Coming to terms with quantified reasoning

Kovács, Laura; Robillard, Simon; Воронков, Андрей

doi:10.1145/3093333.3009887

Cited by 16 publications

(11 citation statements)

References 31 publications

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“…The majority of these options are Boolean, some are finitely-valued, some integer-valued and some range over other infinite domains. The method we used here was based on the following ideas, already described in [17].…”

Section: Resultsmentioning

confidence: 99%

Unification with Abstraction and Theory Instantiation in Saturation-based Reasoning

Reger¹,

Suda²,

Воронков³

2017

EasyChair Preprints

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This paper explores two new inference rules for reasoning with quantifiers and theories in a saturation-based first-order theorem prover. The focus here is on non-ground clauses, complementing our recent work on AVATAR modulo theories for ground theory reasoning. The current implementation focuses on complete theories, e.g. various versions of arithmetic, but we also sketch how to work with incomplete theories. The first new rule utilises theory constraint solving (an SMT solver) to perform reasoning within a clause to find an instance where we can remove one or more theory literals. This utilises the power of SMT solvers for theory reasoning with non-ground clauses, reasoning which is currently achieved by the addition of prolific theory axioms. The second new rule is unification with abstraction where the notion of unification is extended to introduce constraints where theory terms may not otherwise unify e.g. p(2) may unify with ¬p(x + 1) ∨ q(x) to produce 2 x + 1 ∨ q(x). This abstraction is performed lazily, as needed, to allow the superposition theorem prover to make as much progress as possible without the search space growing too quickly. Additionally, the first rule can be used to discharge the constraints introduced by the second. These rules were implemented within the Vampire theorem prover and experimental results show that they are useful for solving a considerable number of previously unsolved problems.

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Section: Resultsmentioning

confidence: 99%

Unification with Abstraction and Theory Instantiation in Saturation-based Reasoning

Reger¹,

Suda²,

Воронков³

2017

EasyChair Preprints

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“…. , τ n ) used in the input, Vampire defines a term algebra [9] with the single constructor t and n destructors π 1 , . .…”

Section: Polymorphic Theory Of First Class Tuplesmentioning

confidence: 99%

A FOOLish Encoding of the Next State Relations of Imperative Programs

Kotelnikov¹,

Kovács²,

Воронков³

2018

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Abstract. Automated theorem provers are routinely used in program analysis and verification for checking program properties. These properties are translated from program fragments to formulas expressed in the logic supported by the theorem prover. Such translations can be complex and require deep knowledge of how theorem provers work in order for the prover to succeed on the translated formulas. Our previous work introduced FOOL, a modification of first-order logic that extends it with syntactical constructs resembling features of programming languages. One can express program properties directly in FOOL and leave translations to plain first-order logic to the theorem prover. In this paper we present a FOOL encoding of the next state relations of imperative programs. Based on this encoding we implement a translation of imperative programs annotated with their pre-and post-conditions to partial correctness properties of these programs. We present experimental results that demonstrate that program properties translated using our method can be efficiently checked by the first-order theorem prover Vampire.

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“…Some automatic provers have native support for datatypes [28,38,42]; for these, Sledgehammer generates native definitions, which are often more efficient and complete than first-order axiomatizations. Blanchette also collaborated with the developers of the SMT solver CVC4 to add codatatypes to their solver [42].…”

Section: Tool Integrationmentioning

confidence: 99%

Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic

Julian

Blanchette

Bouzy³

et al. 2017

Frontiers of Combining Systems

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Abstract. We describe a line of work that started in 2011 towards enriching Isabelle/HOL's language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)induction. In contrast with other systems offering codatatypes, no additional axioms or logic extensions are necessary with our approach.

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Coming to terms with quantified reasoning

Cited by 16 publications

References 31 publications

Unification with Abstraction and Theory Instantiation in Saturation-based Reasoning

Unification with Abstraction and Theory Instantiation in Saturation-based Reasoning

A FOOLish Encoding of the Next State Relations of Imperative Programs

Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic

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