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-Require Import Crypto.Compilers.Syntax.
-Require Import Crypto.Compilers.Rewriter.
-Require Import Crypto.Util.Tactics.RewriteHyp.
-
-Section language.
- Context {base_type_code : Type}
- {interp_base_type : base_type_code -> Type}
- {op : flat_type base_type_code -> flat_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}.
-
- Local Notation flat_type := (flat_type base_type_code).
- Local Notation type := (type base_type_code).
- Local Notation interp_type := (interp_type interp_base_type).
- Local Notation interp_flat_type := (interp_flat_type interp_base_type).
- Local Notation exprf := (@exprf base_type_code op interp_base_type).
- Local Notation expr := (@expr base_type_code op interp_base_type).
- Local Notation Expr := (@Expr base_type_code op).
-
- Section specialized.
- Context {rewrite_op_expr : forall src dst (opc : op src dst), exprf src -> exprf dst}
- (Hrewrite : forall src dst opc args,
- interpf interp_op (rewrite_op_expr src dst opc args)
- = interp_op _ _ opc (interpf interp_op args)).
-
- Lemma interpf_rewrite_opf {t} (e : exprf t)
- : interpf interp_op (rewrite_opf rewrite_op_expr e) = interpf interp_op e.
- Proof using Type*.
- induction e; simpl; unfold LetIn.Let_In; rewrite_hyp ?*; reflexivity.
- Qed.
-
- Lemma interp_rewrite_op {t} (e : expr t)
- : forall x, interp interp_op (rewrite_op rewrite_op_expr e) x = interp interp_op e x.
- Proof using Type*.
- destruct e; intro x; apply interpf_rewrite_opf.
- Qed.
- End specialized.
-
- Lemma InterpRewriteOp
- {rewrite_op_expr}
- (Hrewrite : forall src dst opc args,
- interpf interp_op (rewrite_op_expr interp_base_type src dst opc args)
- = interp_op _ _ opc (interpf interp_op args))
- {t} (e : Expr t)
- : forall x, Interp interp_op (RewriteOp rewrite_op_expr e) x = Interp interp_op e x.
- Proof using Type.
- apply interp_rewrite_op; assumption.
- Qed.
-End language.
-
-Hint Rewrite @InterpRewriteOp using assumption : reflective_interp.