Require Import Coq.ZArith.ZArith.
Require Import Crypto.Language.
Require Import Crypto.LanguageWf.
Require Import Crypto.RewriterProofsTactics.
Require Import Crypto.RewriterRulesProofs.

Module Compilers.
  Import Language.Compilers.
  Import Language.Compilers.defaults.
  Import LanguageWf.Compilers.
  Import RewriterProofsTactics.Compilers.RewriteRules.GoalType.
  Import RewriterProofsTactics.Compilers.RewriteRules.Tactic.

  Module Import RewriteRules.
    Section __.
      Context (invert_low invert_high : Z (*log2wordmax*) -> Z -> @option Z)
              (Hlow : forall s v v', invert_low s v = Some v' -> v = Z.land v' (2^(s/2)-1))
              (Hhigh : forall s v v', invert_high s v = Some v' -> v = Z.shiftr v' (s/2)).

      Definition VerifiedRewriterToFancy : VerifiedRewriter.
      Proof using All. make_rewriter false fancy_rewrite_rules_proofs. Defined.

      Definition RewriteToFancy {t} : Expr t -> Expr t.
      Proof using invert_low invert_high.
        let v := (eval hnf in (@Rewrite VerifiedRewriterToFancy t)) in exact v.
      Defined.

      Lemma Wf_RewriteToFancy {t} e (Hwf : Wf e) : Wf (@RewriteToFancy t e).
      Proof using All. now apply VerifiedRewriterToFancy. Qed.

      Lemma Interp_gen_RewriteToFancy {cast_outside_of_range t} e (Hwf : Wf e)
        : expr.Interp (@ident.gen_interp cast_outside_of_range) (@RewriteToFancy t e)
          == expr.Interp (@ident.gen_interp cast_outside_of_range) e.
      Proof using All. now apply VerifiedRewriterToFancy. Qed.

      Lemma Interp_RewriteToFancy {t} e (Hwf : Wf e) : Interp (@RewriteToFancy t e) == Interp e.
      Proof using All. apply Interp_gen_RewriteToFancy; assumption. Qed.
    End __.
  End RewriteRules.

  Module Export Hints.
    Hint Resolve Wf_RewriteToFancy : wf.
    Hint Rewrite @Interp_gen_RewriteToFancy @Interp_RewriteToFancy : interp.
  End Hints.
End Compilers.