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-Require Import Crypto.Compilers.SmartMap.
-Require Import Crypto.Compilers.Wf.
-Require Import Crypto.Compilers.Relations.
-Require Import Crypto.Compilers.Named.Context.
-Require Import Crypto.Compilers.Named.Syntax.
-Require Import Crypto.Compilers.Named.ContextDefinitions.
-Require Import Crypto.Compilers.Named.InterpretToPHOASInterp.
-Require Import Crypto.Compilers.Named.CompileInterp.
-Require Import Crypto.Compilers.Named.CompileInterpSideConditions.
-Require Import Crypto.Compilers.Named.CompileWf.
-Require Import Crypto.Compilers.Named.PositiveContext.
-Require Import Crypto.Compilers.Named.PositiveContext.Defaults.
-Require Import Crypto.Compilers.Named.PositiveContext.DefaultsProperties.
-Require Import Crypto.Compilers.Syntax.
-Require Import Crypto.Compilers.GeneralizeVar.
-Require Import Crypto.Compilers.InterpSideConditions.
-Require Import Crypto.Util.Decidable.
-Require Import Crypto.Util.Option.
-Require Import Crypto.Util.Sigma.
-Require Import Crypto.Util.PointedProp.
-Require Import Crypto.Util.Tactics.BreakMatch.
-
-Section language.
- Context {base_type_code : Type}
- {op : flat_type base_type_code -> flat_type base_type_code -> Type}
- (base_type_code_beq : base_type_code -> base_type_code -> bool)
- (base_type_code_bl_transparent : forall x y, base_type_code_beq x y = true -> x = y)
- (base_type_code_lb : forall x y, x = y -> base_type_code_beq x y = true)
- (failb : forall var t, @Syntax.exprf base_type_code op var (Tbase t))
- {interp_base_type : base_type_code -> Type}
- (interp_op : forall src dst, op src dst -> interp_flat_type interp_base_type src -> interp_flat_type interp_base_type dst).
-
- Local Notation GeneralizeVar
- := (@GeneralizeVar
- base_type_code op base_type_code_beq base_type_code_bl_transparent
- failb).
-
- Local Notation PositiveContextOk := (@PositiveContextOk base_type_code _ base_type_code_beq base_type_code_bl_transparent base_type_code_lb).
-
- Local Instance dec_base_type_code_eq : DecidableRel (@eq base_type_code).
- Proof.
- refine (fun x y => (if base_type_code_beq x y as b return base_type_code_beq x y = b -> Decidable (x = y)
- then fun pf => left (base_type_code_bl_transparent _ _ pf)
- else fun pf => right _) eq_refl).
- { clear -pf base_type_code_lb.
- let pf := pf in
- abstract (intro; erewrite base_type_code_lb in pf by eassumption; congruence). }
- Defined.
-
- Local Arguments Compile.compile : simpl never.
- Lemma interp_GeneralizeVar
- {t} (e1 e2 : expr base_type_code op t)
- (Hwf : wf e1 e2)
- e'
- (He' : GeneralizeVar e1 = Some e')
- : forall v, Interp interp_op e' v = interp interp_op e2 v.
- Proof using base_type_code_lb.
- unfold GeneralizeVar.GeneralizeVar, option_map in *.
- break_innermost_match_hyps; inversion_option; subst; intro.
- change (interp interp_op (?e ?var) ?v') with (Interp interp_op e v').
- unfold Interp, InterpretToPHOAS.Named.InterpToPHOAS, InterpretToPHOAS.Named.InterpToPHOAS_gen.
- match goal with |- ?L = ?R => cut (Some L = Some R); [ congruence | ] end.
- setoid_rewrite <- interp_interp_to_phoas.
- { erewrite (interp_compile (ContextOk:=PositiveContextOk)) with (e':=e2);
- [ reflexivity | auto | .. | eassumption ];
- auto using name_list_unique_default_names_for. }
- { eapply (wf_compile (ContextOk:=PositiveContextOk) (make_var':=fun _ => id)) with (e':= e2);
- [ auto | .. | eassumption ];
- auto using name_list_unique_default_names_for. }
- Qed.
-
- Lemma InterpGeneralizeVar
- {t} (e : Expr base_type_code op t)
- (Hwf : Wf e)
- e'
- (He' : GeneralizeVar (e _) = Some e')
- : forall v, Interp interp_op e' v = Interp interp_op e v.
- Proof using base_type_code_lb. eapply interp_GeneralizeVar; eauto. Qed.
-End language.