In computer science, separation logic is an extension of Hoare logic, a way of reasoning about programs. It was developed by John C. Reynolds, Peter O'Hearn, Samin Ishtiaq and Hongseok Yang, drawing upon early work by Rod Burstall. The assertion language of separation logic is a special case of the logic of bunched implications (BI). A CACM review article by O'Hearn charts developments in the subject to early 2019.

Separation logic facilitates reasoning about:

Separation logic supports the developing field of research described by Peter O'Hearn and others as local reasoning, whereby specifications and proofs of a program component mention only the portion of memory used by the component, and not the entire global state of the system. Applications include automated program verification (where an algorithm checks the validity of another algorithm) and automated parallelization of software.

Separation logic assertions describe "states" consisting of a store and a heap, roughly corresponding to the state of local (or stack-allocated) variables and dynamically-allocated objects in common programming languages such as C and Java. A store ${\displaystyle s}$ is a function mapping variables to values. A heap ${\displaystyle h}$ is a partial function mapping memory addresses to values. Two heaps ${\displaystyle h}$ and ${\displaystyle h'}$ are disjoint (denoted ${\displaystyle h\,\bot \,h'}$) if their domains do not overlap (i.e., for every memory address ${\displaystyle \ell }$, at least one of ${\displaystyle h(\ell )}$ and ${\displaystyle h'(\ell )}$ is undefined).

The logic allows to prove judgements of the form ${\displaystyle s,h\models P}$, where ${\displaystyle s}$ is a store, ${\displaystyle h}$ is a heap, and ${\displaystyle P}$ is an assertion over the given store and heap. Separation logic assertions (denoted as ${\displaystyle P}$, ${\displaystyle Q}$, ${\displaystyle R}$) contain the standard Boolean connectives and, in addition, ${\displaystyle \mathbf {e} \mathbf {m} \mathbf {p} }$, ${\displaystyle e\mapsto e'}$, ${\displaystyle P\ast Q}$, and ${\displaystyle P{-\!\!\ast }\,Q}$, where ${\displaystyle e}$ and ${\displaystyle e'}$ are expressions.

The operators ${\displaystyle \ast }$ and ${\displaystyle -\!\!\ast }$ share some properties with the classical conjunction and implication operators. They can be combined using an inference rule similar to modus ponens

and they form an adjunction, i.e., ${\displaystyle s,h\cup h'\models P\ast Q\Rightarrow R}$ if and only if ${\displaystyle s,h\models P\Rightarrow Q-\!\!\ast \,R}$ for ${\displaystyle h\,\bot \,h'}$; more precisely, the adjoint operators are ${\displaystyle \_\ast Q}$ and ${\displaystyle Q-\!\!\ast \,\_}$.

In separation logic, Hoare triples have a slightly different meaning than in Hoare logic. The triple ${\displaystyle \{P\}\ C\ \{Q\}}$ asserts that if the program ${\displaystyle C}$ executes from an initial state satisfying the precondition ${\displaystyle P}$ then the program will not go wrong (e.g., have undefined behaviour), and if it terminates, then the final state will satisfy the postcondition ${\displaystyle Q}$. In essence, during its execution, ${\displaystyle C}$ may access only memory locations whose existence is asserted in the precondition or that have been allocated by ${\displaystyle C}$ itself.