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Diffstat (limited to 'src/Compilers/MapCastByDeBruijnInterp.v')
| -rw-r--r-- | src/Compilers/MapCastByDeBruijnInterp.v | 116 |
1 files changed, 116 insertions, 0 deletions
diff --git a/src/Compilers/MapCastByDeBruijnInterp.v b/src/Compilers/MapCastByDeBruijnInterp.v new file mode 100644 index 000000000..5d8156f09 --- /dev/null +++ b/src/Compilers/MapCastByDeBruijnInterp.v @@ -0,0 +1,116 @@ +Require Import Crypto.Compilers.SmartMap. +Require Import Crypto.Compilers.Wf. +Require Import Crypto.Compilers.Relations. +Require Import Crypto.Compilers.Named.Syntax. +Require Import Crypto.Compilers.Named.ContextDefinitions. +Require Import Crypto.Compilers.Named.MapCastInterp. +Require Import Crypto.Compilers.Named.MapCastWf. +Require Import Crypto.Compilers.Named.InterpretToPHOASInterp. +Require Import Crypto.Compilers.Named.CompileInterp. +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.MapCastByDeBruijn. +Require Import Crypto.Util.Decidable. +Require Import Crypto.Util.Option. +Require Import Crypto.Util.Sigma. +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) + {interp_base_type_bounds : base_type_code -> Type} + (interp_op_bounds : forall src dst, op src dst -> interp_flat_type interp_base_type_bounds src -> interp_flat_type interp_base_type_bounds dst) + (pick_typeb : forall t, interp_base_type_bounds t -> base_type_code). + Local Notation pick_type v := (SmartFlatTypeMap pick_typeb v). + Context (cast_op : forall t tR (opc : op t tR) args_bs, + op (pick_type args_bs) (pick_type (interp_op_bounds t tR opc args_bs))) + (cast_backb: forall t b, interp_base_type (pick_typeb t b) -> interp_base_type t). + Let cast_back : forall t b, interp_flat_type interp_base_type (pick_type b) -> interp_flat_type interp_base_type t + := fun t b => SmartFlatTypeMapUnInterp cast_backb. + Context (inboundsb : forall t, interp_base_type_bounds t -> interp_base_type t -> Prop). + Let inbounds : forall t, interp_flat_type interp_base_type_bounds t -> interp_flat_type interp_base_type t -> Prop + := fun t => interp_flat_type_rel_pointwise inboundsb (t:=t). + Context (interp_op_bounds_correct + : forall t tR opc bs + (v : interp_flat_type interp_base_type t) + (H : inbounds t bs v), + inbounds tR (interp_op_bounds t tR opc bs) (interp_op t tR opc v)) + (pull_cast_back + : forall t tR opc bs + (v : interp_flat_type interp_base_type (pick_type bs)) + (H : inbounds t bs (cast_back t bs v)), + interp_op t tR opc (cast_back t bs v) + = + cast_back _ _ (interp_op _ _ (cast_op _ _ opc bs) v)). + + Local Notation MapCast + := (@MapCast + base_type_code op base_type_code_beq base_type_code_bl_transparent + failb interp_base_type_bounds interp_op_bounds pick_typeb cast_op). + + 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. + abstract (intro; erewrite base_type_code_lb in pf by eassumption; congruence). } + Defined. + + Local Arguments Compile.compile : simpl never. + Lemma MapCastCorrect + {t} (e : Expr base_type_code op t) + (Hwf : Wf e) + (input_bounds : interp_flat_type interp_base_type_bounds (domain t)) + : forall {b} e' (He':MapCast e input_bounds = Some (existT _ b e')) + v v' (Hv : @inbounds _ input_bounds v /\ cast_back _ _ v' = v), + Interp interp_op_bounds e input_bounds = b + /\ @inbounds _ b (Interp interp_op e v) + /\ cast_back _ _ (Interp interp_op e' v') = (Interp interp_op e v). + Proof using base_type_code_lb interp_op_bounds_correct pull_cast_back. + unfold MapCastByDeBruijn.MapCast, MapCastCompile, MapCastDoCast, MapCastDoInterp, option_map; intros b e'. + break_innermost_match; try congruence; intros ? v v'. + inversion_option; inversion_sigma; subst; simpl in *; intros. + lazymatch goal with + | [ H : MapCast.map_cast _ _ _ _ _ _ = Some _ |- _ ] + => eapply map_cast_correct with (t:=Arrow _ _) (oldValues:=empty) (newValues:=empty) in H; + [ destruct H; split; [ | eassumption ] | try eassumption.. ] + end; + try solve [ eassumption + | auto using PositiveContextOk with typeclass_instances + | repeat first [ rewrite !lookupb_empty by (apply PositiveContextOk; assumption) + | intro + | congruence ] ]; + unfold Interp; + [ match goal with + | [ H : ?y = Some ?b |- ?x = ?b ] + => cut (y = Some x); [ congruence | ] + end + | + | change (interp interp_op (?e ?var) ?v') with (Interp interp_op e v'); + unfold Interp, InterpretToPHOAS.Named.InterpToPHOAS, InterpretToPHOAS.Named.InterpToPHOAS_gen; + rewrite <- interp_interp_to_phoas; [ reflexivity | ] ]. + { erewrite (interp_compile (ContextOk:=PositiveContextOk)) with (e':=e _); + [ reflexivity | auto | .. | eassumption ]; + auto using name_list_unique_DefaultNamesFor. } + { erewrite (interp_compile (ContextOk:=PositiveContextOk)) with (e':=e _); + [ reflexivity | auto | .. | eassumption ]; + auto using name_list_unique_DefaultNamesFor. } + { intro; eapply wf_map_cast with (t := Arrow _ _) (fValues := empty); eauto using PositiveContextOk with typeclass_instances. + { eapply (wf_compile (ContextOk:=PositiveContextOk)) with (e':= e _); + [ auto | .. | eassumption ]; + auto using name_list_unique_DefaultNamesFor. } + { intros ???; rewrite lookupb_empty by apply PositiveContextOk; congruence. } } + Qed. +End language. |