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Superposition with Datatypes and Codatatypes
[chapter]
2018
Lecture Notes in Computer Science
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Both techniques are refutationally complete with respect to nonstandard models of datatypes and nonbranching codatatypes. ...
They take into account the acyclicity of datatype values and the existence and uniqueness of cyclic codatatype values. ...
We also thank Mark Summerfield and the anonymous reviewers for suggesting textual improvements. ...
doi:10.1007/978-3-319-94205-6_25
fatcat:peou2nkwu5czfj7xxq5rlbzhzi
A Decision Procedure for (Co)datatypes in SMT Solvers
[chapter]
2015
Lecture Notes in Computer Science
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We present a decision procedure that combines reasoning about datatypes and codatatypes. ...
The dual of the acyclicity rule for datatypes is a uniqueness rule that identifies observationally equal codatatype values, including cyclic values. ...
theory solver for datatypes in CVC4. ...
doi:10.1007/978-3-319-21401-6_13
fatcat:itn4t2xfgbbpti372aks3zf2te
A Decision Procedure for (Co)datatypes in SMT Solvers
2016
Journal of automated reasoning
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We present a decision procedure that combines reasoning about datatypes and codatatypes. ...
The dual of the acyclicity rule for datatypes is a uniqueness rule that identifies observationally equal codatatype values, including cyclic values. ...
theory solver for datatypes in CVC4. ...
doi:10.1007/s10817-016-9372-6
fatcat:dy4ek27mufedxgnepocebkzf3q
A verified prover based on ordered resolution
2019
Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019
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The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning. ...
As a step towards verifying modern provers, we specify, using Isabelle/HOL, a purely functional first-order ordered resolution prover and establish its soundness and refutational completeness. ...
An earlier version of this paper was included as a chapter of Schlichtkrull's Ph.D. thesis [36] with the same authors' list. ...
doi:10.1145/3293880.3294100
dblp:conf/cpp/SchlichtkrullBT19
fatcat:ftlcitpp7rbsbevdkf6nl6r25y
Coming to terms with quantified reasoning
2017
Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages - POPL 2017
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provers with additional inference rules. ...
We also show that Vampire implementing our methods outperforms existing SMT solvers able to deal with algebraic data types. ...
the EPSRC grant ReVeS: Reasoning for Verification and Security. ...
doi:10.1145/3009837.3009887
fatcat:26soclwzs5gkbkc5ao2t42vg7m
Coming to Terms with Quantified Reasoning
[article]
2016
arXiv
pre-print
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provers with additional inference rules. ...
We also show that Vampire implementing our methods outperforms existing SMT solvers able to deal with algebraic data types. ...
the EPSRC grant ReVeS: Reasoning for Verification and Security. ...
arXiv:1611.02908v1
fatcat:gfxm4sj7prgcrdpl3ymffnhp4m
Formalizing Bachmair and Ganzinger's Ordered Resolution Prover
[chapter]
2018
Lecture Notes in Computer Science
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We developed general infrastructure and methodology that can form the basis of completeness proofs for related calculi, including superposition. ...
We present an Isabelle/HOL formalization of the first half of Bachmair and Ganzinger's chapter on resolution theorem proving, culminating with a refutationally complete first-order prover based on ordered ...
Unlike datatypes, codatatypes allow infinite values-e.g., LCons 0 (LCons 1 (LCons 2 . . .) ). ...
doi:10.1007/978-3-319-94205-6_7
fatcat:hmjoecj5obe2ji6ldifhh3yfbu
Deduction Beyond First-Order Logic (Dagstuhl Seminar 17371)
2018
Dagstuhl Reports
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Much research in the past two decades was dedicated to automating first-order logic with equality. However, applications often need reasoning beyond this logic. ...
The aim of the seminar was to bring together first-order automated reasoning experts and researchers working on deduction methods and tools that go beyond first-order logic. ...
We discussed different abstractions and refinement strategies for reasoning with large first-order theories. ...
doi:10.4230/dagrep.7.9.26
dblp:journals/dagstuhl-reports/BlanchetteFST17
fatcat:yfc3wk2fwngc3i2dmjwrz3gsgi
A Comprehensive Framework for Saturation Theorem Proving
[chapter]
2020
Lecture Notes in Computer Science
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We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution or superposition. ...
It allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures in such a way that the static refutational completeness of a calculus immediately ...
We thank Alexander Bentkamp for discussions about prover architectures for higher-order logic and for feedback from instantiating the framework, Mathias ...
doi:10.1007/978-3-030-51074-9_18
fatcat:2fb33hm7djhu5pofxbdca3cggu
A modular Isabelle framework for verifying saturation provers
2021
Proceedings of the 10th ACM SIGPLAN International Conference on Certified Programs and Proofs
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We present a formalization in Isabelle/HOL of a comprehensive framework for proving the completeness of automatic theorem provers based on resolution, superposition, or other saturation calculi. ...
As a case study, we re-verified Bachmair and Ganzinger's resolution prover RP to show the benefits of modularity. ...
comments and suggestions. ...
doi:10.1145/3437992.3439912
fatcat:cpcmx7adpzgvzhkch5nm4ozjb4
Towards Strong Higher-Order Automation for Fast Interactive Verification
unpublished
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With higher-order superposition and higher-order SMT in place, highly automatic provers could be built on modern superposition provers and SMT solvers, following a stratified architecture reminiscent of ...
From this point of view, it seems desirable to enrich superposition and SMT (satisfiability modulo theories) with higher-order reasoning in a careful manner, to preserve their good properties. ...
functions or formulas) and for reasoning about λ -terms, polymorphic types, (co)datatypes, and (co)induction. ...
doi:10.29007/3ngx
fatcat:phg6can6eraqfdw2vybzq3sbyy
EPiC Series in Computing Towards Strong Higher-Order Automation for Fast Interactive Verification
2017
EPiC Series in Computing
unpublished
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With higher-order superposition and higher-order SMT in place, highly automatic provers could be built on modern superposition provers and SMT solvers, following a stratified architecture reminiscent of ...
From this point of view, it seems desirable to enrich superposition and SMT (satisfiability modulo theories) with higher-order reasoning in a careful manner, to preserve their good properties. ...
functions or formulas) and for reasoning about λ -terms, polymorphic types, (co)datatypes, and (co)induction. ...
fatcat:v7eyz4yfxjd6zh3mw6q6t37bua
History of Interactive Theorem Proving
[chapter]
2014
Handbook of the History of Logic
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ACKNOWLEDGEMENTS The authors are grateful to Jörg Siekmann for inviting them to prepare this chapter and for his patience in the face of our lengthy delays. ...
The helpful review of the official reader Larry Paulson as well as useful comments from Mike Gordon, Tom Hales and J Moore, have significantly improved the eventual form of the chapter. ...
, 1998; Homeier, 2005] , more general forms of recursive datatypes with infinite branching, nested and mutual recursion or dual codatatypes [Gunter, 1993; Harrison, 1995a; Berghofer and Wenzel, 1999; ...
doi:10.1016/b978-0-444-51624-4.50004-6
fatcat:sngnxnl3ivectj5taj3dgsaa7m
Deep Learning for Computer Vision (Dagstuhl Seminar 17391) Body-Centric Computing (Dagstuhl Seminar 17392)
unpublished
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This report documents the program and the outcomes of Dagstuhl Seminar 17361 "Finite and Algorithmic Model Theory". ...
We discussed different abstractions and refinement strategies for reasoning with large first-order theories. Acknowledgments. ...
This We presented an approach to reasoning with large theories which is based on the abstractionrefinement framework [1]. ...
fatcat:7srdlw7mxfhrpiwdxshf2n455y