CN115687166A - Formal verification method and system - Google Patents
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Abstract
The invention discloses a formal verification method and a formal verification system, and belongs to the technical field of computer software design and test. The method comprises the following steps: the following operations are performed in the Isabelle environment: building a basic execution model of an operating system represented by a state machine; describing the function point requirements of the operating system by using a meta language according to a basic execution model to obtain the requirement formalization specification of the operating system, and verifying the correctness; describing a data structure and an algorithm flow of the operating system by using a state list to obtain a design formalization specification of the operating system, and verifying design conformity; describing a source code of an operating system by adopting Simpl language to obtain a source code formalization specification of the operating system; and verifying the correctness and the conformity by using Simpl Hall logic. The invention has higher universality, is convenient for automatic realization, and can be applied to the verification of the operating system in various safety critical fields.
Description
Technical Field
The invention belongs to the technical field of computer software design and test, and particularly relates to a formal verification method and a formal verification system for an embedded operating system.
Background
As the bottom layer supporters and managers of the software, the safety and the reliability of the operating system are particularly important, and a tiny bug can cause the breakdown of the whole system. However, because the operating system has a complex structure, it is difficult for developers to ensure that the functional design of the operating system can completely meet the corresponding safety specifications, and therefore, researchers generally adopt a strict formal verification method to design and implement the operating system.
Currently, in the research of operating system formalization, formalization verification of a micro kernel, a partition operating system and a kernel is mainly included. And the L4.Verified item completes the correctness verification of the microkernel source program of the L4 operating system: there is no deadlock, livelock, null pointer usage, buffer overflow, arithmetic exceptions, and use of uninitialized variables. The INTERGRITY-178B separation kernel completes EAL6+ level verification, and the AAPM7G isolation processor completes EAL7 level verification.
Although the existing formalization method has a good effect in industrial practice, the problems of incomplete verification degree, low verification efficiency and the like still exist when the formalization method is adopted for verifying the operating system. Firstly, most operating system formal verification only performs functional correctness verification on individual key modules or verifies system security at a high abstraction level, but not overall verification from an attribute end to a source code end. But the overall security of the operating system requires that the interaction behavior of all the constituent modules does not violate the security attributes and that the source code achieve consistency with the security attributes. Secondly, although the formalization method is approved in terms of ensuring the security, correctness and reliability of the software, the formalization method is limited by the verification efficiency, and thus has not been widely applied in the industry. Thus, for some embedded operating systems, such as complex group intelligence operating systems, current automated formal verification techniques are not adaptable to the scale of these systems.
Disclosure of Invention
The invention discloses a formal verification method and a formal verification system for an operating system, which are used for realizing multi-level specification description and safety verification from an attribute level to a source code level for an embedded operating system.
In the 1 st aspect of the invention, a formal verification method is disclosed, which is used for formally verifying an embedded operating system, and comprises the following steps: the following operations are performed in the Isabelle environment:
building a basic execution model of an operating system represented by a state machine; describing the function point requirement of the operating system by using a meta language according to the basic execution model to obtain a requirement formalization specification of the operating system;
verifying the requirement correctness of the operating system based on the requirement formalization specification;
describing a data structure and an algorithm flow of the operating system by using a state list to obtain a design formalization specification of the operating system;
constructing a refinement relationship between the requirement formalization specification and the design formalization specification to verify design compliance of the operating system;
describing the source code of the operating system by adopting Simpl language to obtain the source code formalization specification of the operating system;
and verifying the correctness and the conformity of the source code formalization specification by using Simpl Hall logic.
In other embodiments, the building of the basic execution model of the operating system represented by the state machine includes: constructing a basic execution model covering the basic object of the operating system, and representing the basic execution model by using a state machine; wherein the state machine comprises states and actions, the states comprising basic objects and abstract data structures of the operating system, the actions comprising basic actions and system calls of the operating system.
In other embodiments, the state machine is formally described by adopting an inductive structure execution path, the execution path includes a system state of each step of operation, a head of each execution path is a system state before operation, a tail of each execution path is a system state after operation, all execution paths which meet the conversion of the two system states are induced to form an execution path set for representing the operation of the operating system, and all the system states and the execution path set are combined to obtain the basic execution model represented by the state machine.
In other embodiments, the verifying the requirement correctness of the operating system based on the requirement formalization specification includes: and verifying whether the pre-state and the post-state of each operation of the operating system meet the invariance property.
In other embodiments, the constructing a refinement relationship between the requirement formalization specification and the design formalization specification to verify the design compliance of the operating system includes:
respectively constructing state-event track sets of the requirement formalization specification and the design formalization specification, and comparing the state-event track sets of the requirement formalization specification and the design formalization specification to obtain a state variable set and an event set which are added to the design formalization specification relative to the requirement formalization specification;
and judging whether the newly added state variable set and the event set meet the refinement relation of a preset condition.
In other embodiments, the design formalization specification uses record to define data structures and module states and definition to define a state sheet design specification.
In the 2 nd aspect of the invention, a formal verification system is disclosed, which is used for performing formal verification on an embedded operating system and comprises the following units which run in an Isabelle environment:
a requirement formalization unit configured to: building a basic execution model of an operating system represented by a state machine; describing the function point requirement of the operating system by using a meta language according to the basic execution model to obtain a requirement formalization specification of the operating system;
a requirement verification unit configured to: verifying the requirement correctness of the operating system based on the requirement formalization specification;
a design formalization unit configured to: describing a data structure and an algorithm flow of the operating system by using a state list to obtain a design formalization specification of the operating system;
a design verification unit configured to: constructing a refinement relationship between the requirement formalization specification and the design formalization specification to verify design compliance of the operating system;
an implementation formalization unit configured to: describing the source code of the operating system by adopting Simpl language to obtain the source code formalization specification of the operating system; and
an implementation verification unit configured to: and verifying the correctness and the conformity of the source code formalization specification by using Simpl Hall logic.
In other embodiments, the verifying the correctness of the operating system requirement by the requirement verifying unit includes: and verifying whether the pre-state and the post-state of each operation of the operating system meet the invariance property.
In other embodiments, the design verification unit includes:
a comparison module configured to: respectively constructing state-event track sets of the requirement formalization specification and the design formalization specification, and comparing the state-event track sets of the requirement formalization specification and the design formalization specification to obtain a state variable set and an event set which are newly added to the design formalization specification relative to the requirement formalization specification;
a verification module configured to: and judging whether the newly added state variable set and the event set meet the refinement relation of a preset condition.
The method has better universality, can be directly applied to various safety key fields, and can ensure that the operating system reaches the CC authentication standard. Meanwhile, the method is convenient for automatic realization, thereby reducing the labor cost input and having an important promotion effect on the autonomous control of high-safety and reliable software.
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Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments thereof, made with reference to the following drawings:
FIG. 1 is a schematic diagram of a technical architecture for hierarchical construction and validation of an operating system according to the present invention;
fig. 2 is a flowchart illustrating a formal verification method of an operating system according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant invention and not restrictive of the invention. It should be noted that, for convenience of description, only the portions related to the related invention are shown in the drawings.
It should be noted that the embodiments and features of the embodiments may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
Interpretation of terms:
Isabelle/HOL: the method is a formalized method and tool environment with industrial maturity, and the formal proof resource library comprises more than 300 open source items, and 150 more than ten thousand rows of formal conventions and proofs in total.
ROS: is an english abbreviation of Robot Operating System (Robot Operating System).
The invention takes an embedded operating system as an example, carries out layered construction and verification on the operating system, divides main modules of formal verification of the operating system into six main modules, namely formal specification of requirements, formal specification of design, formal specification of source codes, correctness verification of requirements, conformance verification of design and conformance verification of the source codes, and the relationship among the modules is shown in figure 1. The modules are in an import relationship, namely after the upper-layer module is developed, the modules are imported to the lower-layer module for multiplexing as a basis. Meanwhile, in the formal verification module, modules of upper and lower layers need to be introduced to verify the compliance between the upper and lower layers, and the verification architecture is shown in fig. 1.
According to an aspect of the present invention, there is disclosed an embedded operating system formal verification method executed in an Isabelle environment, as shown in fig. 2, the method comprising the steps of:
step 1, constructing a basic execution model of an operating system represented by a state machine; and describing the function point requirement of the operating system by using a meta language according to the basic execution model to obtain the requirement formalization specification of the operating system.
In order to describe the complete requirements of a certain operating system, the application first establishes a basic execution model of the operating system, wherein the model comprises functions of process (thread) scheduling, memory management and the like, and then forms a requirement formalization specification by combining with a function point formalization specification of a specific operating system.
Based on the structure of the reaction type system, a basic execution model of the operating system is constructed, basic objects such as threads, a basic scheduler, system calls and the like of the operating system are covered, and the execution model is given in a state machine mode. Illustratively, the state machine model is formally represented using an inductively constructed execution path that contains the system state for each step of execution.
In some examples, the step specifically includes:
and 11, constructing a state machine model.
The state machine model includes two parts, a state and an action. Wherein a state is an abstract data structure of a base object and an operating system, and actions are base actions and system calls of the operating system.
The state machine model is formally described by inductively constructing an execution path, wherein the execution path comprises the system state executed by each step. The head of each execution path is the system state before conversion, the tail is the system state after conversion, and all paths which are in accordance with the conversion of the two states are summarized to form an execution path set for representing the operation of the operating system. And combining all the state and execution path sets to obtain a basic execution model represented by a state machine.
And step 12, according to the function point requirements of the actual operating system, according to the previously constructed system basic execution model, in the environment of a theorem proving tool Isabelle, performing instantiation modeling on the function point requirements based on an Isabelle meta language to obtain the formalization specification of the function point requirements.
And 2, verifying the requirement correctness of the operating system based on the requirement formalization specification.
After the formal specification construction of the operating system requirements is completed, the invariants are used to define the correctness of the operating system requirements, namely whether the before and after states of each operation of the operating system meet the invariants is verified. The method specifically comprises the following steps:
and step 21, constructing the invariance property comprising an initial part, a maintaining part and a terminating part.
Initialization means that it is guaranteed that the invariance is true at the time of initialization. By held is meant that the invariance is true at the beginning and end of each operation. Termination refers to the process being terminated if it can be terminated under certain conditions, at which time the process can achieve the correct result desired.
And step 22, performing derivation verification on the invariance property on the front and back states of each operation based on an Isabelle tool, namely the front and back states of each operation can meet the property.
And step 23, summarizing all reachable paths from the initial state S0, and verifying that all states in all reachability sets conform to the property.
And summarizing all reachable paths starting from the initial state S0, and verifying that all states in all reachability sets conform to the property, so that the unmanned aerial vehicle operating system is proved to meet the property in each operation, and required correctness verification is completed.
And 3, describing a data structure and an algorithm flow of the operating system by using a state list to obtain a design formalization specification of the operating system.
The formal specification of the operating system design mainly includes specific data structures and algorithm flows in the operating system. The method specifically comprises the following steps:
and step 31, establishing a state list basic model.
The State Monad basic model comprises a basic State Monad function, a State Monad statement, exception capture and processing and circulation.
The basic state monaural function includes: the method comprises the steps of returning a function, binding the function, obtaining the function and setting the function.
The state sheet statement includes: the set element selection statement, the set union statement, the state selection statement, the failure statement, the assertion statement, the acquisition statement, the modification statement, the conditional decision statement and the exception statement.
The exception capture and handling comprises: capture exceptions, handle exceptions, exception handlers.
The circulation comprises the following steps: loop result set, loop abort, while loop, exception loop.
And 32, establishing a data structure formalization specification, and formalizing and modeling the data structure in a functional language mode by using a state single function and a state single statement.
And step 33, establishing a formal specification of the algorithm flow, formally describing the algorithm flow through a state list statement, a state list basic function, exception capture, processing and circulation according to the formally described data structure, and establishing the formal specification of the algorithm flow.
And 4, constructing a refinement relation between the requirement formalized specification and the design formalized specification so as to verify the design compliance of the operating system.
The present invention ensures that the design specification conforms to all of the proven theorems/lemmas of the demand specification through strict refinement certification. The method specifically comprises the following steps:
and step 41, defining a state sheet Hall logic rule.
Hall Logic (Floyd-Home Logic) is a form of Logic used for verification of the correctness of a computer system. The Hall triplet { P } f { Q } is the most basic formulation in Hall logic. Where the pre-assertion P represents the pre-condition, f represents the algorithm executed, and the post-assertion Q represents the post-condition. And if the state is stopped and stopped in the state described by the post condition Q, the Hall triple { P } f { Q } is called true.
And 42, constructing a state-event track set of the requirement layer and the design layer, and comparing states and events in the two sets described by the requirement layer specification and the design layer specification to obtain a newly added state variable set and a newly added event set in the design layer specification.
And 43, verifying the conformity refinement relation of the requirement layer and the design layer.
The formal specification of the design layer is defined as a state machine M: m = (S, E, Φ, S0). Where S is the state space, E is the event set, S0 is the initial state, φ: E → (S, S) is the state transition function. According to the newly added state variable set in the design layer specification obtained in step 42, verification of the refinement relationship is performed in the following manner, that is, the refinement relationship of the newly added state variable set satisfying the following conditions is verified:
(1) Given a requirement layer Specification M S And design layer Specification M D Using a state refinement function R S ：S S →S D And event refinement function: r is E ：e S →e D U { τ } performs refinement mapping, and refinement that satisfies a certain design layer state is a certain demand layer state; where τ refers to an event without any action.
(2) The event refinement function is a fill-shot and satisfies: 8704est R E e≠τ 
(s,t) ∈φ D e → (R S s, R S t) ∈φ S (R E e)。
(3) The newly added state in the design layer cannot change the state of the demand layer, i.e.: 8704est R E e＝τ 
(s,t) ∈φ D e → R S s ＝ R S t。
And 5, describing the source code of the operating system by adopting Simpl language to obtain the source code formalization specification of the operating system.
Illustratively, the operating system derives a formalized specification of the source code based on a C/C + + code implementation. The invention adopts Simpl language to establish the formal specification of the source code of the operating system, the formal specification of the source code is equivalent to the C/C + + code in semantics, and the C/C + + code can be verified after the formal specification of the source code is verified.
The source code formalization specification is established by defining the grammar of the Simpl language and the semantics of the Simpl language and describing each C/C + + code by the Simpl language.
And 6, verifying the correctness and the conformity of the source code formalization specification by using Simpl Hall logic.
The source code correctness verification and the conformance verification are completed under an Isabelle theorem proving tool, and the conformance verification can be completed by the design layer specification and the source code specification based on a unified theorem prover. Specifically, the method for verifying the correctness of the source code specification based on the Hall logic and verifying the source code layer conformance design of the operating system based on the correctness of the source code specification comprises the following steps of:
and step 61, verifying the correctness of the source code formalization specification by adopting Simpl Hall logic.
The source code formalization specification is established correspondingly according to the C/C + + source code by adopting Simpl language, and the source code correctness verification is ensured to pass. And the verification is passed, which means that the source code is verified to be correct.
And step 62, verifying the conformity.
If the corresponding state can be found in the design layer specification, the state expressed by the source code formalization specification represents that the conformity verification is passed; otherwise, checking the source code formalization specification and the source code implementation, searching for problems, and performing conformance verification again until the verification is passed.
The formal verification method for the operating system provided by the invention has higher universality and applicability, and can be directly applied to various safety key fields including unmanned vehicles, unmanned aerial vehicles, aviation, aerospace, rail transit and the like.
The formal verification method provided by the invention can enable the operating system to reach the standard of CC authentication, realizes certain degree of automation, reduces the investment of labor cost, and has an important promotion effect on the autonomous control of high-safety and reliable software.
According to another aspect of the present invention, there is also disclosed a formal verification system for an operating system, the system comprising the following elements operating in an Isabelle environment:
a demand formalization unit configured to: building a basic execution model of an operating system represented by a state machine; and describing the function point requirement of the operating system by using a meta language in an Isabelle environment according to the basic execution model to obtain a requirement formalization specification of the operating system.
A requirement verification unit configured to: verifying the requirement correctness of the operating system based on the requirement formalization specification. Specifically, it is verified whether the pre-and post-state of each operation of the operating system satisfies the invariance property.
A design formalization unit configured to: and describing a data structure and an algorithm flow of the operating system by using a state sheet in an Isabelle environment to obtain a design formalization specification of the operating system.
A design verification unit configured to: constructing a refinement relationship between the requirement formalization specification and the design formalization specification to verify design compliance of the operating system.
Illustratively, the design verification unit includes:
a comparison module configured to: and respectively constructing state-event track sets of the requirement formalization specification and the design formalization specification, and comparing the state-event track sets of the requirement formalization specification and the design formalization specification to obtain a state variable set and an event set which are newly added to the design formalization specification relative to the requirement formalization specification.
A verification module configured to: and judging whether the newly added state variable set and the event set meet the refinement relation of a preset condition.
An implementation formalization unit configured to: and describing the source code of the operating system by adopting Simpl language to obtain the source code formalization specification of the operating system.
An implementation verification unit configured to: and verifying the correctness and the conformity of the source code formalization specification by using Simpl Hall logic.
In addition, the present invention also discloses an electronic device, comprising: a memory for storing a computer program; a processor, data coupled to the memory, for implementing the formal verification method when executing the computer program.
Furthermore, a computer-readable storage medium is disclosed, on which a computer program is stored which, when being executed by a processor, carries out the formal verification method.
Although the present invention has been described in more detail by the above embodiments, the present invention is not limited to the above embodiments, and modifications and equivalent substitutions may be made to the technical solutions of the embodiments of the present invention without departing from the spirit and scope of the invention.
Claims (9)
1. A formal verification method for formally verifying an embedded operating system, the method comprising: the following operations are performed in the Isabelle environment:
building a basic execution model of an operating system represented by a state machine; describing the function point requirement of the operating system by using a meta language according to the basic execution model to obtain a requirement formalization specification of the operating system;
verifying the requirement correctness of the operating system based on the requirement formalization specification;
describing a data structure and an algorithm flow of the operating system by using a state list to obtain a design formalization specification of the operating system;
constructing a refinement relationship between the requirement formalization specification and the design formalization specification to verify the design compliance of the operating system;
describing the source code of the operating system by adopting Simpl language to obtain the source code formalization specification of the operating system;
and verifying the correctness and the conformity of the source code formalization specification by using Simpl Hall logic.
2. The formal verification method of claim 1 wherein the building of an operating system base execution model represented in a state machine comprises: constructing a basic execution model covering the basic object of the operating system, and representing the basic execution model by using a state machine; wherein the state machine comprises states and actions, the states comprising basic objects and abstract data structures of an operating system, the actions comprising basic actions and system calls of the operating system.
3. The formal verification method of claim 2, wherein the state machine is formally described by using an induction-constructed execution path, the execution path includes a system state of each step of operation, a head of each execution path is a system state before operation, a tail of each execution path is a system state after operation, all execution paths that meet the transition of the two system states are induced to form an execution path set for representing the operation of the operating system, and all the system states and the execution path set are combined to obtain the basic execution model represented by the state machine.
4. The formal verification method of claim 1 wherein verifying the correctness of the requirements of the operating system based on the requirements formalization specification comprises: and verifying whether the pre-state and the post-state of each operation of the operating system meet the invariance property.
5. The formal verification method of claim 1 wherein the constructing a refinement relationship between the requirement formal specification and the design formal specification to verify design compliance of the operating system comprises:
respectively constructing state-event track sets of the requirement formalization specification and the design formalization specification, and comparing the state-event track sets of the requirement formalization specification and the design formalization specification to obtain a state variable set and an event set which are newly added to the design formalization specification relative to the requirement formalization specification;
and judging whether the newly added state variable set and the event set meet the refinement relation of a preset condition.
6. The formal verification method of claim 1 wherein the design formalization specification uses record to define data structures and module states and definition to define state sheet design specifications.
7. A formal verification system for formalized verification of an embedded operating system, comprising the following elements operating in an Isabelle environment:
a demand formalization unit configured to: constructing a basic execution model of an operating system represented by a state machine; describing the function point requirement of the operating system by using a meta language according to the basic execution model to obtain the requirement formalization specification of the operating system;
a requirement verification unit configured to: verifying the requirement correctness of the operating system based on the requirement formalization specification;
a design formalization unit configured to: describing a data structure and an algorithm flow of the operating system by using a state list to obtain a design formalization specification of the operating system;
a design verification unit configured to: constructing a refinement relationship between the requirement formalization specification and the design formalization specification to verify design compliance of the operating system;
an implementation formalization unit configured to: describing the source code of the operating system by adopting Simpl language to obtain the source code formalization specification of the operating system; and
an implementation verification unit configured to: and verifying the correctness and the conformity of the source code formalization specification by using Simpl Hall logic.
8. The formal verification system according to claim 7, wherein the requirement verification unit verifies correctness of operating system requirements, comprising: and verifying whether the pre-state and the post-state of each operation of the operating system meet the invariance property.
9. The formal verification system of claim 7, wherein the design verification unit comprises:
a comparison module configured to: respectively constructing state-event track sets of the requirement formalization specification and the design formalization specification, and comparing the state-event track sets of the requirement formalization specification and the design formalization specification to obtain a state variable set and an event set which are newly added to the design formalization specification relative to the requirement formalization specification;
a verification module configured to: and judging whether the newly added state variable set and the event set meet the refinement relation of a preset condition.
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