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Require Import Coq.ZArith.ZArith.
Require Import Crypto.Util.CPSNotations.
Require Import Crypto.Util.ZRange.
Require Import Crypto.Util.Tactics.BreakMatch.
Require Import Crypto.Util.Option.
Require Import Crypto.Util.Decidable.
Require Import Crypto.Experiments.NewPipeline.Language.
Require Import Crypto.Experiments.NewPipeline.LanguageInversion.
Require Import Crypto.Experiments.NewPipeline.GENERATEDIdentifiersWithoutTypes.
Import EqNotations.
Module Compilers.
Import Language.Compilers.
Import GENERATEDIdentifiersWithoutTypes.Compilers.
Module pattern.
Import GENERATEDIdentifiersWithoutTypes.Compilers.pattern.
Local Lemma quick_invert_eq_option {A} (P : Type) (x y : option A) (H : x = y)
: match x, y return Type with
| Some _, None => P
| None, Some _ => P
| _, _ => True
end.
Proof. subst y; destruct x; constructor. Qed.
Local Lemma quick_invert_neq_option {A} (P : Type) (x y : option A) (H : x <> y)
: match x, y return Type with
| Some _, None => True
| None, Some _ => True
| None, None => P
| Some x, Some y => x <> y
end.
Proof. destruct x, y; try congruence; trivial. Qed.
Local Lemma Some_neq_None {A x} : @Some A x <> None. Proof. congruence. Qed.
Module Raw.
Module ident.
Import GENERATEDIdentifiersWithoutTypes.Compilers.pattern.Raw.ident.
Global Instance eq_ident_Decidable : DecidableRel (@eq ident) := ident_eq_dec.
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 ].
Qed.
Lemma type_of_invert_bind_args t idc p f
: @invert_bind_args t idc p = Some f -> t = type_of p f.
Proof.
intro pf; exact (proj1_sig (@to_typed_invert_bind_args_gen t idc p f pf)).
Defined.
Lemma to_typed_invert_bind_args t idc p f (pf : @invert_bind_args t idc p = Some f)
: @to_typed p f = rew [Compilers.ident.ident] @type_of_invert_bind_args t idc p f pf in idc.
Proof.
exact (proj2_sig (@to_typed_invert_bind_args_gen t idc p f pf)).
Defined.
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).
Proof.
split; intro H;
[ | specialize (fun f1 f2 => H _ (@to_typed p f1) _ (@to_typed p f2)) ];
destruct p; cbn in *; try solve [ reflexivity | exfalso; discriminate ];
repeat first [ progress intros *
| match goal with
| [ |- ?x = ?x ] => reflexivity
| [ |- ?x = ?x -> _ ] => intros _
| [ |- None <> None -> ?P ] => exact (@quick_invert_neq_option _ P None None)
| [ |- Some _ <> None -> _ ] => intros _
| [ |- None <> Some _ -> _ ] => intros _
| [ H : forall x y, Some _ <> None -> _ |- _ ] => specialize (fun x y => H x y Some_neq_None)
| [ 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
| break_innermost_match_step
| congruence ].
Qed.
End ident.
End Raw.
Module ident.
Import GENERATEDIdentifiersWithoutTypes.Compilers.pattern.ident.
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.
Lemma is_simple_strip_types_iff_type_vars_nil {t} idc
: Raw.ident.is_simple (@strip_types t idc) = true
<-> type_vars idc = List.nil.
Proof. destruct idc; cbn; intuition congruence. Qed.
Local Lemma None_neq_Some_fast {T} {P : T -> Prop} {v} : @None T = Some v -> P v.
Proof. congruence. Qed.
Local Lemma Some_eq_Some_subst_fast {T v1} {P : T -> Prop}
: P v1 -> forall v2, Some v1 = Some v2 -> P v2.
Proof. congruence. 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.
Proof.
cbv [unify to_typed].
repeat first [ match goal with
| [ |- forall v, None = Some v -> _ ] => refine (@None_neq_Some_fast _ _)
| [ |- forall v, Some _ = Some v -> _ ] => refine (@Some_eq_Some_subst_fast _ _ _ _)
end
| break_innermost_match_step
| reflexivity
| progress intros
| progress cbv [type.subst_default base.subst_default] in *
| progress Compilers.type.inversion_type ].
Qed.
End ident.
End pattern.
End Compilers.
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