Formal Verification

VeridianOS employs formal verification techniques to mathematically prove the correctness, security, and safety properties of critical system components. This chapter covers the formal verification approach, tools, and methodologies used throughout the system.

Overview

Design Philosophy

Formal verification in VeridianOS serves multiple crucial purposes:

  1. Security Assurance: Mathematical proof of security properties
  2. Safety Guarantees: Verification of critical system invariants
  3. Correctness Validation: Proof that code matches specifications
  4. Compliance: Meeting high-assurance security requirements
  5. Trust: Building confidence in system reliability

Verification Scope

┌─────────────────────────────────────────────────────────────┐
│                    Verification Layers                     │
├─────────────────────────────────────────────────────────────┤
│ Application Layer    │ Model Checking, Contract Verification │
├─────────────────────────────────────────────────────────────┤
│ Service Layer        │ Protocol Verification, API Contracts  │
├─────────────────────────────────────────────────────────────┤
│ Driver Layer         │ Device Model Verification             │
├─────────────────────────────────────────────────────────────┤
│ Kernel Layer         │ Functional Correctness, Safety Props  │
├─────────────────────────────────────────────────────────────┤
│ Hardware Layer       │ Hardware Model Verification           │
└─────────────────────────────────────────────────────────────┘

Verification Tools and Frameworks

Primary Tools

1. Kani (Rust Model Checker)

  • Built on CBMC (Bounded Model Checking)
  • Direct integration with Rust code
  • Memory safety and bounds checking
  • Automatic test generation

2. CBMC (C Bounded Model Checker)

  • C/C++ code verification
  • Bit-precise verification
  • Concurrency analysis
  • Safety property checking

3. SMACK/Boogie

  • LLVM bitcode verification
  • Intermediate verification language
  • Multi-language support
  • Powerful assertion language

4. Dafny

  • High-level specification language
  • Contract-driven development
  • Automatic verification condition generation
  • Ghost code for specifications

Verification Architecture

#![allow(unused)]
fn main() {
// Verification tool integration
use kani::*;
use contracts::*;

#[cfg(kani)]
mod verification {
    use super::*;
    
    #[kani::proof]
    fn verify_capability_creation() {
        let object_id: u32 = kani::any();
        let rights: u16 = kani::any();
        
        // Assume valid inputs
        kani::assume(object_id < MAX_OBJECT_ID);
        kani::assume(rights & VALID_RIGHTS_MASK == rights);
        
        let cap = create_capability(object_id, rights);
        
        // Assert properties
        assert!(cap.object_id() == object_id);
        assert!(cap.rights() == rights);
        assert!(cap.generation() > 0);
    }
}
}

Memory Safety Verification

Rust Memory Safety

Rust's ownership system provides compile-time memory safety, but formal verification adds additional guarantees:

#![allow(unused)]
fn main() {
#[cfg(kani)]
mod memory_verification {
    use kani::*;
    
    // Verify frame allocator memory safety
    #[kani::proof]
    fn verify_frame_allocator_safety() {
        let mut allocator = FrameAllocator::new();
        
        // Allocate some frames
        let frame1 = allocator.allocate(1);
        let frame2 = allocator.allocate(1);
        
        // Verify no double allocation
        assert!(frame1.is_ok());
        assert!(frame2.is_ok());
        
        if let (Ok(f1), Ok(f2)) = (frame1, frame2) {
            // Frames must be different
            assert!(f1.start_address() != f2.start_address());
            
            // Frames must not overlap
            assert!(f1.start_address() + PAGE_SIZE <= f2.start_address() ||
                   f2.start_address() + PAGE_SIZE <= f1.start_address());
        }
    }
    
    // Verify virtual memory manager
    #[kani::proof]
    fn verify_page_table_operations() {
        let mut page_table = PageTable::new();
        let virt_addr: VirtAddr = kani::any();
        let phys_addr: PhysAddr = kani::any();
        
        // Assume valid addresses
        kani::assume(virt_addr.is_page_aligned());
        kani::assume(phys_addr.is_page_aligned());
        
        // Map page
        let result = page_table.map_page(virt_addr, phys_addr, PageFlags::READ_WRITE);
        assert!(result.is_ok());
        
        // Verify mapping
        let lookup = page_table.translate(virt_addr);
        assert!(lookup.is_some());
        assert_eq!(lookup.unwrap().start_address(), phys_addr);
    }
}
}

C Code Memory Safety

For C components, CBMC provides memory safety verification:

// capability.c - Capability system verification
#include <cbmc.h>

// Verify capability validation
void verify_capability_validation() {
    capability_t cap;
    __CPROVER_assume(cap != 0);  // Non-null capability
    
    rights_t required_rights;
    __CPROVER_assume(required_rights != 0);
    
    bool result = validate_capability(cap, required_rights);
    
    // If validation succeeds, capability must have required rights
    if (result) {
        rights_t cap_rights = get_capability_rights(cap);
        __CPROVER_assert((cap_rights & required_rights) == required_rights,
                        "Validated capability has required rights");
    }
}

// Verify IPC message handling
void verify_ipc_message_bounds() {
    char message[MAX_MESSAGE_SIZE];
    size_t message_len;
    
    __CPROVER_assume(message_len <= MAX_MESSAGE_SIZE);
    
    // Simulate message processing
    int result = process_ipc_message(message, message_len);
    
    // Verify no buffer overflow occurred
    __CPROVER_assert(__CPROVER_buffer_size(message) >= message_len,
                    "Message processing respects buffer bounds");
}

Capability System Verification

Capability Properties

The capability system must satisfy several critical security properties:

// capability_system.dfy - Dafny specification
module CapabilitySystem {
    // Capability type definition
    datatype Capability = Capability(
        objectId: nat,
        rights: set<Right>,
        generation: nat
    )
    
    datatype Right = Read | Write | Execute | Create | Delete
    
    // Capability table
    type CapabilityTable = map<CapabilityId, Capability>
    
    // Security properties
    predicate ValidCapabilityTable(table: CapabilityTable) {
        forall cap_id :: cap_id in table ==> 
            table[cap_id].generation > 0
    }
    
    // No capability forge property
    predicate NoForge(table1: CapabilityTable, table2: CapabilityTable, op: Operation) {
        forall cap_id :: cap_id in table2 && cap_id !in table1 ==>
            op.CreatesCapability(cap_id)
    }
    
    // Capability derivation property
    predicate ValidDerivation(parent: Capability, child: Capability) {
        child.objectId == parent.objectId &&
        child.rights <= parent.rights &&
        child.generation >= parent.generation
    }
    
    // Method to create capability
    method CreateCapability(objectId: nat, rights: set<Right>) 
        returns (cap: Capability)
        ensures cap.objectId == objectId
        ensures cap.rights == rights
        ensures cap.generation > 0
    {
        cap := Capability(objectId, rights, 1);
    }
    
    // Method to derive capability
    method DeriveCapability(parent: Capability, newRights: set<Right>)
        returns (child: Capability)
        requires newRights <= parent.rights
        ensures ValidDerivation(parent, child)
        ensures child.rights == newRights
    {
        child := Capability(parent.objectId, newRights, parent.generation);
    }
    
    // Theorem: Capability derivation preserves security
    lemma DerivationPreservesSecurity(parent: Capability, rights: set<Right>)
        requires rights <= parent.rights
        ensures ValidDerivation(parent, DeriveCapability(parent, rights))
    {
        // Proof automatically verified by Dafny
    }
}

Capability Invariants

#![allow(unused)]
fn main() {
// Rust capability verification with Kani
#[cfg(kani)]
mod capability_verification {
    use super::*;
    use kani::*;
    
    // Verify capability generation is always positive
    #[kani::proof]
    fn verify_capability_generation() {
        let object_id: u32 = kani::any();
        let rights: u16 = kani::any();
        
        let cap = Capability::new(object_id, rights);
        assert!(cap.generation() > 0);
    }
    
    // Verify capability derivation reduces rights
    #[kani::proof]
    fn verify_capability_derivation() {
        let parent = create_test_capability();
        let new_rights: u16 = kani::any();
        
        // Assume new rights are subset of parent rights
        kani::assume((new_rights & parent.rights()) == new_rights);
        
        let child = parent.derive(new_rights).unwrap();
        
        // Child must have subset of parent's rights
        assert!((child.rights() & parent.rights()) == child.rights());
        
        // Child must reference same object
        assert_eq!(child.object_id(), parent.object_id());
        
        // Child generation must be >= parent generation
        assert!(child.generation() >= parent.generation());
    }
    
    // Verify no capability forgery
    #[kani::proof]
    fn verify_no_capability_forgery() {
        let cap_table = CapabilityTable::new();
        let fake_cap: u64 = kani::any();
        
        // Attempt to validate forged capability
        let result = cap_table.validate(fake_cap, Rights::READ);
        
        // Forged capability should always fail validation
        // (unless by extreme coincidence it matches a real one)
        if !cap_table.contains(fake_cap) {
            assert!(!result);
        }
    }
}
}

IPC System Verification

Message Ordering and Delivery

---- MODULE IpcProtocol ----
EXTENDS Naturals, Sequences, TLC

VARIABLES 
    channels,      \* Set of all channels
    messages,      \* Messages in transit
    delivered      \* Successfully delivered messages

Init == 
    /\ channels = {}
    /\ messages = {}
    /\ delivered = {}

\* Create new IPC channel
CreateChannel(channel_id) ==
    /\ channel_id \notin channels
    /\ channels' = channels \union {channel_id}
    /\ UNCHANGED <<messages, delivered>>

\* Send message on channel
SendMessage(channel_id, sender, receiver, msg) ==
    /\ channel_id \in channels
    /\ messages' = messages \union {[
         channel: channel_id,
         sender: sender,
         receiver: receiver, 
         message: msg,
         timestamp: TLCGet("level")
       ]}
    /\ UNCHANGED <<channels, delivered>>

\* Receive message from channel
ReceiveMessage(channel_id, receiver) ==
    /\ \E m \in messages : 
         /\ m.channel = channel_id 
         /\ m.receiver = receiver
         /\ delivered' = delivered \union {m}
         /\ messages' = messages \ {m}
    /\ UNCHANGED channels

\* System invariants
TypeInvariant == 
    /\ channels \subseteq Nat
    /\ \A m \in messages : 
         /\ m.channel \in channels
         /\ m.timestamp \in Nat

\* Safety property: Messages are delivered in order
MessageOrdering == 
    \A m1, m2 \in delivered :
        /\ m1.channel = m2.channel
        /\ m1.sender = m2.sender  
        /\ m1.receiver = m2.receiver
        /\ m1.timestamp < m2.timestamp
        => \* m1 was delivered before m2 in sequence

\* Liveness property: All sent messages eventually delivered
MessageDelivery == 
    \A m \in messages : <>(m \in delivered)

Spec == Init /\ [][
    \E channel_id, sender, receiver, msg :
        \/ CreateChannel(channel_id)
        \/ SendMessage(channel_id, sender, receiver, msg)  
        \/ ReceiveMessage(channel_id, receiver)
]_<<channels, messages, delivered>>
====

Zero-Copy Verification

#![allow(unused)]
fn main() {
// Verify zero-copy IPC implementation
#[cfg(kani)]
mod zero_copy_verification {
    use super::*;
    use kani::*;
    
    #[kani::proof]
    fn verify_shared_memory_isolation() {
        // Create two processes
        let process1_id: ProcessId = kani::any();
        let process2_id: ProcessId = kani::any();
        kani::assume(process1_id != process2_id);
        
        // Create shared region
        let region_size: usize = kani::any();
        kani::assume(region_size > 0 && region_size <= MAX_REGION_SIZE);
        
        let shared_region = SharedRegion::new(region_size, Permissions::READ_write());
        
        // Map to both processes
        let addr1 = shared_region.map_to_process(process1_id).unwrap();
        let addr2 = shared_region.map_to_process(process2_id).unwrap();
        
        // Addresses should be different (isolation)
        assert!(addr1 != addr2);
        
        // But should reference same physical memory
        assert_eq!(
            virt_to_phys(addr1).unwrap(),
            virt_to_phys(addr2).unwrap()
        );
    }
    
    #[kani::proof]
    fn verify_capability_passing() {
        let sender: ProcessId = kani::any();
        let receiver: ProcessId = kani::any();
        let capability: u64 = kani::any();
        
        // Send capability via IPC
        let message = IpcMessage::new()
            .add_capability(capability)
            .build();
            
        let result = send_message(sender, receiver, message);
        assert!(result.is_ok());
        
        // Receiver should now have capability
        let received = receive_message(receiver).unwrap();
        assert!(received.capabilities().contains(&capability));
        
        // Sender should lose capability (move semantics)
        assert!(!process_has_capability(sender, capability));
    }
}
}

Scheduler Verification

Real-Time Properties

// scheduler.dfy - Real-time scheduler verification
module Scheduler {
    type TaskId = nat
    type Priority = nat  
    type Time = nat
    
    datatype Task = Task(
        id: TaskId,
        priority: Priority,
        wcet: Time,        // Worst-case execution time
        period: Time,      // Period for periodic tasks
        deadline: Time     // Relative deadline
    )
    
    datatype TaskState = Ready | Running | Blocked | Completed
    
    type Schedule = seq<(TaskId, Time)>  // (task_id, start_time) pairs
    
    // Schedulability analysis for Rate Monotonic
    function UtilizationBound(tasks: set<Task>): real {
        (set t | t in tasks :: real(t.wcet) / real(t.period)).Sum()
    }
    
    predicate IsSchedulable(tasks: set<Task>) {
        |tasks| as real * (Power(2.0, 1.0 / |tasks| as real) - 1.0) >= 
        UtilizationBound(tasks)
    }
    
    // Verify deadline satisfaction
    predicate DeadlinesSatisfied(tasks: set<Task>, schedule: Schedule) {
        forall i :: 0 <= i < |schedule| ==>
            exists t :: t in tasks && t.id == schedule[i].0 ==>
                schedule[i].1 + t.wcet <= t.deadline
    }
    
    // Priority inversion freedom
    predicate NoPriorityInversion(tasks: set<Task>, schedule: Schedule) {
        forall i, j :: 0 <= i < j < |schedule| ==>
            exists t1, t2 :: t1 in tasks && t2 in tasks &&
                t1.id == schedule[i].0 && t2.id == schedule[j].0 ==>
                t1.priority >= t2.priority || schedule[i].1 + t1.wcet <= schedule[j].1
    }
    
    // Method to create rate monotonic schedule
    method RateMonotonicSchedule(tasks: set<Task>) returns (schedule: Schedule)
        requires IsSchedulable(tasks)
        ensures DeadlinesSatisfied(tasks, schedule)
        ensures NoPriorityInversion(tasks, schedule)
    {
        // Implementation with proof obligations
        schedule := [];
        // ... scheduling algorithm implementation
    }
}

Context Switch Verification

// context_switch_verification.c
#include <cbmc.h>

// Verify context switch preserves register state
void verify_context_switch() {
    // Create two task contexts
    struct task_context task1, task2;
    
    // Initialize with arbitrary values
    task1.rax = nondet_uint64();
    task1.rbx = nondet_uint64();
    task1.rcx = nondet_uint64();
    // ... all registers
    
    task2.rax = nondet_uint64();
    task2.rbx = nondet_uint64();
    task2.rcx = nondet_uint64();
    // ... all registers
    
    // Save original values
    uint64_t orig_task1_rax = task1.rax;
    uint64_t orig_task2_rax = task2.rax;
    
    // Perform context switch
    context_switch(&task1, &task2);
    
    // Verify register values preserved
    __CPROVER_assert(task1.rax == orig_task1_rax, 
                    "Task 1 RAX preserved");
    __CPROVER_assert(task2.rax == orig_task2_rax, 
                    "Task 2 RAX preserved");
}

// Verify atomic context switch
void verify_context_switch_atomicity() {
    struct task_context *current_task = get_current_task();
    struct task_context *next_task = get_next_task();
    
    __CPROVER_assume(current_task != next_task);
    __CPROVER_assume(current_task != NULL);
    __CPROVER_assume(next_task != NULL);
    
    // Context switch should be atomic - no interruption
    context_switch(current_task, next_task);
    
    // After switch, current task should be next_task
    __CPROVER_assert(get_current_task() == next_task,
                    "Context switch completed atomically");
}

Security Properties Verification

Information Flow Security

// information_flow.dfy - Information flow verification
module InformationFlow {
    type SecurityLevel = Low | High
    type Value = int
    type Variable = string
    
    datatype Expr = 
        | Const(value: Value)
        | Var(name: Variable)
        | Plus(left: Expr, right: Expr)
        | If(cond: Expr, then: Expr, else: Expr)
    
    type Environment = map<Variable, (Value, SecurityLevel)>
    
    // Security labeling function
    function SecurityLabel(expr: Expr, env: Environment): SecurityLevel {
        match expr {
            case Const(_) => Low
            case Var(name) => 
                if name in env then env[name].1 else Low
            case Plus(left, right) =>
                Max(SecurityLabel(left, env), SecurityLabel(right, env))
            case If(cond, then, else) =>
                Max(SecurityLabel(cond, env), 
                    Max(SecurityLabel(then, env), SecurityLabel(else, env)))
        }
    }
    
    function Max(a: SecurityLevel, b: SecurityLevel): SecurityLevel {
        if a == High || b == High then High else Low
    }
    
    // Non-interference property
    predicate NonInterference(expr: Expr, env1: Environment, env2: Environment) {
        // If low-security variables are same in both environments
        (forall v :: v in env1 && v in env2 && env1[v].1 == Low ==> 
            env1[v].0 == env2[v].0) ==>
        // Then evaluation results are same if expression is low-security
        (SecurityLabel(expr, env1) == Low ==> 
            Eval(expr, env1) == Eval(expr, env2))
    }
    
    function Eval(expr: Expr, env: Environment): Value {
        match expr {
            case Const(value) => value
            case Var(name) => if name in env then env[name].0 else 0
            case Plus(left, right) => Eval(left, env) + Eval(right, env)
            case If(cond, then, else) => 
                if Eval(cond, env) != 0 then Eval(then, env) else Eval(else, env)
        }
    }
    
    // Theorem: Well-typed expressions satisfy non-interference
    lemma WellTypedNonInterference(expr: Expr, env1: Environment, env2: Environment)
        ensures NonInterference(expr, env1, env2)
    {
        // Proof by structural induction on expressions
    }
}

Access Control Verification

#![allow(unused)]
fn main() {
// Access control model verification
#[cfg(kani)]
mod access_control_verification {
    use super::*;
    use kani::*;
    
    // Verify access control matrix properties
    #[kani::proof]  
    fn verify_access_control_matrix() {
        let subject: SubjectId = kani::any();
        let object: ObjectId = kani::any();
        let operation: Operation = kani::any();
        
        let matrix = AccessControlMatrix::new();
        
        // If access is granted, subject must have proper capability
        if matrix.check_access(subject, object, operation) {
            let capability = matrix.get_capability(subject, object).unwrap();
            assert!(capability.allows(operation));
        }
    }
    
    // Verify Bell-LaPadula security model
    #[kani::proof]
    fn verify_bell_lapadula() {
        let subject_level: SecurityLevel = kani::any();
        let object_level: SecurityLevel = kani::any();
        let operation: Operation = kani::any();
        
        let result = bell_lapadula_check(subject_level, object_level, operation);
        
        match operation {
            Operation::Read => {
                // Simple security property: no read up
                if result {
                    assert!(subject_level >= object_level);
                }
            }
            Operation::Write => {
                // Star property: no write down  
                if result {
                    assert!(subject_level <= object_level);
                }
            }
            _ => {}
        }
    }
    
    // Verify discretionary access control
    #[kani::proof]
    fn verify_discretionary_access() {
        let owner: SubjectId = kani::any();
        let requestor: SubjectId = kani::any();
        let object: ObjectId = kani::any();
        let permissions: Permissions = kani::any();
        
        let acl = AccessControlList::new(owner);
        
        // Only owner can grant permissions
        if acl.grant_access(requestor, object, permissions, owner).is_ok() {
            // Verify permission was actually granted
            assert!(acl.check_access(requestor, object, permissions));
        }
        
        // Non-owners cannot grant permissions they don't have
        let non_owner: SubjectId = kani::any();
        kani::assume(non_owner != owner);
        
        let result = acl.grant_access(requestor, object, permissions, non_owner);
        if !acl.check_access(non_owner, object, permissions) {
            assert!(result.is_err());
        }
    }
}
}

Hardware Interface Verification

Device Driver Verification

// device_driver.dfy - Device driver specification
module DeviceDriver {
    type RegisterAddress = nat
    type RegisterValue = bv32
    type MemoryAddress = nat
    
    datatype DeviceState = Uninitialized | Ready | Busy | Error
    
    class NetworkDriver {
        var state: DeviceState
        var registers: map<RegisterAddress, RegisterValue>
        var txBuffer: seq<bv8>
        var rxBuffer: seq<bv8>
        
        constructor()
            ensures state == Uninitialized
            ensures |txBuffer| == 0
            ensures |rxBuffer| == 0
        {
            state := Uninitialized;
            registers := map[];
            txBuffer := [];
            rxBuffer := [];
        }
        
        method Initialize() 
            requires state == Uninitialized
            modifies this
            ensures state == Ready
        {
            // Device initialization sequence
            WriteRegister(CONTROL_REG, RESET_BIT);
            WriteRegister(CONTROL_REG, ENABLE_BIT);
            
            state := Ready;
        }
        
        method WriteRegister(addr: RegisterAddress, value: RegisterValue)
            modifies this.registers
            ensures registers[addr] == value
        {
            registers := registers[addr := value];
        }
        
        method SendPacket(packet: seq<bv8>)
            requires state == Ready
            requires |packet| > 0
            modifies this
            ensures state == Ready || state == Error
        {
            if |txBuffer| + |packet| <= TX_BUFFER_SIZE {
                txBuffer := txBuffer + packet;
                WriteRegister(TX_CONTROL, START_TX);
            } else {
                state := Error;
            }
        }
        
        // Safety property: Device state transitions are valid
        predicate ValidStateTransition(oldState: DeviceState, newState: DeviceState) {
            match oldState {
                case Uninitialized => newState == Ready || newState == Error
                case Ready => newState == Busy || newState == Error  
                case Busy => newState == Ready || newState == Error
                case Error => newState == Uninitialized  // Reset only
            }
        }
    }
}

DMA Safety Verification

// dma_verification.c - DMA operation verification
#include <cbmc.h>

struct dma_descriptor {
    uintptr_t src_addr;
    uintptr_t dst_addr; 
    size_t length;
    uint32_t flags;
};

// Verify DMA operation doesn't violate memory safety
void verify_dma_memory_safety() {
    struct dma_descriptor desc;
    
    // Non-deterministic values
    desc.src_addr = nondet_uintptr_t();
    desc.dst_addr = nondet_uintptr_t(); 
    desc.length = nondet_size_t();
    desc.flags = nondet_uint32();
    
    // Assume valid DMA setup
    __CPROVER_assume(desc.length > 0);
    __CPROVER_assume(desc.src_addr != 0);
    __CPROVER_assume(desc.dst_addr != 0);
    
    // Assume no overflow
    __CPROVER_assume(desc.src_addr + desc.length > desc.src_addr);
    __CPROVER_assume(desc.dst_addr + desc.length > desc.dst_addr);
    
    int result = setup_dma_transfer(&desc);
    
    if (result == 0) {  // Success
        // Verify DMA doesn't access kernel memory
        __CPROVER_assert(desc.src_addr < KERNEL_SPACE_START ||
                        desc.src_addr >= KERNEL_SPACE_END,
                        "DMA source not in kernel space");
                        
        __CPROVER_assert(desc.dst_addr < KERNEL_SPACE_START ||
                        desc.dst_addr >= KERNEL_SPACE_END,
                        "DMA destination not in kernel space");
        
        // Verify DMA buffers don't overlap with critical structures
        __CPROVER_assert(!overlaps_with_page_tables(desc.src_addr, desc.length),
                        "DMA source doesn't overlap page tables");
        __CPROVER_assert(!overlaps_with_page_tables(desc.dst_addr, desc.length),
                        "DMA destination doesn't overlap page tables");
    }
}

// Verify DMA completion handling
void verify_dma_completion() {
    volatile uint32_t *status_reg = (volatile uint32_t*)DMA_STATUS_REG;
    
    // Wait for DMA completion
    while (!(*status_reg & DMA_COMPLETE_BIT)) {
        // Busy wait
    }
    
    // Verify completion status is valid
    __CPROVER_assert(*status_reg & (DMA_COMPLETE_BIT | DMA_ERROR_BIT),
                    "DMA completion status is valid");
    
    // Clear completion bit
    *status_reg = DMA_COMPLETE_BIT;
    
    // Verify bit was cleared
    __CPROVER_assert(!(*status_reg & DMA_COMPLETE_BIT),
                    "DMA completion bit cleared");
}

Automated Verification Pipeline

Continuous Integration

# .github/workflows/verification.yml
name: Formal Verification

on: [push, pull_request]

jobs:
  kani-verification:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v3
      
      - name: Install Kani
        run: |
          cargo install --locked kani-verifier
          cargo kani setup
          
      - name: Run Kani verification
        run: |
          cd kernel
          cargo kani --all-targets
          
      - name: Upload verification report
        uses: actions/upload-artifact@v3
        with:
          name: kani-report
          path: target/kani/
          
  cbmc-verification:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v3
      
      - name: Install CBMC
        run: |
          sudo apt-get update
          sudo apt-get install cbmc
          
      - name: Verify C components
        run: |
          find . -name "*.c" -path "*/verification/*" | \
          xargs -I {} cbmc {} --bounds-check --pointer-check
          
  dafny-verification:
    runs-on: ubuntu-latest
    steps:
      - uses: actions/checkout@v3
      
      - name: Install Dafny
        run: |
          wget https://github.com/dafny-lang/dafny/releases/latest/download/dafny-4.x.x-x64-ubuntu-20.04.zip
          unzip dafny-*.zip
          sudo mv dafny /usr/local/
          
      - name: Verify specifications
        run: |
          find . -name "*.dfy" | xargs /usr/local/dafny/dafny verify

Verification Scripts

#!/bin/bash
# scripts/verify-all.sh - Complete verification suite

set -e

echo "Starting formal verification suite..."

# Rust verification with Kani
echo "Running Kani verification..."
cd kernel
cargo kani --all-targets --verbose
cd ..

# C verification with CBMC  
echo "Running CBMC verification..."
find . -name "*_verification.c" -exec cbmc {} \
    --bounds-check \
    --pointer-check \
    --memory-leak-check \
    --unwind 10 \;

# TLA+ model checking
echo "Running TLA+ model checking..."
cd specifications
for spec in *.tla; do
    echo "Checking $spec..."
    tlc -workers auto "$spec"
done
cd ..

# Dafny verification
echo "Running Dafny verification..."
find . -name "*.dfy" -exec dafny verify {} \;

echo "All verifications completed successfully!"

Performance Impact

Verification Overhead

#![allow(unused)]
fn main() {
// Conditional compilation for verification
#[cfg(all(kani, feature = "verify-all"))]
mod expensive_verification {
    // Only run expensive proofs when explicitly requested
    #[kani::proof]
    #[kani::unwind(1000)]  // Higher unwind bound
    fn verify_complex_algorithm() {
        // Expensive verification that takes long to run
    }
}

#[cfg(kani)]
mod standard_verification {
    // Fast verification for CI
    #[kani::proof]
    #[kani::unwind(10)]    // Lower unwind bound
    fn verify_basic_properties() {
        // Quick checks for basic properties
    }
}
}

Verification Metrics

#![allow(unused)]
fn main() {
// Automated verification metrics collection
#[cfg(feature = "verification-metrics")]
mod metrics {
    use std::time::Instant;
    
    pub fn measure_verification_time<F>(name: &str, f: F) 
    where F: FnOnce() {
        let start = Instant::now();
        f();
        let duration = start.elapsed();
        
        println!("Verification '{}' took: {:?}", name, duration);
        
        // Store metrics for analysis
        store_verification_metric(name, duration);
    }
    
    fn store_verification_metric(name: &str, duration: Duration) {
        // Implementation to store metrics
    }
}
}

Future Enhancements

Advanced Verification Techniques

  1. Compositional Verification: Verify large systems by composing smaller verified components
  2. Assume-Guarantee Reasoning: Modular verification with interface contracts
  3. Probabilistic Verification: Verify properties with probabilistic guarantees
  4. Quantum-Safe Verification: Verify cryptographic properties against quantum attacks

Tool Integration Roadmap

Phase 5: Advanced verification tools

  • SMACK/Boogie integration for LLVM IR verification
  • VeriFast for C program verification
  • SPARK for Ada-style contracts in Rust

Phase 6: Cutting-edge techniques

  • Machine learning assisted verification
  • Automated invariant discovery
  • Continuous verification in development

This comprehensive formal verification approach ensures that VeridianOS achieves the highest levels of assurance for security-critical applications while maintaining practical development workflows.