Extracting Symbolic Transitions from TLA$^{+}$ Specifications

Abstract

In $\textsc {TLA}^{+}$, a system specification is written as a logical formula that restricts the system behavior. As a logic, $\textsc {TLA}^{+}$ does not have assignments and other imperative statements that are used by model checkers to compute the successor states of a system state. Model checkers compute successors either explicitly — by evaluating program statements — or symbolically — by translating program statements to an SMT formula and checking its satisfiability. To efficiently enumerate the successors, TLA’s model checker TLC introduces side effects. For instance, an equality $x' = e$ is interpreted as an assignment of e to the yet unbound variable x.

Inspired by TLC, we introduce an automatic technique for discovering expressions in $\textsc {TLA}^{+}$ formulas such as $x' = e$ and $x' \in \{e_1, \dots , e_k\}$ that can be provably used as assignments. In contrast to TLC, our technique does not explicitly evaluate expressions, but it reduces the problem of finding assignments to the satisfiability of an SMT formula. Hence, we give a way to slice a $\textsc {TLA}^{+}$ formula in symbolic transitions, which can be used as an input to a symbolic model checker. Our prototype implementation successfully extracts symbolic transitions from a few $\textsc {TLA}^{+}$ benchmarks.

Supported by the Vienna Science and Technology Fund (WWTF) through project APALACHE (ICT15-103) and the Austrian Science Fund (FWF) through Doctoral College LogiCS (W1255-N23).