TeXipedia

leadsto

Indicates a progression, transformation, or leads-to relationship in mathematical or logical expressions.

Overview

Commonly employed in mathematical logic, computer science, and formal proofs to denote sequential relationships or transformations between states or expressions.

  • Frequently used in transition systems and rewrite rules to show evolution of states
  • Appears in algorithm analysis to indicate progression of computational steps
  • Popular in theoretical computer science for describing program semantics and operational reasoning
  • Serves as a more specialized alternative to regular arrows when indicating directed transformation

Examples

Showing evolution or transformation in dynamical systems.

xnxx_n \leadsto x_{\infty}
x_n \leadsto x_{\infty}

Indicating convergence or limiting behavior in sequences.

{an}L\{a_n\} \leadsto L
\{a_n\} \leadsto L

Representing state transitions in process flows.

ABCA \leadsto B \leadsto C
A \leadsto B \leadsto C