Nitrox 1.0

Jasmin C. Blanchette¹
¹Technische Universität München, Germany

Architecture

Nitrox is the first-order logic version of Nitpick [BN10], a counterexample generator for Isabelle/HOL [NPW02]. The name is a combination of Nitpick and Paradox. Nitrox is little more than a TPTP FOF parser. Nitpick's backend is the relational model finder Kodkod [TJ07] developed by Emina Torlak at MIT.

Strategies

Nitpick is optimized to work with higher-order logic (HOL) and its definitional principles (e.g., (co)inductive predicates, (co)inductive datatypes, (co)recursive functions). When invoked on untyped first-order problem, few of its optimizations come into play, and the problem handed to Kodkod is essentially a first-order relational logic (FORL) rendering of the TPTP FOF problem. One exception is nested quantifiers, which Nitpick optimizes before Kodkod gets a chance to look at them [BN10]. Should Nitrox prove successful in the competition, 99% of the credit should go to Emina Torlak.

Implementation

Nitpick is part of Isabelle/HOL and is written in Standard ML. Kodkod is written in Java.

Expected Competition Performance

Since Nitpick was designed for HOL, it doesn't have any type inference à la Paradox. It also doesn't use the SAT solver incrementally, which penalizes it a bit (but not as much as the missing type inference). Kodkod itself is known to perform less well on FOF than Paradox, because it is designed and optimized for a somewhat different logic, FORL. On the other hand, Kodkod's symmetry breaking seems better calibrated than Paradox's. Hence, we expect Nitrox to end up in second place.

References

BN10: Blanchette J. C., Nipkow T. (2010), Nitpick: A Counterexample Generator for Higher-Order Logic Based on a Relational Model Finder, ITP 2010.
NPW09: Nipkow T., Paulson L. C., Wenzel M. (2009), Isabelle/HOL: A Proof Assistant for Higher-Order Logic, http://www.cl.cam.ac.uk/research/hvg/Isabelle/dist/Isabelle/doc/tutorial.pdf.
TJ07: Torlak E., Jackson D. (2010), Kodkod: A Relational Model Finder, TACAS 2007.