# Verifying Distributed Systems with Isabelle/HOL

Formal proofs for the reliability of distributed algorithms.

- **Source:** [Martin Kleppmann](https://martin.kleppmann.com)
- **Published:** 2022-10-12
- **Topic:** [Data & AI](https://brifing.si/c/data-ai)
- **Original article:** <http://martin.kleppmann.com/2022/10/12/verifying-distributed-systems-isabelle.html>
- **On Brifing:** https://brifing.si/s/c72562f6-c34d-4780-88e1-c6b7558c32f5

## Challenges of Distributed Systems

Distributed systems are widely used in daily life, such as internet services. However, implementing these systems is challenging due to the unpredictability of networks. Issues like message delays, losses, or multiple transmissions affect system reliability.

## Unreliable Message Transmission

In distributed systems, communication between processes relies on unreliable message transmission. When a process does not receive a response to its request, it cannot determine whether the request was lost or the process crashed.

## Complexity of Distributed Algorithms

Distributed algorithms must provide strong guarantees regardless of message order. These algorithms manage complex operations like database transactions and replication, where informal reasoning methods fall short.

## Importance of Formal Proofs

Formal proofs are crucial for ensuring the correctness of distributed algorithms. Model checkers cannot test all combinations of concurrent activities. Therefore, tools like Isabelle/HOL are used to create formal proofs.

## Modeling with Isabelle/HOL

Isabelle/HOL models distributed systems using structures like functions, lists, and sets. Each process is identified by a unique ID, and algorithm execution proceeds in discrete time steps.

## Linear Sequence of Time Steps

Although processes run in parallel in reality, a linear sequence of time steps suffices in Isabelle/HOL. This is achieved by modeling communication through message sending and receiving.

## Process States and Events

Each process has a local state that is updated only by that process. A process cannot read the state of another process. The system's overall state is defined as the collection of all processes' local states.

## Crash and Recovery Events

A process crash is modeled by the process no longer taking steps. If processes are allowed to recover after crashing, a crash-recovery event is added. This event deletes the process's volatile memory state while preserving its stable storage state.

## Safety Properties

When proving safety properties of algorithms, no assumptions are made about which process executes in which time step. This ensures the algorithm can tolerate arbitrary message delays.

## Liveness Properties

To prove liveness properties, fairness assumptions are made, such as every non-crashed process eventually taking a step. However, proofs so far have focused only on safety properties.

## Step Function

Distributed algorithms are expressed through a step function. This function takes the process ID, local state, and the occurred event as inputs. It returns the new state of the process and the messages to be sent.

## Sources covering this story

- http://martin.kleppmann.com/2022/10/12/verifying-distributed-systems-isabelle.html — 

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_Summary written by Brifing from the original reporting. Copyright in the original article belongs to its publisher; read the full piece at the link above._