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A mathematically precise description of permitted behaviour. A formal specification for the microkernel file-read example's service could relate an authorized request to the exact returned bytes; a formal specification of its microkernel's IPC need only describe the protected transport operation. They state different obligations.

For the summation loop verification, require a nonnegative integer input $n$ and a returned value $s$ satisfying $2s=n(n+1)$. The formal specification describes what answer is acceptable without requiring this particular loop: another implementation may satisfy the same contract. State separately whether partial correctness or total correctness is required. A Hoare triple packages the precondition, the program and the postcondition; Hoare logic supplies rules for establishing such claims.

Precision alone does not ensure a useful requirement. The postcondition $s\ge 0$ permits returning zero for every nonnegative integer input; it does not specify the intended triangular number. Conversely, an impossible precondition permits no starts, making a universal correctness claim vacuous. Check both that intended inputs are admitted and that admitted outputs express the intended task.

Communication between operating-system processes, including controlled message delivery and deliberately shared computer memory. A microkernel supplies IPC across protection domains, allowing user-space services to cooperate without making all their private computer memory accessible to each other.

An interrupt redirects CPU execution to an interrupt handler in response to an event. Here the main case is an asynchronous hardware interrupt: a timer or device requests attention independently of the instruction currently being executed. A device completing a receive operation can announce that its data is ready while the CPU is running another program. Interrupt-driven input-output illustrates this with an explicit timeline. ^[ref]

A synchronous processor exception, such as a page fault caused by a particular memory access, is tied to instruction execution. A system call is an intentional program request for an operating-system kernel service. These routes can share entry machinery, and an instruction named a software interrupt can implement a system call, but this does not make that request an asynchronous device event. For example, the Linux kernel on x86 documents separate entries for external interrupts, divide exceptions, syscall and int 0x80. ^[ref]

The usual device route is a request through an interrupt controller, architecture-specific entry, and dispatch to an interrupt handler. In the Linux kernel, generic handling separates controller operations from flow handling and device driver callbacks. Requests can arrive through a pin or a message, and several devices can share a request source. Routing, priorities and interrupt masking determine which requests can be delivered; notification therefore need not mean immediate execution of the interrupt handler. ^[ref][ref]

The CPU and entry code preserve the state needed to resume interrupted execution, including the instruction pointer. Handling may enter a higher processor privilege level when interrupting ordinary program execution, but an interrupt can also arrive while privileged code is already running. The protected entry route and handler placement depend on the architecture and operating system; a microkernel need not place all device driver work where a monolithic kernel does. An interrupt entry is also distinct from a context switch to another operating-system process. ^[ref][ref]

// Target: computer-science.bigb

The operating-system kernel is the core of an operating system, controlling access to resources and supplying mechanisms used by operating-system processes. Processor privilege levels let it enforce boundaries that ordinary programs cannot simply overwrite. The operating-system kernel connects process scheduling, virtual memory and file system operations; a system call requests a service across that boundary. A monolithic kernel and a microkernel divide services differently, so the location of every file system service is a design choice.

For the toy file system, opening a resolves its directory entry to inode 42, establishes an open file description, and returns file descriptor 3. Later reads use that file descriptor to reach the existing open file description, without resolving the spelling a again. This explains how unlinking an open file preserves access: the open reference survives the directory entry. The per-operating-system process table interpreting 3 is maintained by the operating-system kernel; 3 itself is the small integer passed by the program, not inode 42. ^[ref]

An operating-system kernel design retaining essential protected mechanisms while moving services into user-space services. Address spaces, software threads and IPC form a useful small foundation: the operating-system kernel protects private state and controls communication, while a file system service interprets requests about files. This separation of mechanism and policy permits different service implementations to use the same protected interface. ^[ref]

The useful question is which authority a service needs. A device driver may require access to a device while having no permission to overwrite an unrelated application's computer memory. A microkernel makes such protection domains possible; their actual boundaries depend on the chosen memory protection and security capabilities.

Consider an original toy file system service in address space B and a client in address space A, on one CPU. The service holds a five-byte cached file containing LIME followed by a newline. The client already has service handle 9, permission to read that file, and a security capability to send requests to IPC endpoint E. Handle 9 is interpreted by the service; it is neither a virtual address nor an operating-system kernel object identifier. All relevant memory pages are resident, and this read needs no device driver.

This protocol is an illustrative design, not an actual seL4 file system interface. Its call/reply structure follows seL4's documented IPC: seL4_Call waits using reply authority, and small payloads can travel in processor registers. ^[ref]

An ordinary pointer in A refers to A's address space. Sending its numeric value does not make B's private computer memory appear there. This example explicitly transfers bytes. Sharing a mapped memory page instead would require intentional memory protection permissions and a protocol for ownership and synchronization; passing a pointer alone establishes neither.

The same IPC mechanism could carry WRITE, but this client could still be refused by the service's read-only handle policy. Conversely, possession of an IPC endpoint security capability permits communication without automatically granting access to every file the service manages. The separation of mechanism and policy appears twice: endpoint authority gates delivery, and the service's handle policy gates the requested operation.

Suppose the user-space service stops after receiving request 7, before replying. Assume that its private memory pages are not writable mappings of the client's or an unrelated service's computer memory, and that it lacks security capabilities to change their software threads. A failed store in the service cannot directly overwrite that private state through ordinary CPU address translation. Those assumptions establish a particular isolation boundary, not a successful read.

The client can remain blocked waiting for request 7. An unrelated runnable service may continue if process scheduling and resources permit, but clients that depend on the stopped service still lose access to its service. A separately authorized recovery manager would need to detect the failure, rebuild the service's state and arrange communication with its replacement. The microkernel architecture by itself supplies none of those application-specific recovery decisions.

A missing reply also does not reveal whether a service crashed, is delayed by process scheduling, or entered an infinite computation. For a read, retrying after recovery may be straightforward; for a modifying operation, absence of a reply does not prove that the modification never happened. Recovery must account for ambiguous completed operations and any required file-system crash consistency.

The boundary changes with authority. A deliberately shared writable memory page allows the service to change its shared contents; a security capability controlling another software thread permits the corresponding control operations. A device driver with uncontrolled DMA can bypass ordinary CPU memory protection. Thus service placement and actual permissions must be considered together. ^[ref]

False as a general performance claim. A microkernel moves services into separate protection domains, which can require extra messages, scheduling and address-space transitions. A monolithic kernel can often call a service directly within its own privileged address space. The microkernel gains isolation and modularity, but these do not imply greater speed. Efficient implementations and particular workloads can change the comparison; the architecture alone gives no universal ordering.

A microkernel using security capabilities to control access to operating-system kernel objects, including IPC endpoints and software threads. An IPC endpoint connects cooperating user-space services; its security capabilities are distinct from the service-defined handle 9 in the microkernel file-read example. ^[ref]

Distinguishing the operations a system can enforce from the choices about how to use them. In a microkernel, a protected IPC operation can deliver requests while a user-space service decides which files a caller may read. The division is a design choice: every real mechanism still has rules and limits.

An operating system service executing at an application's processor privilege level, outside the operating-system kernel. A microkernel can host a file system or device driver this way. Its granted security capabilities and memory protection determine its authority; the label user-space service does not imply that it has little authority.