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Require Import Coq.ZArith.ZArith.
Require Import Crypto.Assembly.GF25519.
Require Import Crypto.Specific.GF25519.
Require Import Crypto.Util.Tuple.
Axiom is_bounded : forall (x : Specific.GF25519.fe25519), bool. (* Pull from Specific.GF25519Bounded when the latest changes to master are merged into this branch *)
(* Totally fine to edit these definitions; DO NOT change the type signatures at all *)
Definition ExprBinOp : Type
:= @PhoasCommon.interp_type Z GF25519.FE -> @PhoasCommon.interp_type Z GF25519.FE -> @HL.HL.expr Z (@PhoasCommon.interp_type Z) GF25519.FE.
Definition ExprUnOp : Type
:= @PhoasCommon.interp_type Z GF25519.FE -> @HL.HL.expr Z (@PhoasCommon.interp_type Z) GF25519.FE.
Definition interp_bexpr : ExprBinOp -> Specific.GF25519.fe25519 -> Specific.GF25519.fe25519 -> Specific.GF25519.fe25519
:= fun f x y => HL.HL.interp (E := Evaluables.ZEvaluable) (t := GF25519.FE) (f x y).
Definition interp_uexpr : ExprUnOp -> Specific.GF25519.fe25519 -> Specific.GF25519.fe25519
:= fun f x => HL.HL.interp (E := Evaluables.ZEvaluable) (t := GF25519.FE) (f x).
Definition radd : ExprBinOp := GF25519.AddExpr.ge25519_add.
Definition rsub : ExprBinOp := GF25519.SubExpr.ge25519_sub.
Definition rmul : ExprBinOp := GF25519.MulExpr.ge25519_mul.
Definition ropp : ExprUnOp := GF25519.OppExpr.ge25519_opp.
Axiom rfreeze : ExprUnOp.
(*Axiom radd_correct : forall x y, interp_bexpr radd x y = carry_add x y.
Axiom rsub_correct : forall x y, interp_bexpr rsub x y = carry_sub x y.*)
Lemma rmul_correct : forall x y, interp_bexpr rmul x y = mul x y.
Proof.
cbv [interp_bexpr rmul GF25519.MulExpr.ge25519_mul]; intros.
apply proj2_sig.
Qed.
Axiom rfreeze_correct : forall x, interp_uexpr rfreeze x = freeze x.
Local Notation binop_bounded op
:= (forall x y,
is_bounded x = true
-> is_bounded y = true
-> is_bounded (interp_bexpr op x y) = true) (only parsing).
Local Notation unop_bounded op
:= (forall x,
is_bounded x = true
-> is_bounded (interp_uexpr op x) = true) (only parsing).
Axiom radd_bounded : binop_bounded radd.
Axiom rsub_bounded : binop_bounded rsub.
Axiom rmul_bounded : binop_bounded rmul.
Axiom ropp_bounded : unop_bounded ropp.
Axiom rfreeze_bounded : unop_bounded rfreeze.
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