Add MapCastWf

1 files changed, 235 insertions, 0 deletions

diff --git a/src/Reflection/Named/MapCastWf.v b/src/Reflection/Named/MapCastWf.v
new file mode 100644
index 000000000..d5015a87c
--- /dev/null
+++ b/src/Reflection/Named/MapCastWf.v
@@ -0,0 +1,235 @@
+Require Import Coq.Bool.Sumbool.
+Require Import Coq.Logic.Eqdep_dec.
+Require Import Crypto.Reflection.SmartMap.
+Require Import Crypto.Reflection.Relations.
+Require Import Crypto.Reflection.Syntax.
+Require Import Crypto.Reflection.Named.Syntax.
+Require Import Crypto.Reflection.Named.ContextDefinitions.
+Require Import Crypto.Reflection.Named.ContextProperties.
+Require Import Crypto.Reflection.Named.ContextProperties.SmartMap.
+Require Import Crypto.Reflection.Named.Wf.
+Require Import Crypto.Reflection.Named.MapCast.
+Require Import Crypto.Util.PointedProp.
+Require Import Crypto.Util.ZUtil.
+Require Import Crypto.Util.Bool.
+Require Import Crypto.Util.Option.
+Require Import Crypto.Util.Sigma.
+Require Import Crypto.Util.Decidable.
+Require Import Crypto.Util.Tactics.BreakMatch.
+Require Import Crypto.Util.Tactics.SpecializeBy.
+Require Import Crypto.Util.Tactics.DestructHead.
+
+Local Open Scope nexpr_scope.
+Section language.
+  Context {base_type_code : Type}
+          {op : flat_type base_type_code -> flat_type base_type_code -> Type}
+          {Name : Type}
+          {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 t v := (SmartFlatTypeMap pick_typeb (t:=t) 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)))
+          {BoundsContext : Context Name interp_base_type_bounds}
+          (BoundsContextOk : ContextOk BoundsContext)
+          {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)
+          (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 t b) -> interp_flat_type interp_base_type t
+    := fun t b => SmartFlatTypeMapUnInterp cast_backb.
+  Context {Context : Context Name interp_base_type}
+          (ContextOk : ContextOk Context)
+          (base_type_dec : DecidableRel (@eq base_type_code))
+          (Name_dec : DecidableRel (@eq Name)).
+
+  Local Notation mapf_cast := (@mapf_cast _ op Name _ interp_op_bounds pick_typeb cast_op BoundsContext).
+  Local Notation map_cast := (@map_cast _ op Name _ interp_op_bounds pick_typeb cast_op BoundsContext).
+
+  Local Ltac handle_options_step :=
+    match goal with
+    | _ => progress inversion_option
+    | [ H : ?x = Some _ |- context[?x] ] => rewrite H
+    | [ H : ?x = None |- context[?x] ] => rewrite H
+    | [ H : ?x = Some _, H' : context[?x] |- _ ] => rewrite H in H'
+    | [ H : ?x = None, H' : context[?x] |- _ ] => rewrite H in H'
+    | [ H : Some _ <> None \/ _ |- _ ] => clear H
+    | [ H : Some ?x <> Some ?y |- _ ] => assert (x <> y) by congruence; clear H
+    | [ H : None <> Some _ |- _ ] => clear H
+    | [ H : Some _ <> None |- _ ] => clear H
+    | [ H : ?x <> ?x \/ _ |- _ ] => destruct H; [ exfalso; apply H; reflexivity | ]
+    | [ H : _ \/ None = Some _ |- _ ] => destruct H; [ | exfalso; clear -H; congruence ]
+    | [ H : _ \/ Some _ = None |- _ ] => destruct H; [ | exfalso; clear -H; congruence ]
+    | [ H : ?x = Some ?y, H' : ?x = Some ?y' |- _ ]
+      => assert (y = y') by congruence; (subst y' || subst y)
+    | _ => progress simpl @option_map
+    | _ => progress unfold option_map in *
+    end.
+
+  Local Ltac handle_lookupb_step :=
+    let do_eq_dec dec t t' :=
+        first [ constr_eq t t'; fail 1
+              | lazymatch goal with
+                | [ H : t = t' |- _ ] => fail 1
+                | [ H : t <> t' |- _ ] => fail 1
+                | [ H : t = t' -> False |- _ ] => fail 1
+                | _ => destruct (dec t t')
+                end ] in
+    let do_type_dec := do_eq_dec base_type_dec in
+    match goal with
+    | _ => progress unfold dec in *
+    | _ => handle_options_step
+    (* preprocess *)
+    | [ H : context[lookupb (extend _ _ _) _] |- _ ]
+      => first [ rewrite (fun C => lookupb_extend C base_type_dec Name_dec) in H by assumption
+               | setoid_rewrite (fun C => lookupb_extend C base_type_dec Name_dec) in H; [ | assumption.. ] ]
+    | [ |- context[lookupb (extend _ _ _) _] ]
+      => first [ rewrite (fun C => lookupb_extend C base_type_dec Name_dec) by assumption
+               | setoid_rewrite (fun C => lookupb_extend C base_type_dec Name_dec); [ | assumption.. ] ]
+    | _ => progress subst
+    (* handle multiple hypotheses *)
+    | [ H : find_Name _ ?n ?N = Some ?t', H'' : context[find_Name_and_val _ _ ?t ?n ?N ?x ?default] |- _ ]
+      => do_type_dec t t'
+    (* clear the default value *)
+    | [ H : context[find_Name_and_val ?tdec ?ndec ?t ?n (T:=?T) ?N ?V ?default] |- _ ]
+      => lazymatch default with None => fail | _ => idtac end;
+         rewrite find_Name_and_val_split in H
+    (* generic handlers *)
+    | [ H : find_Name _ ?n ?N = Some ?t', H' : ?t <> ?t', H'' : context[find_Name_and_val _ _ ?t ?n ?N ?x ?default] |- _ ]
+      => erewrite find_Name_and_val_wrong_type in H'' by eassumption
+    | [ H : context[find_Name _ _ (SmartFlatTypeMapInterp2 _ _ _)] |- _ ]
+      => rewrite find_Name_SmartFlatTypeMapInterp2 with (base_type_code_dec:=base_type_dec) in H
+    | [ H : find_Name_and_val _ _ _ _ _ _ _ = None |- _ ]
+      => apply find_Name_and_val_None_iff in H
+    (* destructers *)
+    | [ |- context[find_Name_and_val ?tdec ?ndec ?t ?n ?N ?V ?default] ]
+      => destruct (find_Name_and_val tdec ndec t n N V default) eqn:?
+    | [ H : context[match find_Name_and_val ?tdec ?ndec ?t ?n ?N ?V ?default with _ => _ end] |- _ ]
+      => destruct (find_Name_and_val tdec ndec t n N V default) eqn:?
+    | [ H : context[match find_Name ?ndec ?n ?N with _ => _ end] |- _ ]
+      => destruct (find_Name ndec n N) eqn:?
+    | [ H : context[match base_type_dec ?x ?y with _ => _ end] |- _ ]
+      => destruct (base_type_dec x y)
+    | [ H : context[match Name_dec ?x ?y with _ => _ end] |- _ ]
+      => destruct (Name_dec x y)
+    end.
+
+  Local Ltac handle_exists_in_goal :=
+    lazymatch goal with
+    | [ |- exists v, Some ?k = Some v /\ @?B v ]
+      => exists k; split; [ reflexivity | ]
+    | [ |- exists v, Some ?k = Some v ]
+      => exists k; reflexivity
+    | [ |- (exists v, None = Some v /\ @?B v) ]
+      => exfalso
+    | [ |- ?A /\ (exists v, Some ?k = Some v /\ @?B v) ]
+      => cut (A /\ B k); [ clear; solve [ intuition eauto ] | cbv beta ]
+    | [ |- ?A /\ (exists v, None = Some v /\ @?B v) ]
+      => exfalso
+    end.
+  Local Ltac specializer_t_step :=
+    match goal with
+    | [ H : ?T, H' : ?T |- _ ] => clear H
+    | [ H : forall x, Some _ = Some x -> _ |- _ ] => specialize (H _ eq_refl)
+    | [ H : ?x = Some _, IH : forall a b, ?x = Some _ -> _ |- _ ]
+      => specialize (IH _ _ H)
+    | [ H : ?x = Some _, IH : forall a, ?x = Some _ -> _ |- _ ]
+      => specialize (IH _ H)
+    | [ H : forall t n v, lookupb ?ctx n = _ -> _, H' : lookupb ?ctx ?n' = _ |- _ ]
+      => specialize (H _ _ _ H')
+    | _ => progress specialize_by auto
+    end.
+
+  Local Ltac break_t_step :=
+    first [ progress subst
+          | progress destruct_head'_ex
+          | progress destruct_head'_and
+          | progress inversion_option
+          | progress inversion_sigma
+          | progress autorewrite with push_prop_of_option in *
+          | progress break_match_hyps ].
+
+  Local Ltac do_specialize_IHe :=
+    repeat match goal with
+           | [ IH : context[mapf_cast _ ?e], H' : mapf_cast ?ctx ?e = _ |- _ ]
+             => let check_tac _ := (rewrite H' in IH) in
+                first [ specialize (IH ctx); check_tac ()
+                      | specialize (fun a => IH a ctx); check_tac ()
+                      | specialize (fun a b => IH a b ctx); check_tac () ]
+           | [ H : forall x y z w, Some _ = Some _ -> _ |- _ ]
+             => first [ specialize (H _ _ _ _ eq_refl)
+                      | specialize (fun x y => H x y _ _ eq_refl) ]
+           | [ H : forall x y z, Some _ = Some _ -> _ |- _ ]
+             => first [ specialize (H _ _ _ eq_refl)
+                      | specialize (fun x => H x _ _ eq_refl) ]
+           | [ H : forall x y, Some _ = Some _ -> _ |- _ ]
+             => first [ specialize (H _ _ eq_refl)
+                      | specialize (fun x => H x _ eq_refl) ]
+           | _ => progress specialize_by_assumption
+           | [ H : forall a b, prop_of_option (Named.wff a ?e) -> _, H' : prop_of_option (Named.wff _ ?e) |- _ ]
+             => specialize (fun b => H _ b H')
+           | [ H : forall a b, prop_of_option (Named.wff a ?e) -> _, H' : forall v, prop_of_option (Named.wff _ ?e) |- _ ]
+             => specialize (fun b v => H _ b (H' v))
+           | [ H : forall b v, _ -> prop_of_option (Named.wff b ?e) |- prop_of_option (Named.wff ?ctx ?e) ]
+             => specialize (H ctx)
+           end.
+
+  Local Ltac t_step :=
+    first [ progress intros
+          | progress simpl in *
+          | break_t_step
+          | handle_lookupb_step
+          | handle_exists_in_goal
+          | apply conj
+          | solve [ auto | exfalso; auto ]
+          | specializer_t_step
+          | progress do_specialize_IHe
+          | match goal with
+            | [ IH : forall v, _ -> ?T, v' : interp_flat_type _ _ |- ?T ]
+              => apply (IH (cast_back _ _ v')); clear IH
+            end ].
+  Local Ltac t := repeat t_step.
+
+
+  Lemma wff_mapf_cast
+        {t} (e:exprf base_type_code op Name t)
+    : forall
+        (oldValues:Context)
+        (newValues:Context)
+        (varBounds:BoundsContext)
+        {b} e' (He':mapf_cast varBounds e = Some (existT _ b e'))
+        (Hwf : prop_of_option (Named.wff oldValues e))
+        (Hctx:forall {t} n v,
+            lookupb (t:=t) oldValues n = Some v
+            -> exists b, lookupb (t:=t) varBounds n = Some b
+                         /\ exists v', lookupb (t:=pick_typeb t b) newValues n = Some v'),
+      prop_of_option (Named.wff newValues e').
+  Proof. induction e; t. Qed.
+
+  Lemma wf_map_cast
+        {t} (e:expr base_type_code op Name t)
+        (input_bounds : interp_flat_type interp_base_type_bounds (domain t))
+    : forall
+        (oldValues:Context)
+        (newValues:Context)
+        (varBounds:BoundsContext)
+        {b} e' (He':map_cast varBounds e input_bounds = Some (existT _ b e'))
+        (Hwf : Named.wf oldValues e)
+        (Hctx:forall {t} n v,
+            lookupb (t:=t) oldValues n = Some v
+            -> exists b, lookupb (t:=t) varBounds n = Some b
+                         /\ exists v', lookupb (t:=pick_typeb t b) newValues n = Some v'),
+      Named.wf newValues e'.
+  Proof.
+    unfold Named.wf, map_cast, option_map, interp; simpl; intros.
+    repeat first [ progress subst
+                 | progress inversion_option
+                 | progress inversion_sigma
+                 | progress break_match_hyps
+                 | progress destruct_head' sigT
+                 | progress simpl in * ].
+    match goal with v : _ |- _ => specialize (Hwf (cast_back _ _ v)) end.
+    eapply wff_mapf_cast; eauto; [].
+    t.
+  Qed.
+End language.