# Method Summarization

## Overview

Method summarization is a mechanism that allows the user to provide a concise, high-level description of the behavior of a method. It serves as a guide for the underlying solvers to more efficiently reason about the method’s behavior and helps to avoid timeouts, especially in cases where complex computations or undecidable problems are involved.

## How Summarization Helps Solvers

1. Efficiency Improvement:

• Timeout Avoidance: Summarization provides a way to guide the solver efficiently by providing a more abstract, high-level view of the method, potentially avoiding the need for detailed exploration.

• Faster Analysis: By focusing on essential properties, summarization can lead to faster analysis, as the solver doesn’t need to explore every intricate detail of the method.

2. Abstraction of Complex Logic:

• Complex Computations: When dealing with functions involving complex mathematical operations or undecidable problems, summarization allows the user to abstract away unnecessary details, making it easier for the solver to reason about the method’s behavior.

## Syntax

```methods {
// Method summarization syntax
function methodName(parameters) returns returnType =>
summaryExpression;
}
```

## Example: Summarization for a complex function

```function multiply(uint256 x, uint256 y) returns uint256 {
return x * y;
}
methods {
function complexFunction(uint256 x, uint256 y) returns bool =>
exists uint256 z . z == multiply(x, y);
}

rule myRule(uint256 a, uint256 b) {
// Using the summarized method in a rule
require complexFunction(a, b);
// ...
}
```

In the example above, `complexFunction` involves a complex multiplication of `x` and `y`. The summarization `exists uint256 z . z == x * y;` provides a high-level description, emphasizing the existence of a product `z` that satisfies the multiplication relationship.

## Important Considerations

1. Limitations of Summarization:

• Summarization is a trade-off between precision and efficiency. While it can significantly improve solver performance, it may introduce over- or under-approximations. over-approximation means we may use too general behaviors to prove the desired property. under-approximations means we potentially miss out on behaviors.

• Care should be taken to ensure that the summarization captures the critical aspects of the method’s behavior.

2. Choosing Summarization Techniques:

• The choice of summarization techniques depends on the nature of the method and the specific verification goals.

• Users may experiment with different summarization strategies to find the right balance between precision and efficiency. for more information, see Summarization.

## Summary

Method summarization in CVL provides a powerful tool for enhancing the efficiency of verification by guiding solvers to focus on essential aspects of a method’s behavior. By abstracting away unnecessary details, summarization helps prevent timeouts in situations involving complex computations or undecidable problems. Users should carefully design and choose summarizations that strike the right balance between precision and efficiency for their specific verification tasks.