# Counterexample Guided Quantifier Instantiation for Synthesis in SMT

Counterexample Guided Quantifier Instantiation for Synthesis in SMT” by Andrew Reynolds, Morgan Deters, Viktor Kuncak, Clark Barrett, and Cesare Tinelli. In Proceedings of the 27^th International Conference on Computer Aided Verification (CAV '15), (Daniel Kroening and Corina S. P\u{a}s\u{a}reanu, eds.), July 2015, pp. 198-216. San Francisco, CA.

## Abstract

We introduce the first program synthesis engine implemented inside an SMT solver. We present an approach that extracts solution functions from unsatisfiability proofs of the negated form of synthesis conjectures. We also discuss novel counterexample-guided techniques for quantifier instantiation that we use to make finding such proofs practically feasible. A particularly important class of specifications are single-invocation properties, for which we present a dedicated algorithm. To support syntax restrictions on generated solutions, our approach can transform a solution found without restrictions into the desired syntactic form. As an alternative, we show how to use evaluation function axioms to embed syntactic restrictions into constraints over algebraic datatypes, and then use an algebraic datatype decision procedure to drive synthesis. Our experimental evaluation on syntax-guided synthesis benchmarks shows that our implementation in the CVC4 SMT solver is competitive with state-of-the-art tools for synthesis.

BibTeX entry:

@inproceedings{RDK+15,
author = {Andrew Reynolds and Morgan Deters and Viktor Kuncak and Clark
Barrett and Cesare Tinelli},
editor = {Daniel Kroening and Corina S. P\u{a}s\u{a}reanu},
title = {Counterexample Guided Quantifier Instantiation for Synthesis
in {SMT}},
booktitle = {Proceedings of the {\it 27^{th}} International Conference
on Computer Aided Verification (CAV '15)},
series = {Lecture Notes in Computer Science},
volume = {9206},
number = {2},
pages = {198--216},
publisher = {Springer},
month = jul,
year = {2015},
note = {San Francisco, CA},
url = {http://www.cs.nyu.edu/~barrett/pubs/RDK+15.pdf}
}


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