### Summary

Separation Logic is a theory used to reason about computer programs. It deals with mutable data structures allowing easier interpretation of a program’s memory allocation and deallocation.

### ELI5

Imagine you are a librarian. You have a system to keep track of all the books based on their categories. Sometimes you remove books (deallocate) or add new ones (allocate). Separation Logic is like that system, helping keep track of these changes in a computer program.

### In-depth explanation

Separation Logic is a subdiscipline of Hoare Logic that extends the latter’s capacity to mutate data structures. It provides a more scalable way to reason about program correctness, especially concerning memory allocation and deallocation. At a basic level, it can be thought to describe “who owns what,” establishing clear boundaries amongst various parts of memory and their associated computations.

The primary element in Separation Logic is the ‘separating conjunction’, denoted as ‘*’. Given two assertions P and Q, we say that `P * Q` holds over a certain piece of memory if it can be split into two disjoint parts - one satisfying P and the other satisfying Q.

This logic owes its effectiveness to ‘Frame Rule’, which allows local reasoning about portions of a program. Through ‘Frame Rule’, one can insist that a command does not affect specific parts of the state. This isolates the effect of commands, enabling easy composition and the scaling of automated reasoning to larger codebases.

Separation Logic has several applications, from understanding concurrent programs, memory-manipulating programs to complicated linked structure manipulations. It forms the basis of program verifiers and static analyzers, enhancing their reliability and ensuring robust coding behavior.

Hoare Logic, Formal Verification, Deductive Verification, Proof-Carrying Code, Local Reasoning, Mutating Data Structures