Add aborted MapCastByDeBruijnWf

I'm not sure exactly why the wf proof requires cast_backb in map_cast;
it seems to be used as a dumb way of instantiating the
context-extension on the input expression tree (since we're only given
the context-extension values on the output expression, which has a
different type).

1 files changed, 94 insertions, 0 deletions

diff --git a/src/Reflection/MapCastByDeBruijnWf.v b/src/Reflection/MapCastByDeBruijnWf.v
new file mode 100644
index 000000000..b4edb51c8
--- /dev/null
+++ b/src/Reflection/MapCastByDeBruijnWf.v
@@ -0,0 +1,94 @@
+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.MapCastWf.
+Require Import Crypto.Reflection.Named.InterpretToPHOASWf.
+Require Import Crypto.Reflection.Named.CompileWf.
+Require Import Crypto.Reflection.Named.PositiveContext.
+Require Import Crypto.Reflection.Named.PositiveContext.Defaults.
+Require Import Crypto.Reflection.Named.PositiveContext.DefaultsProperties.
+Require Import Crypto.Reflection.LinearizeWf.
+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 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.
+
+  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')),
+      Wf e'.
+  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.
+    unfold InterpretToPHOAS.Named.InterpToPHOAS, InterpretToPHOAS.Named.InterpToPHOAS_gen.
+    eapply (@wf_interp_to_phoas
+              base_type_code op FMapPositive.PositiveMap.key _ _ _ _
+              (PositiveContext base_type_code _ base_type_code_beq base_type_code_bl_transparent)
+              (PositiveContext base_type_code _ base_type_code_beq base_type_code_bl_transparent)
+              PositiveContextOk PositiveContextOk
+              (failb _) (failb _) _ e1);
+      (eapply wf_map_cast with (oldValues:=empty); eauto using PositiveContextOk with typeclass_instances);
+      try (eapply (wf_compile (ContextOk:=PositiveContextOk));
+           [ apply wf_linearize; eauto | .. | eassumption ]);
+      try solve [ auto using name_list_unique_DefaultNamesFor
+                | intros ???; rewrite lookupb_empty by apply PositiveContextOk; congruence ].
+    (* XXX why do we need cast_backb for arbitrary var ? *)
+  Abort.
+End language.