abstract contract GasAbstraction is AbstractFiatTokenV2, EIP712Domain {
    bytes32
        public constant TRANSFER_WITH_AUTHORIZATION_TYPEHASH = 0x7c7c6cdb67a18743f49ec6fa9b35f50d52ed05cbed4cc592e13b44501c1a2267;
    // = keccak256("TransferWithAuthorization(address from,address to,uint256 value,uint256 validAfter,uint256 validBefore,bytes32 nonce)")
    bytes32
        public constant APPROVE_WITH_AUTHORIZATION_TYPEHASH = 0x808c10407a796f3ef2c7ea38c0638ea9d2b8a1c63e3ca9e1f56ce84ae59df73c;
    // = keccak256("ApproveWithAuthorization(address owner,address spender,uint256 value,uint256 validAfter,uint256 validBefore,bytes32 nonce)")
    bytes32
        public constant INCREASE_ALLOWANCE_WITH_AUTHORIZATION_TYPEHASH = 0x424222bb050a1f7f14017232a5671f2680a2d3420f504bd565cf03035c53198a;
    // = keccak256("IncreaseAllowanceWithAuthorization(address owner,address spender,uint256 increment,uint256 validAfter,uint256 validBefore,bytes32 nonce)")
    bytes32
        public constant DECREASE_ALLOWANCE_WITH_AUTHORIZATION_TYPEHASH = 0xb70559e94cbda91958ebec07f9b65b3b490097c8d25c8dacd71105df1015b6d8;
    // = keccak256("DecreaseAllowanceWithAuthorization(address owner,address spender,uint256 decrement,uint256 validAfter,uint256 validBefore,bytes32 nonce)")
    bytes32
        public constant CANCEL_AUTHORIZATION_TYPEHASH = 0x158b0a9edf7a828aad02f63cd515c68ef2f50ba807396f6d12842833a1597429;
    // = keccak256("CancelAuthorization(address authorizer,bytes32 nonce)")

    enum AuthorizationState { Unused, Used, Canceled }

    /**
     * @dev authorizer address => nonce => authorization state
     */
    mapping(address => mapping(bytes32 => AuthorizationState))
        private _authorizationStates;

    event AuthorizationUsed(address indexed authorizer, bytes32 indexed nonce);
    event AuthorizationCanceled(
        address indexed authorizer,
        bytes32 indexed nonce
    );

    /**
     * @notice Returns the state of an authorization
     * @param authorizer    Authorizer's address
     * @param nonce         Nonce of the authorization
     * @return Authorization state
     */
    function authorizationState(address authorizer, bytes32 nonce)
        external
        view
        returns (AuthorizationState)
    {
        return _authorizationStates[authorizer][nonce];
    }

    /**
     * @notice Verify a signed transfer authorization and execute if valid
     * @param from          Payer's address (Authorizer)
     * @param to            Payee's address
     * @param value         Amount to be transferred
     * @param validAfter    The time after which this is valid (unix time)
     * @param validBefore   The time before which this is valid (unix time)
     * @param nonce         Unique nonce
     * @param v             v of the signature
     * @param r             r of the signature
     * @param s             s of the signature
     */
    function _transferWithAuthorization(
        address from,
        address to,
        uint256 value,
        uint256 validAfter,
        uint256 validBefore,
        bytes32 nonce,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        _requireValidAuthorization(from, nonce, validAfter, validBefore);

        bytes memory data = abi.encode(
            TRANSFER_WITH_AUTHORIZATION_TYPEHASH,
            from,
            to,
            value,
            validAfter,
            validBefore,
            nonce
        );
        require(
            EIP712.recover(DOMAIN_SEPARATOR, v, r, s, data) == from,
            "FiatTokenV2: invalid signature"
        );

        _markAuthorizationAsUsed(from, nonce);
        _transfer(from, to, value);
    }

    /**
     * @notice Verify a signed authorization for an increase in the allowance
     * granted to the spender and execute if valid
     * @param owner         Token owner's address (Authorizer)
     * @param spender       Spender's address
     * @param increment     Amount of increase in allowance
     * @param validAfter    The time after which this is valid (unix time)
     * @param validBefore   The time before which this is valid (unix time)
     * @param nonce         Unique nonce
     * @param v             v of the signature
     * @param r             r of the signature
     * @param s             s of the signature
     */
    function _increaseAllowanceWithAuthorization(
        address owner,
        address spender,
        uint256 increment,
        uint256 validAfter,
        uint256 validBefore,
        bytes32 nonce,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        _requireValidAuthorization(owner, nonce, validAfter, validBefore);

        bytes memory data = abi.encode(
            INCREASE_ALLOWANCE_WITH_AUTHORIZATION_TYPEHASH,
            owner,
            spender,
            increment,
            validAfter,
            validBefore,
            nonce
        );
        require(
            EIP712.recover(DOMAIN_SEPARATOR, v, r, s, data) == owner,
            "FiatTokenV2: invalid signature"
        );

        _markAuthorizationAsUsed(owner, nonce);
        _increaseAllowance(owner, spender, increment);
    }

    /**
     * @notice Verify a signed authorization for a decrease in the allowance
     * granted to the spender and execute if valid
     * @param owner         Token owner's address (Authorizer)
     * @param spender       Spender's address
     * @param decrement     Amount of decrease in allowance
     * @param validAfter    The time after which this is valid (unix time)
     * @param validBefore   The time before which this is valid (unix time)
     * @param nonce         Unique nonce
     * @param v             v of the signature
     * @param r             r of the signature
     * @param s             s of the signature
     */
    function _decreaseAllowanceWithAuthorization(
        address owner,
        address spender,
        uint256 decrement,
        uint256 validAfter,
        uint256 validBefore,
        bytes32 nonce,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        _requireValidAuthorization(owner, nonce, validAfter, validBefore);

        bytes memory data = abi.encode(
            DECREASE_ALLOWANCE_WITH_AUTHORIZATION_TYPEHASH,
            owner,
            spender,
            decrement,
            validAfter,
            validBefore,
            nonce
        );
        require(
            EIP712.recover(DOMAIN_SEPARATOR, v, r, s, data) == owner,
            "FiatTokenV2: invalid signature"
        );

        _markAuthorizationAsUsed(owner, nonce);
        _decreaseAllowance(owner, spender, decrement);
    }

    /**
     * @notice Verify a signed approval authorization and execute if valid
     * @param owner         Token owner's address (Authorizer)
     * @param spender       Spender's address
     * @param value         Amount of allowance
     * @param validAfter    The time after which this is valid (unix time)
     * @param validBefore   The time before which this is valid (unix time)
     * @param nonce         Unique nonce
     * @param v             v of the signature
     * @param r             r of the signature
     * @param s             s of the signature
     */
    function _approveWithAuthorization(
        address owner,
        address spender,
        uint256 value,
        uint256 validAfter,
        uint256 validBefore,
        bytes32 nonce,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        _requireValidAuthorization(owner, nonce, validAfter, validBefore);

        bytes memory data = abi.encode(
            APPROVE_WITH_AUTHORIZATION_TYPEHASH,
            owner,
            spender,
            value,
            validAfter,
            validBefore,
            nonce
        );
        require(
            EIP712.recover(DOMAIN_SEPARATOR, v, r, s, data) == owner,
            "FiatTokenV2: invalid signature"
        );

        _markAuthorizationAsUsed(owner, nonce);
        _approve(owner, spender, value);
    }

    /**
     * @notice Attempt to cancel an authorization
     * @param authorizer    Authorizer's address
     * @param nonce         Nonce of the authorization
     * @param v             v of the signature
     * @param r             r of the signature
     * @param s             s of the signature
     */
    function _cancelAuthorization(
        address authorizer,
        bytes32 nonce,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        _requireUnusedAuthorization(authorizer, nonce);

        bytes memory data = abi.encode(
            CANCEL_AUTHORIZATION_TYPEHASH,
            authorizer,
            nonce
        );
        require(
            EIP712.recover(DOMAIN_SEPARATOR, v, r, s, data) == authorizer,
            "FiatTokenV2: invalid signature"
        );

        _authorizationStates[authorizer][nonce] = AuthorizationState.Canceled;
        emit AuthorizationCanceled(authorizer, nonce);
    }

    /**
     * @notice Check that an authorization is unused
     * @param authorizer    Authorizer's address
     * @param nonce         Nonce of the authorization
     */
    function _requireUnusedAuthorization(address authorizer, bytes32 nonce)
        private
        view
    {
        require(
            _authorizationStates[authorizer][nonce] ==
                AuthorizationState.Unused,
            "FiatTokenV2: authorization is used or canceled"
        );
    }

    /**
     * @notice Check that authorization is valid
     * @param authorizer    Authorizer's address
     * @param nonce         Nonce of the authorization
     * @param validAfter    The time after which this is valid (unix time)
     * @param validBefore   The time before which this is valid (unix time)
     */
    function _requireValidAuthorization(
        address authorizer,
        bytes32 nonce,
        uint256 validAfter,
        uint256 validBefore
    ) private view {
        require(
            now > validAfter,
            "FiatTokenV2: authorization is not yet valid"
        );
        require(now < validBefore, "FiatTokenV2: authorization is expired");
        _requireUnusedAuthorization(authorizer, nonce);
    }

    /**
     * @notice Mark an authorization as used
     * @param authorizer    Authorizer's address
     * @param nonce         Nonce of the authorization
     */
    function _markAuthorizationAsUsed(address authorizer, bytes32 nonce)
        private
    {
        _authorizationStates[authorizer][nonce] = AuthorizationState.Used;
        emit AuthorizationUsed(authorizer, nonce);
    }
}
/**
 * @title Gas Abstraction
 * @notice Provide internal implementation for gas-abstracted transfers and
 * approvals
 * @dev Contracts that inherit from this must wrap these with publicly
 * accessible functions, optionally adding modifiers where necessary
 */
function _cancelAuthorization(
        address authorizer,
        bytes32 nonce,
        uint8 v,
        bytes32 r,
        bytes32 s
    ) internal {
        _requireUnusedAuthorization(authorizer, nonce);

        bytes memory data = abi.encode(
            CANCEL_AUTHORIZATION_TYPEHASH,
            authorizer,
            nonce
        );
        require(
            EIP712.recover(DOMAIN_SEPARATOR, v, r, s, data) == authorizer,
            "FiatTokenV2: invalid signature"
        );

        _authorizationStates[authorizer][nonce] = AuthorizationState.Canceled;
        emit AuthorizationCanceled(authorizer, nonce);
    }
/**
 * @notice Attempt to cancel an authorization
 * @param authorizer    Authorizer's address
 * @param nonce         Nonce of the authorization
 * @param v             v of the signature
 * @param r             r of the signature
 * @param s             s of the signature
 */