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Proving Termination of Context-Sensitive Rewriting with MU-TERM
2007
Electronical Notes in Theoretical Computer Science
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Furthermore, we show how to combine them to furnish MU-TERM with an expert which is able to automatically perform the termination proofs. ...
Context-sensitive rewriting (CSR) is a restriction of rewriting which forbids reductions on selected arguments of functions. ...
A direct and automatic proof of μ-termination of R is possible with CSDPs by using an auxiliary polynomial ordering generated by a linear polynomial interpretation (computed by MU-TERM, see Figure 4 ) ...
doi:10.1016/j.entcs.2007.05.041
fatcat:cgu24egybnhezf4mw5zwtqfldy
Complexity Analysis of Term Rewriting Based on Matrix and Context Dependent Interpretations
2008
Foundations of Software Technology and Theoretical Computer Science
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For a given (terminating) term rewriting system one can often estimate its derivational complexity indirectly by looking at the proof method that established termination. ...
of context dependent interpretations and restricted triangular matrix interpretations. ...
(A direct proof of this result, i.e., a proof that argues only about context dependent interpretations, can be found in [15] .) COROLLARY 17. ...
doi:10.4230/lipics.fsttcs.2008.1762
dblp:conf/fsttcs/MoserSW08
fatcat:ntpolclienacfphg7qdc2hptya
CoLoR: a Coq library on well-founded rewrite relations and its application to the automated verification of termination certificates
2011
Mathematical Structures in Computer Science
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We also present its application to the automated verification of termination certificates, as produced by termination tools. ...
Termination is an important property of programs; notably required for programs formulated in proof assistants. ...
Contexts Contexts are defined as terms with a unique hole in a similar way (module AContext): Thanks to the use of dependent types, contexts are well-formed by construction and replacing a hole by some ...
doi:10.1017/s0960129511000120
fatcat:by6ksdib7nfpdjj54sscojozei
Proving Termination Properties with mu-term
[chapter]
2011
Lecture Notes in Computer Science
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of order-sorted rewriting, termination of context-sensitive rewriting, termination of innermost context-sensitive rewriting and termination of rewriting modulo specific axioms. ...
mu-term is a tool which can be used to verify a number of termination properties of (variants of) Term Rewriting Systems (TRSs): termination of rewriting, termination of innermost rewriting, termination ...
The most important one has been the development of the context-sensitive dependency pair framework (CSDP framework, [3, 20] ), for mechanizing proofs of termination of CSR. ...
doi:10.1007/978-3-642-17796-5_12
fatcat:5333qvps3bfgnlfywktz2wqch4
mu-term: Verify Termination Properties Automatically (System Description)
[chapter]
2020
Lecture Notes in Computer Science
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We report on the new version of mu-term, a tool for proving termination properties of variants of rewrite systems, including conditional, context-sensitive, equational, and order-sorted rewrite systems ...
The automatic generation of logical models for suitable firstorder theories and formulas provides a common basis to implement the proofs. ...
Infeasibility in Termination Proofs. ...
doi:10.1007/978-3-030-51054-1_28
fatcat:hfw3ljwsajdm7nzubf4ok6s4de
mu-term: A Tool for Proving Termination of Context-Sensitive Rewriting
[chapter]
2004
Lecture Notes in Computer Science
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The tool implements the generation of the appropriate orderings for proving termination of CSR by means of polynomial interpretations over the rational numbers. ...
In fact, mu-term is the first termination tool which generates term orderings based on such polynomial interpretations. ...
I thank Albert Rubio and Cristina Borralleras for providing most of the proofs (and disproofs) of termination of CSR with CS-RPO summarized in the aforementioned WWW site. ...
doi:10.1007/978-3-540-25979-4_14
fatcat:v7qxcoyarzgt3a5pzcnjp2g55y
Cdiprover3: A Tool for Proving Derivational Complexities of Term Rewriting Systems
[chapter]
2010
Lecture Notes in Computer Science
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This paper describes cdiprover3 a tool for proving termination of term rewrite systems by polynomial interpretations and context dependent interpretations. ...
The methods used by cdiprover3 induce small bounds on the derivational complexity of the considered system. We explain the tool in detail, and give an overview of the employed proof methods. ...
In Section 3., we briefly describe polynomial and context dependent interpretations, which are used by cdiprover3. ...
doi:10.1007/978-3-642-14729-6_11
fatcat:k5rt4ximf5gl7d2ceujmc5n5mm
CeTA - A Tool for Certified Termination Analysis
[article]
2012
arXiv
pre-print
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Since the first termination competition in 2004 it is of great interest, whether a proof that has been automatically generated by a termination tool, is indeed correct. ...
Hence the interest in automated certification of termination proofs. This led to the general approach of using proof assistants (like Coq and Isabelle) for certification. ...
For dpTrans , the dependency pairs are provided by dps . ...
arXiv:1208.1591v1
fatcat:m4ozzjbfx5cddic2riokjvmm4m
Typed syntactic meta-programming
2013
SIGPLAN notices
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and proof tactics. ...
Our system supports typesafe construction and analysis of terms, types and typing contexts. ...
The first reduction rule interprets an empty context by the unit type . ...
doi:10.1145/2544174.2500575
fatcat:7bi6pljz3rcutnwdi2xnz6zrdi
Typed syntactic meta-programming
2013
Proceedings of the 18th ACM SIGPLAN international conference on Functional programming - ICFP '13
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and proof tactics. ...
Our system supports typesafe construction and analysis of terms, types and typing contexts. ...
The first reduction rule interprets an empty context by the unit type . ...
doi:10.1145/2500365.2500575
dblp:conf/icfp/DevrieseP13
fatcat:v3cztsz4inc2dbx3tig6gc5vdm
A Mechanised Semantics for HOL with Ad-hoc Overloading
[article]
2020
arXiv
pre-print
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In this paper, we present a mechanised proof that HOL with ad-hoc overloading is consistent. All our results have been formalised in the HOL4 theorem prover. ...
This termination proof is quite laborious, at 495 lines of proof script. ...
Our termination criterion on contexts, however, is not executable as expressed. ...
arXiv:2002.10212v2
fatcat:uz7qmnbbc5d2lbv5d2dzc7g5ne
Termination proofs for higher-order rewrite systems
[chapter]
1994
Lecture Notes in Computer Science
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The result is a proof technique for the termination of a HRS, similar to the proof technique \Termination by interpretation in a wellfounded monotone algebra", described in 8, 19] . ...
This paper deals with termination proofs for Higher-Order Rewrite Systems (HRSs), introduced in 12]. ...
qy:(qy) 2qy:2(qy)
The Model of Hereditarily Monotonic Functionals We try to apply the general idea of the proof technique \termination by interpretation" for TRSs in 8, 19] to HRSs. ...
doi:10.1007/3-540-58233-9_14
fatcat:w3fhd2cpafcthiepevrsix7xj4
Proof Theory at Work: Complexity Analysis of Term Rewrite Systems
[article]
2009
arXiv
pre-print
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Abstract In this paper we study context dependent interpretations, a semantic termination method extending interpretations over the natural numbers, introduced by Hofbauer. ...
Derivational Complexities Induced by Polynomial Context Dependent Interpretations Proof. We proceed by induction on t. As t ∈ T (F), the evaluation is independent of the assignment. ...
In interpreting defined and dependency pair symbols, we restrict to polynomials whose coefficients are in the range {0, 1, . . . , 5}. ...
arXiv:0907.5527v2
fatcat:jxonbatpw5hdlabp5z7swfrgdy
Towards the Certification of Complexity Proofs
[article]
2012
arXiv
pre-print
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We report on our formalization of matrix-interpretation in Isabelle/HOL. Matrices are required to certify termination proofs and we wish to utilize them for complexity proofs, too. ...
For the latter aim, only basic methods have already been integrated, and we discuss some upcoming problems which arise when formalizing more complicated results on matrix-interpretations, which are based ...
Our formalization of matrix interpretations for termination proofs in presented in Sec. 3. We discuss the extension to complexity proofs in Sec. 4 where we also discuss some open problems. ...
arXiv:1208.1609v1
fatcat:wvir2f2emrdvbd73ydlnqmblye
Termination by Abstraction
[chapter]
2004
Lecture Notes in Computer Science
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Proof. Harmony(→ ∩ , ) follows from Mono( ) and (3,5,7). Turning to the dependency methods: Lemma 9 ([1]). Main ( ) ⇒ Basic ( ). Proof. Follows from (14). Lemma 10. ...
A small number of firms have decided to terminate their independent abstraction schemes. Lemma 7. Right ( ) ⇒ Subterm ( ). Proof. ...
If is such a flat context and t a term (or context), then by [t] we denote the term (or context) f (t 1 , . . . , t i−1 , t, t i+1 , . . . , t n ). ...
doi:10.1007/978-3-540-27775-0_1
fatcat:jh6omiqxzrarfl2eret5lopr3i
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