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Conference Papers Year : 2017

## Congruence Closure with Free Variables

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Haniel Barbosa
• Function : Author
• PersonId : 776201
• IdRef : 204081629
Pascal Fontaine
Andrew Reynolds
• Function : Author

#### Abstract

Many verification techniques nowadays successfully rely on SMT solvers as back-ends to automatically discharge proof obligations. These solvers generally rely on various instantiation techniques to handle quantifiers. We here show that the major instantiation techniques in SMT solving can be cast in a unifying framework for handling quantified formulas with equality and uninterpreted functions. This framework is based on the problem of $E$-ground (dis)unification, a variation of the classic rigid $E$-unification problem. We introduce a sound and complete calculus to solve this problem in practice: Congruence Closure with Free Variables (CCFV). Experimental evaluations of implementations of CCFV in the state-of-the-art solver CVC4 and in the solver veriT exhibit improvements in the former and makes the latter competitive with state-of-the-art solvers in several benchmark libraries stemming from verification efforts.

### Dates and versions

hal-01590918 , version 1 (20-09-2017)

### Identifiers

• HAL Id : hal-01590918 , version 1
• DOI :

### Cite

Haniel Barbosa, Pascal Fontaine, Andrew Reynolds. Congruence Closure with Free Variables. TACAS 2017 - 23rd International Conference on Tools and Algorithms for Construction and Analysis of Systems, Apr 2017, Uppsala, Sweden. pp.220 - 230, ⟨10.1007/10721959_17⟩. ⟨hal-01590918⟩

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