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Rewrite Rule Inference Using Equality Saturation
[article]

2021
*
arXiv
*
pre-print

This paper explores how

arXiv:2108.10436v1
fatcat:254trb66wjbcpku7ifyzsz3mpq
*equality**saturation*, a promising technique that*uses*e-graphs to apply*rewrite**rules*, can also be*used*to*infer**rewrite**rules*. ... We show that*equality**saturation*efficiently shrinks both sets, leading to faster synthesis of smaller, more general rulesets. We prototyped these strategies in a tool dubbed ruler. ... We are grateful to Andrew Reynolds for answering our questions about CVC4's*rule*synthesis component, to Pavel Panchekha and Oliver Flatt for helping*us*run Herbie with Ruler's*rules*, and to Sorawee Porncharoenwase ...##
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Cut Admissibility by Saturation
[chapter]

2014
*
Lecture Notes in Computer Science
*

This also leads

doi:10.1007/978-3-319-08918-8_9
fatcat:iac7kwgrqzecdojd2rdjeumjqy
*us*to introduce an extension of deduction modulo with conditional term*rewriting**rules*. ... In this paper, we show that, in the same way that it is possible to recover confluence*using*Knuth-Bendix completion, one can regain cut admissibility in the general case*using*standard*saturation*techniques ... From Γ, A one can therefore deduce B ∨ L 1 ⊥ ∨ L n ⊥ , Let*us*show that all new clauses in the derivation of ⊓ ⊔ do not involve*equality*: Since Γ is*saturated*up to compositeness, all*inferences**using*...##
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On word problems in Horn theories
[chapter]

1988
*
Lecture Notes in Computer Science
*

We interpret Horn clauses as conditional

doi:10.1007/3-540-19242-5_12
fatcat:fd7yjxw25zakdl7wrc43nflbea
*rewrite**rules*. Then we give sufficient conditions so that the word problem can be decided by conditional normalization in some Horn theories. ... For instance, the clauses 10 and 11 in Example 2 will never be*used*as*rewrite**rules*. ... A Complete Set of*Inference**Rules*for Horn Logic with*Equality*A long-standing problem in theorem proving is to efficiently handle the*equality*relation. ...##
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On word problems in horn theories

1991
*
Journal of symbolic computation
*

We interpret Horn clauses as conditional

doi:10.1016/s0747-7171(08)80134-4
fatcat:fmjkysa7yvbmtlkujlpdbn4vgm
*rewrite**rules*. Then we give sufficient conditions so that the word problem can be decided by conditional normalization in some Horn theories. ... For instance, the clauses 10 and 11 in Example 2 will never be*used*as*rewrite**rules*. ... A Complete Set of*Inference**Rules*for Horn Logic with*Equality*A long-standing problem in theorem proving is to efficiently handle the*equality*relation. ...##
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On narrowing, refutation proofs and constraints
[chapter]

1995
*
Lecture Notes in Computer Science
*

Re nements of narrowing (basic, LSE, etc.) are instances of the technique, but are also de ned here for arbitrary (possibly ordering and/or

doi:10.1007/3-540-59200-8_47
fatcat:xx5kk5ztfffmxmmfbjxjrucfpm
*equality*constrained or not yet convergent or*saturated*) Horn ... We develop a proof technique for dealing with narrowing and refutational theorem proving in a uniform way, clarifying the exact relationship between the existing results in both elds and allowing*us*to ... for*saturated*(under an*inference*system similar to the one*used*here) sets S coincides with the unique perfect model for S under the given term ordering. ...##
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Associative-commutative superposition
[chapter]

1995
*
Lecture Notes in Computer Science
*

It is compatible with an abstract notion of redundancy that covers such simpli cation techniques as tautology deletion, subsumption, and simpli cation by (associative-commutative)

doi:10.1007/3-540-60381-6_1
fatcat:5e5ihgzlhfhvvbo266oruhs4ky
*rewriting*. ...*Using**saturation*up to redundancy, we may*infer*that C 00 is true in I C . ...*Saturation*of clause sets can be achieved by fair application of*inference**rules*. ...##
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From Search to Computation: Redundancy Criteria and Simplification at Work
[chapter]

2013
*
Lecture Notes in Computer Science
*

When executed by a theorem prover, the

doi:10.1007/978-3-642-37651-1_7
fatcat:fr4uqtwvubbtvgjepamaamojeu
*inference**rules*of these calculi usually generate a tremendously growing search space. ... This includes a variant of contextual*rewriting*to decide a subclass of Euclidean geometry, ordered chaining techniques for Church-Rosser and priority queue proofs, contextual*rewriting*and history-dependent ... The paramodulation*rule*embodies the ideas of the resolution calculus and the operation of "replacing*equals*by*equals*" that is fundamental for term*rewriting*. ...##
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Combining algebra and universal algebra in first-order theorem proving: The case of commutative rings
[chapter]

1995
*
Lecture Notes in Computer Science
*

Associative-commutative superposition forms the deductive core of our method, while a convergent

doi:10.1007/bfb0014420
fatcat:h7fr556bpra3tjrlf4jymclqq4
*rewrite*system for commutative rings provides a starting point for more specialized*inferences*tailored ... This result is obtained by the judicious application of the simpli cation techniques a orded by convergent*rewriting*and by a process called symmetrization that embeds*inferences*between single clauses ... Secondly, the*rewrite**rules*in R e may be*used*to simplify clauses in N. The latter aspect will be discussed in the next section. ...##
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Rewrite-based Equational Theorem Proving with Selection and Simplification

1994
*
Journal of Logic and Computation
*

It is often possible to compute the closure of nontrivial sets of clauses under application of non-redundant

doi:10.1093/logcom/4.3.217
fatcat:unag3wwpmzdgzcqdjx7dklezhq
*inferences*. ... We present various refutationally complete calculi for first-order clauses with*equality*that allow for arbitrary selection of negative atoms in clauses. ... One of the more successful approaches to equational theorem proving is based on the*use*of equations as (one-way)*rewrite**rules*. ...##
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Subsumption Demodulation in First-Order Theorem Proving
[article]

2020
*
arXiv
*
pre-print

Motivated by applications of first-order theorem proving to software analysis, we introduce a new

arXiv:2001.10213v1
fatcat:mlqi3hptvnflfchhkhp55w25py
*inference**rule*, called subsumption demodulation, to improve support for reasoning with conditional*equalities*... Our experiments,*using*the TPTP and SMT-LIB repositories, show that subsumption demodulation in Vampire can solve many new problems that could so far not be solved by state-of-the-art reasoners. ... An*inference**rule*is a set of*inferences*and an*inference*system is a set of*inference**rules*. An*inference*system is sound if all its*inference**rules*are sound. ...##
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Subsumption Demodulation in First-Order Theorem Proving
[chapter]

2020
*
Lecture Notes in Computer Science
*

Motivated by applications of first-order theorem proving to software analysis, we introduce a new

doi:10.1007/978-3-030-51074-9_17
fatcat:l3bzolwqqvbb5n2w7vkg2ay7vm
*inference**rule*, called subsumption demodulation, to improve support for reasoning with conditional*equalities*... Our experiments,*using*the TPTP and SMT-LIB repositories, show that subsumption demodulation in Vampire can solve many new problems that could so far not be solved by state-of-the-art reasoners. ... An*inference**rule*is a set of (concrete)*inferences*and an*inference*system is a set of*inference**rules*. An*inference*system is sound if all its*inference**rules*are sound. ...##
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Editorial

1991
*
Journal of symbolic computation
*

Kounalis & Rusinowitch suggest a notion of

doi:10.1016/s0747-7171(08)80129-0
fatcat:524cajbdfze73njq3r7nknovmy
*saturated*set for Horn clauses and give sufficient conditions under which the*use*of*saturated*sets as*rewrite**rules*provides a decision procedure for the word ... Both*inference*systems refine the resolution/paramodulation calculus and incorporate*inference**rules*for simplification by*rewriting*. ... For researchers interested in other aspects of*rewriting*and its applications, we recommend the survey,*Rewrite*Systems by N. Dershowitz and J.-P. ...##
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Automatic 'Descente Infinie' Induction Reasoning
[chapter]

2005
*
Lecture Notes in Computer Science
*

proof, and ii) reasoning modules that perform the computation and allow for modular design of the concrete

doi:10.1007/11554554_20
fatcat:sen7aduonbcerludou3fsda57m
*inference**rules*. ... We present a framework and a methodology to build and analyse automatic provers*using*the 'Descente Infinie' induction principle. ... We thank the anonymous referees and Claus-Peter Wirth for*useful*comments on previous versions of this paper. ...##
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Theorem proving in cancellative abelian monoids (extended abstract)
[chapter]

1996
*
Lecture Notes in Computer Science
*

Strong ordering constraints allow

doi:10.1007/3-540-61511-3_102
fatcat:ft66vqfawbhy3pwnakgyhh6vvq
*us*to restrict to*inferences*that involve the maximal term of the maximal sum in the maximal literal. ... We describe a re ned superposition calculus for cancellative abelian monoids which requires neither explicit*inferences*with the theory clauses nor extended equations or clauses. ... As soon as the clauses contain non-constant free function symbols, we also have to*use*the*inference**rules*of the traditional superposition calculus, i. e.,*equality*resolution, standard superposition, ...##
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Ordered chaining for total orderings
[chapter]

1994
*
Lecture Notes in Computer Science
*

We design new

doi:10.1007/3-540-58156-1_32
fatcat:losit2c3prhvtdxl7mf5qylwoy
*inference*systems for total orderings by applying*rewrite*techniques to chaining calculi. ... We demonstrate that our*inference*systems are compatible with a concept of (global) redundancy for clauses and*inferences*that covers such widely*used*simplification techniques as tautology deletion, subsumption ...*Rewrite*systems Let I be a set of ground atomic formulas and ≻ be a simplification ordering. We*use*the*equalities*and inequalities in I as*rewrite**rules*. ...
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