https://gitlab.com/nomadic-labs/mi-cho-coq
Tip revision: 7ccb33612808dc6eba01b4d54e638e3ebade2924 authored by Raphaƫl Cauderlier on 18 March 2021, 11:08:58 UTC
Use the fuel-free WP in Dexter proofs
Use the fuel-free WP in Dexter proofs
Tip revision: 7ccb336
dexter_verification_ep_addLiquidity.v
(* Open Source License *)
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(* Coq *)
Require Import String.
Require Import Michocoq.macros.
Import syntax.
Import comparable.
Require Import NArith.
Require Import ZArith.
Require Import Coq.Setoids.Setoid.
Require Import Coq.micromega.Lia.
From Coq Require Import Program.Tactics.
(* Mi-Cho-Coq *)
Require Import semantics.
Require Import util.
Import error.
Require List.
(* Dexter *)
Require dexter_definition.
Require dexter_spec.
Require Import dexter_util.
Require Import dexter_spec_util.
Module Spec := dexter_spec.
Module Def := dexter_definition.
Import Def.Storage.
Import Tactics.
Require Import contract_semantics.
(* It's better not to unfold compare in this proof,
* this makes it easier to use util.eqb_eq.
*)
Opaque N.mul.
Opaque N.add.
Opaque Z.modulo.
Opaque compare.
Definition ep_addLiquidity := Eval vm_compute in Def.ep_addLiquidity.
Lemma ep_addLiquidity_same : Def.ep_addLiquidity = ep_addLiquidity.
Proof.
reflexivity.
Qed.
Lemma ep_addLiquidity_correct
(env : @proto_env dexter_definition.self_type)
(p : data dexter_definition.parameter_ep_addLiquidity_ty)
(sto : data dexter_definition.storage_ty)
(ret_ops : Datatypes.list (data operation))
(ret_sto : data dexter_definition.storage_ty) :
eval0_seq_precond env Def.ep_addLiquidity
(fun x => x = (ret_ops, ret_sto, tt))
(p, (sto, tt)) <->
Spec.ep_addLiquidity env p sto ret_ops ret_sto.
Proof.
rewrite ep_addLiquidity_same.
simpl.
destruct_sto sto tokenPool xtzPool lqtTotal selfIsUpdatingTokenPool freezeBaker manager tokenAddress lqtAddress.
destruct p as (owner, (min_lqt_minted, (max_tokens_deposited, deadline))).
simpl.
(* update token *)
apply and_both_0; [apply bool_false_not|].
(* deadline *)
apply and_both_0; [apply check_deadline_correct_alt|].
rewrite mutez_to_nat.
rewrite ex_eq_simpl_some.
rewrite mutez_to_nat. rewrite ex_eq_simpl_some.
rewrite <- !ediv_N_some_iff.
rewrite and_idempotent.
apply and_both_0; [apply tez_to_Z_to_N_neq_zero_iff|].
unfold Spec.mutez_to_nat.
rewrite !(N.mul_comm _ (Z.to_N (tez.to_Z (amount env)))).
rewrite !(N.add_comm 1).
rewrite comparison_to_int_compare_nat_eqb.
fold_mutez.
if_step.
all: rewrite precond_exists; unfold precond_ex.
all: rewrite !ex_and_comm; rewrite <- ex_order; rewrite ex_order3; rewrite ex_order.
all: apply forall_ex; intro xtzPool'.
all: rewrite !ex_and_comm; rewrite ex_order; apply forall_ex; intro lqt_transfer.
all: rewrite !ex_and_comm; apply forall_ex; intro lqt_mintOrBurn.
all: rewrite !Z_gtb_false_leb_iff, !Z_ltb_false_geb_iff,
!comparison_to_int_compare_nat_le, !comparison_to_int_compare_nat_ge.
1: rewrite Spec_Nceiling_mod by now apply N.eqb_eq.
2: rewrite Spec_Nceiling_rem by now apply N.eqb_neq.
all: unfold Spec.lqt.mint, Spec.lqt.mintOrBurn.
all: rewrite N.ge_le_iff; repeat rewrite shim_pair_equal_spec; intuition.
Qed.