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Soundness and Completeness Proofs by Coinductive Methods
2016
Journal of automated reasoning
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We show how codatatypes can be employed to produce compact, high-level proofs of key results in logic: the soundness and completeness of proof systems for variations of first-order logic. ...
Soundness becomes interesting as soon as one allows infinite proofs of first-order formulas. ...
Popescu was partially supported by the EPSRC project Verification of Web-based Systems (VOWS, grant EP/N019547/1) and by the DFG project Security Type Systems and Deduction (grant NI 491/ 13-3). ...
doi:10.1007/s10817-016-9391-3
fatcat:vnleinry7jckjfp3qvgginqs34
Coinductive Soundness of Corecursive Type Class Resolution
[chapter]
2017
Lecture Notes in Computer Science
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This paper shows, for the first time, that corecursive type class resolution and its recent extensions are coinductively sound with respect to the greatest Herbrand models of logic programs and that they ...
Horn clauses and first-order resolution are commonly used for the implementation of type classes in Haskell. ...
), by COST Action IC1202 (TACLe), supported by COST (European Cooperation in Science and Technology), and by EPSRC grant EP/K031864/1-2 "'Coalgebraic Logic Programming for Type Inference". ...
doi:10.1007/978-3-319-63139-4_18
fatcat:jmfbgvz36jgsfiaboiiox5bniy
Coinductive Soundness of Corecursive Type Class Resolution
[article]
2016
arXiv
pre-print
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This paper shows, for the first time, that corecursive type class resolution and its extensions are coinductively sound with respect to the greatest Herbrand models of logic programs and that they are ...
We establish incompleteness results for various fragments of the proof system. ...
Applications -a Software Engineering Approach" (ICT-644235), and by COST Action IC1202 (TACLe), supported by COST (European Cooperation in Science and Technology). ...
arXiv:1608.05233v2
fatcat:w5h4djfwizgsroan7gbmac2rie
Coinduction in Uniform: Foundations for Corecursive Proof Search with Horn Clauses
[chapter]
2019
Lecture Notes in Computer Science
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with recursion controlled by the later modality; and soundness of both proof systems is proven relative to a novel coalgebraic description of complete Herbrand models. ...
We establish proof-theoretic, constructive and coalgebraic foundations for proof search in coinductive Horn clause theories. ...
We would like to thank Damien Pous and the anonymous reviewers for their valuable feedback. ...
doi:10.1007/978-3-030-17184-1_28
fatcat:7azord5jkjhlvdxyir54hjsdqq
Structural Resolution: a Framework for Coinductive Proof Search and Proof Construction in Horn Clause Logic
[article]
2017
arXiv
pre-print
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Finite SLD-computations are inductively sound and complete with respect to least Herbrand models of logic programs. ...
This puts coinductive methods in LP on par with productivity-based observational approaches to coinduction in ITP and TRS. ...
and Tom Schrijvers. ...
arXiv:1511.07865v2
fatcat:6lqbu7vyqzegnchxtiws7ty3fu
Towards Coinductive Theory Exploration in Horn Clause Logic: Position Paper
2018
Electronic Proceedings in Theoretical Computer Science
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To this aim, we propose a coinductive extension of Miller et al's framework of uniform proofs and prove its soundness relative to coinductive models of Horn clause logic. ...
Coinduction occurs in two guises in Horn clause logic: in proofs of self-referencing properties and relations, and in proofs involving construction of (possibly irregular) infinite data. ...
Intuitively, the proof proceeds by defining a scheme by which we can reconstruct a corresponding non-terminating derivation, and then showing that the proofs are sound w.r.t greatest complete Herbrand ...
doi:10.4204/eptcs.278.5
fatcat:e5z3z3pn4rbuvbx3dral2fxqny
A Coalgebraic Foundation for Coinductive Union Types
[chapter]
2014
Lecture Notes in Computer Science
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We obtain inclusion of tree languages as a sound and complete method to show semantic subtyping of recursive types with basic types, product and union, interpreted coinductively. ...
We give a sound and complete characterization of semantic subtyping in terms of inclusion of maximal traces. ...
Existing coinductive proof methods such as [3] [4] [5] are incomplete and involve complex soundness proofs. ...
doi:10.1007/978-3-662-43951-7_6
fatcat:dxksvgigpne67kbrfqjtjiyiim
Tower Induction and Up-to Techniques for CCS with Fixed Points
[chapter]
2017
Lecture Notes in Computer Science
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We present a refinement of Pous' companion-based coinductive proof technique and apply it to CCS with general fixed points. ...
Our induction principle implies a new sufficient condition for soundness of up-to techniques subsuming respectfulness and compatibility. ...
[5] have introduced another enhancement of the coinductive proof method in the form of parameterized coinduction. ...
doi:10.1007/978-3-319-57418-9_17
fatcat:5oehvrfjgzbnria3scuejuli4e
Coinductive Uniform Proofs
[article]
2019
arXiv
pre-print
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To this aim, we propose a coinductive extension of Miller et al framework of uniform proofs and prove its soundness relative to coinductive models of Horn clause logic. ...
Coinduction occurs in two guises in Horn clause logic: in proofs of circular properties and relations, and in proofs involving construction of infinite data. ...
By transitivity of ⊆, I x ⊆ T (I), for all I x . So I ⊆ T (I), by the construction of I . D.3 Proof of Theorem 1 (Soundness of Coinductive Uniform Proofs) Theorem 1 (Soundness of co-hohh proofs). ...
arXiv:1903.07371v1
fatcat:wbq75w5wd5dfxefhevozlz7frm
Coinductive big-step operational semantics for type soundness of Java-like languages
2011
Proceedings of the 13th Workshop on Formal Techniues for Java-Like Programs - FTfJP '11
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We prove that such a semantics is sound w.r.t. the usual small-step operational semantics, and then prove soundness of a conventional nominal type system w.r.t. the coinductive semantics. ...
We define a coinductive semantics for a simple Java-like language by simply interpreting coinductively the rules of a standard big-step operational semantics. ...
The complete proof with all necessary lemmas can be found in a companion paper [2] . Then we show that soundness of the type system w.r.t. ...
doi:10.1145/2076674.2076679
dblp:conf/ecoop/Ancona11
fatcat:2v5n5wmxlfdhvptssuj4vto45u
Proving partial-correctness and invariance properties of transition-system models
2019
Science of Computer Programming
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We embed the proof system in the Coq proof assistant and formally prove its soundness and completeness. ...
The complete proof strategy reduces partial correctness to invariance. ...
We thank the anonymous reviewers of earlier versions of this paper for their useful hints and suggestions, especially the suggestion to use coinduction, and David Nowak for his lessons on coinduction in ...
doi:10.1016/j.scico.2019.102342
fatcat:aqregmbhdfau7i6ncnibu37n7m
Circular Coinduction with Special Contexts
[chapter]
2009
Lecture Notes in Computer Science
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, intuitively
Behavioral Specifications, Intuitively
2 Circular Coinduction
Circular Coinduction, intuitively
Proof System
3 Special Contexts
Intuition
Special Hypothesis Defined by Special Contexts ...
Cuza Univ. of Iasi (UAIC, RO) and Univ. of Illinois
at Urbana-Champaign (UIUC, US)
CIRC implements circular coinduction and circular induction
completely automated
1 Introduction
Behavioral Equivalence ...
Achievements: circular coinduction is a simple an powerful proof method by coinduction special hypotheses defined by the special contexts significantly improves the circular coinduction proof systems the ...
doi:10.1007/978-3-642-10373-5_33
fatcat:q4y7vcdz2nektjfypxisvofqoy
Coinductive Proof Techniques for Language Equivalence
[chapter]
2013
Lecture Notes in Computer Science
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Language equivalence can be checked coinductively by establishing a bisimulation on suitable deterministic automata. ...
Then we extend our enhanced proof method to incorporate language complement and intersection. ...
Conclusions We presented a proof method for language equivalence, based on coinduction and bisimulation-up-to. ...
doi:10.1007/978-3-642-37064-9_42
fatcat:fy6mexeq5bawpovgqdlgae6sqy
The New Normal: We Cannot Eliminate Cuts in Coinductive Calculi, But We Can Explore Them
[article]
2020
arXiv
pre-print
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We show that CoLP by Gupta et al. gives rise to cut-free proofs in CLJ with fixpoint terms, and we formulate and implement a novel method of coinductive theory exploration that provides several heuristics ...
For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less studied in coinductive extensions of sequent calculi. ...
Simon et al. (2006) have shown that the method of loop detection is sound relative to the complete Herbrand models of logic programs. ...
arXiv:2008.03714v1
fatcat:a2vx23xm6za2tbuuz5jxl54tsm
The New Normal: We Cannot Eliminate Cuts in Coinductive Calculi, But We Can Explore Them
2020
Theory and Practice of Logic Programming
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We show that CoLP by Gupta et al. gives rise to cut-free proofs in CLJ with fixpoint terms, and we formulate and implement a novel method of coinductive theory exploration that provides several heuristics ...
For example, Gentzen's classical and intuitionistic calculi LK and LJ enjoy cut elimination. The property is less studied in coinductive extensions of sequent calculi. ...
Simon et al. (2006) have shown that the method of loop detection is sound relative to the complete Herbrand models of logic programs. ...
doi:10.1017/s1471068420000423
fatcat:nsdrc3y2kfb5jab5taalswsxfe
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