Jacobson (1999) proposes an account of anaphora and binding that eschews variables and variable assignments, instead treating pronouns as identity functions and extending functional application with operations that pass up and close off anaphoric dependencies. This paper reviews the central aspects of Jacobson’s variable-free semantics, counterpoising it with the standard, variable-full framework. I discuss conceptual and empirical virtues of Jacobson’s theory, and some shortcomings, one significant. I argue that these limitations can be overcome by drawing on certain design features of the standard account, connect this approach to the computer science concept of ‘applicative functors’ (and thereby to frameworks as varied as alternative semantics and continuations), and clarify which of the variable-free theory’s properties should be regarded as proprietary, and which can be easily repurposed into a theory with variables.