Add Addmitted correctness for MapCastByDeBruijn

1 files changed, 96 insertions, 0 deletions

diff --git a/src/Reflection/MapCastByDeBruijnInterp.v b/src/Reflection/MapCastByDeBruijnInterp.v
new file mode 100644
index 000000000..8595b53cc
--- /dev/null
+++ b/src/Reflection/MapCastByDeBruijnInterp.v
@@ -0,0 +1,96 @@
+Require Import Crypto.Reflection.SmartMap.
+Require Import Crypto.Reflection.Wf.
+Require Import Crypto.Reflection.Relations.
+Require Import Crypto.Reflection.Named.Syntax.
+Require Import Crypto.Reflection.Named.ContextDefinitions.
+Require Import Crypto.Reflection.Named.MapCastInterp.
+Require Import Crypto.Reflection.Named.InterpretToPHOASInterp.
+Require Import Crypto.Reflection.Named.CompileInterp.
+Require Import Crypto.Reflection.Named.PositiveContext.
+Require Import Crypto.Reflection.Named.PositiveContext.Defaults.
+Require Import Crypto.Reflection.LinearizeInterp.
+Require Import Crypto.Reflection.Syntax.
+Require Import Crypto.Reflection.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 var t tR (opc : op t tR) args_bs
+                            (args : exprf base_type_code op (var:=var) (pick_type args_bs)),
+              option (exprf base_type_code op (var:=var) (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))
+          (wff_cast_op
+           : forall var1 var2 t tR opc args_bs args1 args2 G v1 v2,
+              cast_op var1 t tR opc args_bs args1 = Some v1
+              -> cast_op var2 t tR opc args_bs args2 = Some v2
+              -> wff G args1 args2
+              -> wff G v1 v2)
+          (pull_cast_back
+           : forall t tR opc bs
+                    (args : exprf base_type_code op (pick_type bs))
+                    new_e
+                    (Hnew : cast_op _ _ _ opc bs args = Some new_e)
+                    (H : inbounds t bs (cast_back t bs (interpf interp_op args))),
+              interp_op t tR opc (cast_back t bs (interpf interp_op args))
+              =
+              cast_back _ _ (interpf interp_op new_e)).
+
+  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 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.
+
+  Lemma MapCastCorrect
+        {t} (e : Expr base_type_code op t)
+        (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),
+      @inbounds _ b (Interp interp_op e v)
+      /\ cast_back _ _ (Interp interp_op e' v') = (Interp interp_op e v).
+  Proof.
+    unfold MapCastByDeBruijn.MapCast, option_map; intros b e'.
+    break_innermost_match; try congruence; intros ? v v'.
+    inversion_option; inversion_sigma; subst; simpl in *; intros.
+    match goal with
+    | [ H : MapCast.map_cast _ _ _ _ _ _ = Some _ |- _ ]
+      => eapply map_cast_correct with (oldValues:=empty) (newValues:=empty) in H; try eassumption
+    end;
+      try solve [ auto using PositiveContextOk with typeclass_instances
+                | repeat first [ rewrite !lookupb_empty by (apply PositiveContextOk; assumption)
+                               | intro
+                               | congruence ] ].
+  Admitted.
+End language.