Coming to terms with quantified reasoning

Kovács, Laura; Robillard, Simon; Воронков, Андрей

doi:10.1145/3009837.3009887

Cited by 37 publications

(36 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To axiomatize this datatype, we would firstly add an axiom stating nil is never equal to any term of the form cons(h, t) (distinctness axiom). Secondly, we would add an axiom stating that all terms of the form cons(h, t) are equal to each other if the corresponding arguments are equal (injectivity axiom) [7,5]. All of our own encodings of algebraic datatypes as well as the encoding used internally by Vampire 4.1 with support for term algebraic reasoning contain these axioms.…”

Section: Discussionmentioning

confidence: 99%

“…The main difference between the problems encoded in TPTP and the problems encoded in SMTLIB is the encoding of closed algebraic datatypes: For the TPTP encodings, we add axioms that describe the corresponding term algebras for each closed algebraic datatype. These axioms are mostly just like the ones also used internally in Vampire 4.1 with the -tar option [7]. When using SMTLIB, we simply translate our original closed algebraic datatypes syntactically to corresponding constructs in SMTLIB.…”

Section: Setupmentioning

confidence: 99%

“…This version allows using the SMTLIB format (version 2.6) 1 as input, which contains constructs for directly specifying algebraic datatypes. Kovács, Robillard and Voronkov [7] show that this new Vampire 4.1 variant can solve many proof problems with algebraic datatypes which previously, no other prover could solve. Hence, it may be that the new support for algebraic datatypes also proves more of the proof problems we are interested in.…”

Section: Introductionmentioning

confidence: 96%

“…One hypothetical reason for encountering such situations could be our external encoding of algebraic datatypes, which may not be optimal with regard to the search heuristics that Vampire 4.1 employs internally. The most recent version of Vampire 4.1 now includes internal support for algebraic datatypes [7], where reasoning about term algebras is integrated into the superposition calculus. This version allows using the SMTLIB format (version 2.6) 1 as input, which contains constructs for directly specifying algebraic datatypes.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Using Vampire with Support for Algebraic Datatypes in Type Soundness Proofs

Grewe¹,

Pacak²,

Mezini³

EPiC Series in Computing

View full text Add to dashboard Cite

In our ongoing project VeriTaS, we aim at automating soundness proofs for type sys- tems of domain-specific languages. In the past, we successfully used previous Vampire versions for automatically discharging many intermediate proof obligations arising within standard soundness proofs for small type systems. With older Vampire versions, encoding the individual proof problems required manual encoding of algebraic datatypes via the theory of finite term algebras. One of the new Vampire versions now supports the direct specification of algebraic datatypes and integrates reasoning about term algebras into the internally used superposition calculus.In this work, we investigate how many proof problems that typically arise within type soundness proofs different Vampire 4.1 versions can prove. Our test set consists of proof problems from a progress proof of a type system for a subset of SQL. We compare running Vampire 4.1 with our own encodings of algebraic datatypes (in untyped as well as in typed first-order logic) to running Vampire 4.1 with support for algebraic datatypes, which uses SMTLIB as input format. We observe that with our own encodings, Vampire 4.1 still proves more of our input problems. We discuss the differences between our own encoding of algebraic datatypes and the ones used within Vampire 4.1 with support for algebraic datatypes.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: Setupmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Using Vampire with Support for Algebraic Datatypes in Type Soundness Proofs

Grewe¹,

Pacak²,

Mezini³

EPiC Series in Computing

View full text Add to dashboard Cite

show abstract

“…Regarding term algebras, the SMT solvers Z3 and CVC4 both include theory solvers for the ground theory. The automated theorem prover Vampire allows reasoning with term algebras, based on a conservative extension of the theory complemented by dedicated inference rules [7,23].…”

Section: Encoding Of Natural Numbersmentioning

confidence: 99%

Loop Analysis by Quantification over Iterations

Gleiss

Kovács

Robillard

EPiC Series in Computing

Self Cite

View full text Add to dashboard Cite

We present a framework to analyze and verify programs containing loops by using a first-order language of so-called extended expressions. This language can express both functional and temporal properties of loops. We prove soundness and completeness of our framework and use our approach to automate the tasks of partial correctness verification, termination analysis and invariant generation. For doing so, we express the loop semantics as a set of first-order properties over extended expressions and use theorem provers and/or SMT solvers to reason about these properties. Our approach supports full first-order reasoning, including proving program properties with alternation of quantifiers. Our work is implemented in the tool QuIt and successfully evaluated on benchmarks coming from software verification.

show abstract

Induction in Saturation-Based Proof Search

Reger

Воронков

2019

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Many applications of theorem proving, for example program verification and analysis, require first-order reasoning with both quantifiers and theories such as arithmetic and datatypes. There is no complete procedure for reasoning in such theories but the state-of-the-art in automated theorem proving is still able to reason effectively with real-world problems from this rich domain. In this paper we introduce a missing part of the puzzle: automated induction inside a saturation-based theorem prover. Our goal is to incorporate lightweight automated induction in a way that complements the saturation-based approach, allowing us to solve problems requiring a combination of first-order reasoning, theory reasoning, and inductive reasoning. We implement a number of techniques and heuristics and evaluate them within the Vampire theorem prover. Our results show that these new techniques enjoy practical success on real-world problems.

show abstract

Coming to terms with quantified reasoning

Cited by 37 publications

References 19 publications

Using Vampire with Support for Algebraic Datatypes in Type Soundness Proofs

Using Vampire with Support for Algebraic Datatypes in Type Soundness Proofs

Loop Analysis by Quantification over Iterations

Induction in Saturation-Based Proof Search

Contact Info

Product

Resources

About