# E-Matching with Free Variables

@inproceedings{Rmmer2012EMatchingWF, title={E-Matching with Free Variables}, author={Philipp R{\"u}mmer}, booktitle={LPAR}, year={2012} }

E-matching is the most commonly used technique to handle quantifiers in SMT solvers. It works by identifying characteristic sub-expressions of quantified formulae, named triggers, which are matched during proof search on ground terms to discover relevant instantiations of the quantified formula. E-matching has proven to be an efficient and practical approach to handle quantifiers, in particular because triggers can be provided by the user to guide proof search; however, as it is heuristic in…

## 30 Citations

Generic decision procedures for axiomatic rst-order theories

- Mathematics
- 2014

SMT solvers are efficient tools to decide the satisfiability of ground formulas, including a number of built-in theories such as congruence, linear arithmetic, arrays, and bit-vectors. Adding a…

Adding Decision Procedures to SMT Solvers Using Axioms with Triggers

- Mathematics, Computer ScienceJournal of Automated Reasoning
- 2015

This paper proposes a framework based on the notion of instantiation patterns that provides a sound, complete, and terminating solver for her theory in return, and describes and proves a corresponding extension of the traditional Abstract DPLL Modulo Theory framework.

On Satisfiability for Quantified Formulas in Instantiation-Based Procedures

- Mathematics
- 2016

Procedures for first-order logic with equality are used in many modern theorem provers and solvers, yet procedure termination in case of interesting sub-classes of satisfiable formulas remains a…

Reducing the Complexity of Quantified Formulas via Variable Elimination

- Computer Science, MathematicsArXiv
- 2014

This work presents a general simplification of quantified SMT formulas using variable elimination based on an analysis of the ground terms occurring as arguments in function applications and describes how a satisfying model of the resulting formula can be modified to satisfy the original formula.

Congruence Closure with Free Variables

- Computer ScienceTACAS
- 2017

It is shown that the major instantiation techniques in SMT solving can be cast in a unifying framework for handling quantified formulas with equality and uninterpreted functions, and a sound and complete calculus is introduced to solve this problem in practice.

Conflicts, Models and Heuristics for Quantifier Instantiation in SMT

- Computer ScienceVampire@IJCAR
- 2016

An overview of recent advances in quantifier instantiation in SMT is given, including the well-known technique known as E-matching, and new instantiation-based techniques that are specialized to background theories such as linear real and integer arithmetic are mentioned.

Identifying Overly Restrictive Matching Patterns in SMT-based Program Verifiers

- Computer ScienceFM
- 2021

A novel algorithm is designed to synthesize missing triggering terms required to complete a proof, and tool developers can use this information to refine their matching patterns and prevent similar verification errors, or to fix a detected unsoundness.

Triggerless Happy - Intermediate Verification with a First-Order Prover

- Computer ScienceIFM
- 2017

Experiments suggest that first-order provers can help achieve more flexible and robust performance in program verification, while avoiding the pitfalls of having to manually guide instantiation of quantifiers by means of triggers.

Theorem Proving with Bounded Rigid E-Unification

- Mathematics, Computer ScienceCADE
- 2015

It is shown that (simultaneous) BREU is NP-complete, how BREU problems can be encoded as propositional SAT-problems, and used to introduce a sound and complete sequent calculus for first-order logic with equality.

Unification with Abstraction and Theory Instantiation in Saturation-Based Reasoning

- Computer ScienceTACAS
- 2018

Two new inference rules for reasoning with non-ground clauses are introduced by providing a new method of using SMT solvers in saturation-based reasoning and can be used to discharge the constraints introduced by the second.

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