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  • common_reqs.py 26.27 KiB
    from re import M
    from typing import Optional
    
    from z3 import And, Const, Consts, Exists, ExprRef, ModelRef, Not, Or, Solver
    
    from .error_desc_helper import get_user_friendly_name
    from .imc import Requirement, RequirementStore, SMTEncoding, SMTSorts
    from .intermediate_model import DOMLVersion, IntermediateModel
    
    
    def get_consts(smtsorts: SMTSorts, consts: list[str]) -> list[ExprRef]:
        return Consts(" ".join(consts), smtsorts.element_sort)
    
    
    # Assertions
    
    def vm_iface(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        vm, iface = get_consts(smtsorts, ["vm", "iface"])
        return And(
            smtenc.element_class_fun(vm) == smtenc.classes["infrastructure_VirtualMachine"],
            Not(
                Exists(
                    [iface],
                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], iface)
                )
            )
        )
    
    # All software packages can see the interfaces they need through a common network.
    def software_package_iface_net(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        asc_consumer, asc_exposer, siface, net, net_iface, cnode, cdeployment, enode, edeployment, vm = get_consts(
            smtsorts,
            ["asc_consumer", "asc_exposer", "siface", "net", "net_iface", "cnode", "cdeployment", "enode", "edeployment", "vm"]
        )
        return And(
            smtenc.association_rel(asc_consumer, smtenc.associations["application_SoftwareComponent::exposedInterfaces"], siface),
            smtenc.association_rel(asc_exposer, smtenc.associations["application_SoftwareComponent::consumedInterfaces"], siface),
            Not(
                Exists(
                    [cdeployment, cnode, edeployment, enode, net],
                    And(
                        smtenc.association_rel(cdeployment, smtenc.associations["commons_Deployment::component"], asc_consumer),
                        smtenc.association_rel(cdeployment, smtenc.associations["commons_Deployment::node"], cnode),
                        Exists(
                            [vm, net_iface],
                            Or(
                                And(  # asc_consumer is deployed on a component with an interface in network n
                                    smtenc.association_rel(cnode, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                                And(  # asc_consumer is deployed on a container hosted in a VM with an interface in network n
                                    smtenc.association_rel(cnode, smtenc.associations["infrastructure_Container::hosts"], vm),
                                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                                And(  # asc_consumer is deployed on a VM in an AutoScalingGroup with an interface in network n
                                    smtenc.association_rel(cnode, smtenc.associations["infrastructure_AutoScalingGroup::machineDefinition"], vm),
                                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                            )
                        ),
                        smtenc.association_rel(edeployment, smtenc.associations["commons_Deployment::component"], asc_exposer),
                        smtenc.association_rel(edeployment, smtenc.associations["commons_Deployment::node"], enode),
                        Exists(
                            [vm, net_iface],
                            Or(
                                And(  # asc_exposer is deployed on a component with an interface in network n
                                    smtenc.association_rel(enode, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                                And(  # asc_exposer is deployed on a container hosted on a VM with an interface in network n
                                    smtenc.association_rel(enode, smtenc.associations["infrastructure_Container::hosts"], vm),
                                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                                And(  # asc_exposer is deployed on a VM in an AutoScalingGroup with an interface in network n
                                    smtenc.association_rel(enode, smtenc.associations["infrastructure_AutoScalingGroup::machineDefinition"], vm),
                                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                            )
                        )
                    )
                )
            )
        )
    
    
    def software_package_iface_net_v2_1(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        asc_consumer, asc_exposer, siface, net, net_iface, cnode, cdeployment, enode, edeployment, vm, cconf = get_consts(
            smtsorts,
            ["asc_consumer", "asc_exposer", "siface", "net", "net_iface", "cnode", "cdeployment", "enode", "edeployment", "vm", "cconf"]
        )
        return And(
            smtenc.association_rel(asc_consumer, smtenc.associations["application_SoftwareComponent::exposedInterfaces"], siface),
            smtenc.association_rel(asc_exposer, smtenc.associations["application_SoftwareComponent::consumedInterfaces"], siface),
            Not(
                Exists(
                    [cdeployment, cnode, edeployment, enode, net],
                    And(
                        smtenc.association_rel(cdeployment, smtenc.associations["commons_Deployment::component"], asc_consumer),
                        smtenc.association_rel(cdeployment, smtenc.associations["commons_Deployment::node"], cnode),
                        Exists(
                            [vm, net_iface, cconf],
                            Or(
                                And(  # asc_consumer is deployed on a component with an interface in network n
                                    smtenc.association_rel(cnode, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                                And(  # asc_consumer is deployed on a container hosted in a VM with an interface in network n
                                    smtenc.association_rel(cnode, smtenc.associations["infrastructure_Container::configs"], cconf),
                                    smtenc.association_rel(cconf, smtenc.associations["infrastructure_ContainerConfig::host"], vm),
                                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                                And(  # asc_consumer is deployed on a VM in an AutoScalingGroup with an interface in network n
                                    smtenc.association_rel(cnode, smtenc.associations["infrastructure_AutoScalingGroup::machineDefinition"], vm),
                                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                            )
                        ),
                        smtenc.association_rel(edeployment, smtenc.associations["commons_Deployment::component"], asc_exposer),
                        smtenc.association_rel(edeployment, smtenc.associations["commons_Deployment::node"], enode),
                        Exists(
                            [vm, net_iface, cconf],
                            Or(
                                And(  # asc_exposer is deployed on a component with an interface in network n
                                    smtenc.association_rel(enode, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                                And(  # asc_exposer is deployed on a container hosted on a VM with an interface in network n
                                    smtenc.association_rel(enode, smtenc.associations["infrastructure_Container::configs"], cconf),
                                    smtenc.association_rel(cconf, smtenc.associations["infrastructure_ContainerConfig::host"], vm),
                                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                                And(  # asc_exposer is deployed on a VM in an AutoScalingGroup with an interface in network n
                                    smtenc.association_rel(enode, smtenc.associations["infrastructure_AutoScalingGroup::machineDefinition"], vm),
                                    smtenc.association_rel(vm, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::belongsTo"], net),
                                ),
                            )
                        )
                    )
                )
            )
        )
    
    
    # There are no duplicated interfaces.
    def iface_uniq(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        endPointAttr = smtenc.attributes["infrastructure_NetworkInterface::endPoint"]
        ni1, ni2 = get_consts(smtsorts, ["ni1", "ni2"])
        value = Const("value", smtsorts.attr_data_sort)
        return And(
            smtenc.attribute_rel(ni1, endPointAttr, value),
            smtenc.attribute_rel(ni2, endPointAttr, value),
            ni1 != ni2,
        )
    
    # All software components have been deployed to some node.
    def all_SoftwareComponents_deployed(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        sc, deployment, ielem = get_consts(smtsorts, ["sc", "deployment", "ielem"])
        return And(
            smtenc.element_class_fun(sc) == smtenc.classes["application_SoftwareComponent"],
            Not(
                Exists(
                    [deployment, ielem],
                    And(
                        smtenc.association_rel(deployment, smtenc.associations["commons_Deployment::component"], sc),
                        smtenc.association_rel(deployment, smtenc.associations["commons_Deployment::node"], ielem),
                    )
                )
            )
        )
    
    # All abstract infrastructure elements are mapped to an element in the active concretization.
    def all_infrastructure_elements_deployed(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        def checkOneClass(ielem, concr, provider, celem, ielemClass, providerAssoc, celemAssoc):
            return And(
                smtenc.element_class_fun(ielem) == smtenc.classes[ielemClass],
                Not(
                    Exists(
                        [provider, celem],
                        And(
                            smtenc.association_rel(concr, smtenc.associations["concrete_ConcreteInfrastructure::providers"], provider),
                            smtenc.association_rel(provider, smtenc.associations[providerAssoc], celem),
                            smtenc.association_rel(celem, smtenc.associations[celemAssoc], ielem)
                        )
                    )
                )
            )
    
        ielem, concr, provider, celem = get_consts(smtsorts, ["ielem", "concr", "provider", "celem"])
        return And(
            smtenc.element_class_fun(concr) == smtenc.classes["concrete_ConcreteInfrastructure"],
            Or(
                checkOneClass(
                    ielem, concr, provider, celem,
                    "infrastructure_VirtualMachine",
                    "concrete_RuntimeProvider::vms",
                    "concrete_VirtualMachine::maps"
                ),
                checkOneClass(
                    ielem, concr, provider, celem,
                    "infrastructure_Network",
                    "concrete_RuntimeProvider::networks",
                    "concrete_Network::maps"
                ),
                checkOneClass(
                    ielem, concr, provider, celem,
                    "infrastructure_Storage",
                    "concrete_RuntimeProvider::storages",
                    "concrete_Storage::maps"
                ),
                checkOneClass(
                    ielem, concr, provider, celem,
                    "infrastructure_FunctionAsAService",
                    "concrete_RuntimeProvider::faas",
                    "concrete_FunctionAsAService::maps"
                ),
            )
        )
    
    # All elements in the active concretization are mapped to some abstract infrastructure element.
    def all_concrete_map_something(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        def checkOneClass(ielem, provider, celem, providerAssoc, celemAssoc):
            return And(
                smtenc.association_rel(provider, smtenc.associations[providerAssoc], celem),
                Not(
                    Exists(
                        [ielem],
                        smtenc.association_rel(celem, smtenc.associations[celemAssoc], ielem)
                    )
                )
            )
    
        ielem, concr, provider, celem = get_consts(smtsorts, ["ielem", "concr", "provider", "celem"])
        return And(
            smtenc.element_class_fun(concr) == smtenc.classes["concrete_ConcreteInfrastructure"],
            smtenc.association_rel(concr, smtenc.associations["concrete_ConcreteInfrastructure::providers"], provider),
            Or(
                checkOneClass(
                    ielem, provider, celem,
                    "concrete_RuntimeProvider::vms",
                    "concrete_VirtualMachine::maps"
                ),
                checkOneClass(
                    ielem, provider, celem,
                    "concrete_RuntimeProvider::vmImages",
                    "concrete_VMImage::maps"
                ),
                checkOneClass(
                    ielem, provider, celem,
                    "concrete_RuntimeProvider::containerImages",
                    "concrete_ContainerImage::maps"
                ),
                checkOneClass(
                    ielem, provider, celem,
                    "concrete_RuntimeProvider::networks",
                    "concrete_Network::maps"
                ),
                checkOneClass(
                    ielem, provider, celem,
                    "concrete_RuntimeProvider::storages",
                    "concrete_Storage::maps"
                ),
                checkOneClass(
                    ielem, provider, celem,
                    "concrete_RuntimeProvider::faas",
                    "concrete_FunctionAsAService::maps"
                ),
                checkOneClass(
                    ielem, provider, celem,
                    "concrete_RuntimeProvider::group",
                    "concrete_ComputingGroup::maps"
                ),
            )
        )
    
    # def sw_components_have_source_code_property(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
    #     sw_comp, prop = get_consts(smtsorts, ["sw_comp prop"])
    
    #     big_x = smtsorts.attr_data_sort.ss(smtenc.str_symbols["source_code"])
    
    #     return And(
    #         smtenc.element_class_fun(sw_comp) == smtenc.classes["application_SoftwareComponent"],
    #         Not(
    #             Exists([prop], And(
    #                 smtenc.element_class_fun(prop) == smtenc.classes["commons_SProperty"],
    #                 smtenc.attribute_rel(prop, smtenc.attributes["commons_Property::key"], big_x),
    #                 smtenc.association_rel(sw_comp, smtenc.associations["commons_DOMLElement::annotations"], prop)
    #             ))
    #         )
    #     )
    
    def security_group_must_have_iface(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        sg, iface = get_consts(smtsorts, ["sg iface"])
        return And(
            smtenc.element_class_fun(sg) == smtenc.classes["infrastructure_SecurityGroup"],
            Not(Exists([iface], 
                smtenc.association_rel(iface, smtenc.associations["infrastructure_NetworkInterface::associated"], sg)
            ))
        )
    
    # TODO: Check if HTTP should be disabled too
    def external_services_must_have_https(smtenc: SMTEncoding, smtsorts: SMTSorts) -> ExprRef:
        saas, sw_iface, sw_comp, deployment, ielem, net_iface, sec_group, rule = get_consts(smtsorts, 
            ["saas, sw_iface, sw_comp, deployment, ielem, net_iface, sec_group, rule"])
        return And(
            smtenc.element_class_fun(saas) == smtenc.classes["application_SaaS"],
            smtenc.element_class_fun(sec_group) == smtenc.classes["infrastructure_SecurityGroup"],
            Not(Exists([sw_iface, sw_comp, deployment, ielem, net_iface, rule],
                And(
                    smtenc.association_rel(saas, smtenc.associations["application_SaaS::exposedInterfaces"], sw_iface),
                    smtenc.association_rel(sw_comp, smtenc.associations["application_SoftwareComponent::consumedInterfaces"], sw_iface),
                    smtenc.association_rel(deployment, smtenc.associations["commons_Deployment::component"], sw_comp),
                    smtenc.association_rel(deployment, smtenc.associations["commons_Deployment::node"], ielem),
                    smtenc.association_rel(ielem, smtenc.associations["infrastructure_ComputingNode::ifaces"], net_iface),
                    smtenc.association_rel(net_iface, smtenc.associations["infrastructure_NetworkInterface::associated"], sec_group),
                    smtenc.association_rel(sec_group, smtenc.associations["infrastructure_SecurityGroup::rules"], rule),
                    smtenc.attribute_rel(rule, smtenc.attributes["infrastructure_Rule::fromPort"], smtsorts.attr_data_sort.int(443)),
                    smtenc.attribute_rel(rule, smtenc.attributes["infrastructure_Rule::toPort"], smtsorts.attr_data_sort.int(443)),
                    smtenc.attribute_rel(rule, smtenc.attributes["infrastructure_Rule::kind"], smtsorts.attr_data_sort.ss(smtenc.str_symbols["INGRESS"]))
                )
            ))
        )
    
    # Error Descriptions
    
    def ed_vm_iface(solver: Solver, smtsorts: SMTSorts, intermediate_model: IntermediateModel) -> str:
        vm = Const("vm", smtsorts.element_sort)
        vm_name = get_user_friendly_name(intermediate_model, solver.model(), vm)
        if vm_name:
            return f"Virtual machine {vm_name} is connected to no network interface."
        else:
            return "A virtual machine is connected to no network interface."
    
    
    def ed_software_package_iface_net(solver: Solver, smtsorts: SMTSorts, intermediate_model: IntermediateModel) -> str:
        asc_consumer, asc_exposer, siface = get_consts(
            smtsorts,
            ["asc_consumer", "asc_exposer", "siface"]
        )
        model = solver.model()
        asc_consumer_name = get_user_friendly_name(intermediate_model, model, asc_consumer)
        asc_exposer_name = get_user_friendly_name(intermediate_model, model, asc_exposer)
        siface_name = get_user_friendly_name(intermediate_model, model, siface)
        if asc_consumer_name and asc_exposer_name and siface_name:
            return (
                f"Software components '{asc_consumer_name}' and '{asc_exposer_name}' "
                f"are supposed to communicate through interface '{siface_name}', "
                "but they are deployed to nodes that cannot communicate through a common network."
            )
        else:
            return "A software package is deployed on a node that has no access to an interface it consumes."
    
    
    def ed_iface_uniq(solver: Solver, smtsorts: SMTSorts, intermediate_model: IntermediateModel) -> str:
        ni1, ni2 = get_consts(smtsorts, ["ni1", "ni2"])
        model = solver.model()
        ni1_name = get_user_friendly_name(intermediate_model, model, ni1)
        ni2_name = get_user_friendly_name(intermediate_model, model, ni2)
        if ni1_name and ni2_name:
            return f"Network interfaces '{ni1_name}' and '{ni2_name}' share the same IP address."
        else:
            return "Two network interfaces share the same IP address."
    
    
    def ed_all_SoftwareComponents_deployed(solver: Solver, smtsorts: SMTSorts, intermediate_model: IntermediateModel) -> str:
        sc = Const("sc", smtsorts.element_sort)
        sc_name = get_user_friendly_name(intermediate_model, solver.model(), sc)
        if sc_name:
            return f"Software component '{sc_name}' is not deployed to any abstract infrastructure node."
        else:
            return "A software component is not deployed to any abstract infrastructure node."
    
    
    def ed_all_infrastructure_elements_deployed(solver: Solver, smtsorts: SMTSorts, intermediate_model: IntermediateModel) -> str:
        ielem = Const("ielem", smtsorts.element_sort)
        ielem_name = get_user_friendly_name(intermediate_model, solver.model(), ielem)
        if ielem_name:
            return f"Abstract infrastructure element '{ielem_name}' has not been mapped to any element in the active concretization."
        else:
            return "An abstract infrastructure element has not been mapped to any element in the active concretization."
    
    
    def ed_all_concrete_map_something(solver: Solver, smtsorts: SMTSorts, intermediate_model: IntermediateModel) -> str:
        celem = Const("celem", smtsorts.element_sort)
        celem_name = get_user_friendly_name(intermediate_model, solver.model(), celem)
        if celem_name:
            return f"Concrete infrastructure element '{celem_name}' is mapped to no abstract infrastructure element."
        else:
            return "A concrete infrastructure element is mapped to no abstract infrastructure element."
    
    def ed_security_group_must_have_iface(solver: Solver, smtsorts: SMTSorts, intermediate_model: IntermediateModel) -> str:
        sg = Const("sg", smtsorts.element_sort)
        sg_name = get_user_friendly_name(intermediate_model, solver.model(), sg)
        if  sg_name:
            return f"Security group '{sg_name}' is not associated with any network interface."
        else:
            return "A network interface doesn't belong to any security group, or a security group is not associated with any network interface."
    
    def ed_external_services_must_have_https(solver: Solver, smtsorts: SMTSorts, intermediate_model: IntermediateModel) -> str:
        saas = Const("saas", smtsorts.element_sort)
        saas_name = get_user_friendly_name(intermediate_model, solver.model(), saas)
    
        if saas_name:
            return "A Security Group doesn't have a rule to access external service (SaaS) named '{saas_name}' through HTTPS (port 443)."
        else:
            return "A Security Group doesn't have a rule to access an external service (SaaS) through HTTPS (port 443)."
    
    RequirementLists = {
        DOMLVersion.V1_0: [
            (vm_iface, "vm_iface", "All virtual machines must be connected to at least one network interface.", ed_vm_iface),
            (software_package_iface_net, "software_package_iface_net", "All software packages can see the interfaces they need through a common network.", ed_software_package_iface_net),
            (iface_uniq, "iface_uniq", "There are no duplicated interfaces.", ed_iface_uniq),
            (all_SoftwareComponents_deployed, "all_SoftwareComponents_deployed", "All software components have been deployed to some node.", ed_all_SoftwareComponents_deployed),
            (all_infrastructure_elements_deployed, "all_infrastructure_elements_deployed", "All abstract infrastructure elements are mapped to an element in the active concretization.", ed_all_infrastructure_elements_deployed),
            (all_concrete_map_something, "all_concrete_map_something", "All elements in the active concretization are mapped to some abstract infrastructure element.", ed_all_concrete_map_something)
        ],
        DOMLVersion.V2_0: [
            (vm_iface, "vm_iface", "All virtual machines must be connected to at least one network interface.", ed_vm_iface),
            (software_package_iface_net, "software_package_iface_net", "All software packages can see the interfaces they need through a common network.", ed_software_package_iface_net),
            (iface_uniq, "iface_uniq", "There are no duplicated interfaces.", ed_iface_uniq),
            (all_SoftwareComponents_deployed, "all_SoftwareComponents_deployed", "All software components have been deployed to some node.", ed_all_SoftwareComponents_deployed),
            (all_infrastructure_elements_deployed, "all_infrastructure_elements_deployed", "All abstract infrastructure elements are mapped to an element in the active concretization.", ed_all_infrastructure_elements_deployed),
            (all_concrete_map_something, "all_concrete_map_something", "All elements in the active concretization are mapped to some abstract infrastructure element.", ed_all_concrete_map_something),
            (security_group_must_have_iface, "security_group_must_have_iface", "All security group should be a associated to a network interface", ed_security_group_must_have_iface),
            (external_services_must_have_https, "external_services_must_have_https", "All external SaaS should be accessed through HTTPS.", ed_external_services_must_have_https)
        ],
        DOMLVersion.V2_1: [
            (vm_iface, "vm_iface", "All virtual machines must be connected to at least one network interface.", ed_vm_iface),
            (software_package_iface_net_v2_1, "software_package_iface_net", "All software packages can see the interfaces they need through a common network.", ed_software_package_iface_net),
            (iface_uniq, "iface_uniq", "There are no duplicated interfaces.", ed_iface_uniq),
            (all_SoftwareComponents_deployed, "all_SoftwareComponents_deployed", "All software components have been deployed to some node.", ed_all_SoftwareComponents_deployed),
            (all_infrastructure_elements_deployed, "all_infrastructure_elements_deployed", "All abstract infrastructure elements are mapped to an element in the active concretization.", ed_all_infrastructure_elements_deployed),
            (all_concrete_map_something, "all_concrete_map_something", "All elements in the active concretization are mapped to some abstract infrastructure element.", ed_all_concrete_map_something)
        ],
    }
    
    
    CommonRequirements = {ver: RequirementStore([Requirement(*rt, flipped=True) for rt in reqs]) for ver, reqs in RequirementLists.items()}