Definition unify : forall {t t'} (pidc : ident t) (idc : Compilers.ident.ident t') (*evm : EvarMap*), Datatypes.option (type_of_list (@arg_types t pidc)) + := Eval vm_compute in @folded_unify. End ident. End pattern. End Compilers. |