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A Semantic Approach to the Analysis of Rewriting-Based Systems [article]

Salvador Lucas
2017 arXiv   pre-print
rewriting, non-loopingness of conditional rewrite systems, or the secure access to protected pages of a web site modeled as an order-sorted rewrite theory.  ...  In this paper we show that a number of interesting properties of rewriting-based systems can be investigated in this way, including infeasibility and non-joinability of critical pairs in (conditional)  ...  Conclusions and future work We have presented a semantic approach to prove properties of computational systems whose semantics can be given as a Horn theory S.  ... 
arXiv:1709.05095v1 fatcat:q4gcgjyxxzfbbcg5mkahpxkjge

Termination of String Rewriting Proved Automatically

H. Zantema
2005 Journal of automated reasoning  
of an extensive class of string rewriting systems (SRSs).  ...  The tool implementing these techniques is called TORPA: Termination of Rewriting Proved Automatically.  ...  In particular here we think of liveness problems. • The technique of dependency pairs can be seen as a technique by which termination of a rewrite system is proved via proving relative termination of a  ... 
doi:10.1007/s10817-005-6545-0 fatcat:wnbl5dhrafftve4v3zrguxoska

Dependency pairs for proving termination properties of conditional term rewriting systems

Salvador Lucas, José Meseguer
2017 Journal of Logical and Algebraic Methods in Programming  
This can be used to obtain a powerful and more expressive framework for proving termination properties of Conditional Term Rewriting Systems.  ...  semantics of the system.  ...  Termination, V -termination, and operational termination of CTRSs The semantics of rewriting-based computational systems is often described by means of the transitions induced by the rewriting steps.  ... 
doi:10.1016/j.jlamp.2016.03.003 fatcat:hc6ugzjscrhjhlbkdjqzsg656m

Proving Termination of Integer Term Rewriting [chapter]

Carsten Fuhs, Jürgen Giesl, Martin Plücker, Peter Schneider-Kamp, Stephan Falke
2009 Lecture Notes in Computer Science  
When using rewrite techniques for termination analysis of programs, a main problem are pre-defined data types like integers.  ...  We extend term rewriting by built-in integers and adapt the dependency pair framework to prove termination of integer term rewriting automatically. ⋆ In Proc. RTA'09, LNCS.  ...  AProVE08 could only prove termination of 24 of them (20.5 %) and T T T 2 proved termination of 6 examples (5.1 %). This clearly shows the enormous benefits of built-in integers in term rewriting.  ... 
doi:10.1007/978-3-642-02348-4_3 fatcat:dson7pvncfag5ghgb22ddbxf6u

Transformational methodology for proving termination of logic programs

M.R.K. Krishna Rao, Deepak Kapur, R.K. Shyamasundar
1998 The Journal of Logic Programming  
A methodology for proving the termination of well-moded logic programs is developed by reducing the termination problem of logic programs to that of term rewriting systems.  ...  A transformation procedure is presented to derive a term rewriting system from a given well-moded logic program such that the termination of the derived rewrite system implies the termination of the logic  ...  Klop of CWI for their helpful comments. Thanks are also due to the anonymous referees, whose comments have greatly improved the presentation. Dr.  ... 
doi:10.1016/s0743-1066(97)00028-9 fatcat:kp4gnme23ra7fnopvh65wcc7ny

Proving existential termination of normal logic programs [chapter]

Massimo Marchiori
1996 Lecture Notes in Computer Science  
The followed approach is to develop a suitable transformation from logic programs to Term Rewriting Systems (TRSs), such that proving termination of the obtained TRS implies existential termination of  ...  Moreover, the approach i s a l s o a b l e t o c o p e w i t h t h e dual notion of universal termination: in fact, a whole spectrum of termination properties, said k-termination, i s i n vestigated, of  ...  from logic programs into TRSs such t h a t t o p r o ve the universal termination of a logic program it su ces to prove the termination of the transformed term rewriting system.  ... 
doi:10.1007/bfb0014328 fatcat:rble65y7fncptaccx52j64ahuq

Matrix Interpretations for Proving Termination of Term Rewriting [chapter]

Jörg Endrullis, Johannes Waldmann, Hans Zantema
2006 Lecture Notes in Computer Science  
We present a new method for automatically proving termination of term rewriting.  ...  This method allows to prove termination and relative termination.  ...  Proving termination rather than relative termination is a special case of this approach: then S is empty in SN(R/S). to top → R ∪ → S .  ... 
doi:10.1007/11814771_47 fatcat:cbdgy345azcnxajxrkhogudnvi

Matrix Interpretations for Proving Termination of Term Rewriting

Jörg Endrullis, Johannes Waldmann, Hans Zantema
2007 Journal of automated reasoning  
We present a new method for automatically proving termination of term rewriting.  ...  This method allows to prove termination and relative termination.  ...  Proving termination rather than relative termination is a special case of this approach: then S is empty in SN(R/S). to top → R ∪ → S .  ... 
doi:10.1007/s10817-007-9087-9 fatcat:rfyy4j545bhg5fjcnrj3btezay

Proving termination of context-sensitive rewriting by transformation

Salvador Lucas
2006 Information and Computation  
With CSR, we can achieve a terminating behavior with non-terminating term rewriting systems, by pruning (all) infinite rewrite sequences.  ...  Several methods have been developed for proving termination of CSR. Specifically, a number of transformations that permit treating this problem as a standard termination problem have been described.  ...  This condition is based on proving termination of the so-called -rewriting of a (Conditional) TRS, where -rewriting is rewriting restricted to top redexes in terms ( [23, Definition 1] ).  ... 
doi:10.1016/j.ic.2006.07.001 fatcat:we7uzoolhfa3tpd6jnewlc7wty

Proving Termination of Context-Sensitive Rewriting with MU-TERM

Beatriz Alarcón, Raúl Gutiérrez, José Iborra, Salvador Lucas
2007 Electronical Notes in Theoretical Computer Science  
Proving termination of CSR is an interesting problem with several applications in the fields of term rewriting and programming languages.  ...  Context-sensitive rewriting (CSR) is a restriction of rewriting which forbids reductions on selected arguments of functions.  ...  In this way, for a given Term Rewriting System (TRS), we obtain a restriction of the rewrite relation which we call context-sensitive rewriting.  ... 
doi:10.1016/j.entcs.2007.05.041 fatcat:cgu24egybnhezf4mw5zwtqfldy

A methodology for proving termination of logic programs

Bal Wang, R.K. Shyamasundar
1994 The Journal of Logic Programming  
In this paper, we describe a methodology for proving termination of logic programs.  ...  Such a relation enables us to use U-graphs for establishing the universal termination of logic programs.  ...  Shyamasundar et al. [33] provide a characterization of termination of logic programs through the termination characteristics of term-rewriting systems.  ... 
doi:10.1016/0743-1066(94)90004-3 fatcat:5urbmse7pbhuzm7ob3eh7zwrki

mu-term: A Tool for Proving Termination of Context-Sensitive Rewriting [chapter]

Salvador Lucas
2004 Lecture Notes in Computer Science  
These orderings can also be used, in a number of different ways, for proving termination of ordinary rewriting.  ...  Restrictions of rewriting can eventually achieve termination by pruning all infinite rewrite sequences issued from every term. Contextsensitive rewriting (CSR) is an example of such a restriction.  ...  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

Using Well-Founded Relations for Proving Operational Termination

Salvador Lucas
2019 Journal of automated reasoning  
In this paper, we study operational termination, a proof theoretical notion for capturing the termination behavior of computational systems.  ...  We prove that operational termination can be characterized at different levels by means of wellfounded relations on specific formulas which can be obtained from the considered system.  ...  , including Conditional Term Rewriting Systems (CTRSs) [27, 37, 38] , Membership Equational Theories [8] , and Generalized Rewriting Theories [7] , among others (see also [2, 9, 35] ).  ... 
doi:10.1007/s10817-019-09514-2 fatcat:mf6q6qghknebhjwawyijyzpaq4

Methods for Proving Termination of Rewriting-based Programming Languages by Transformation

Francisco Durán, Salvador Lucas, José Meseguer
2009 Electronical Notes in Theoretical Computer Science  
tools for proving termination of (variants of) rewriting.  ...  The operational meaning of such features is often formalized in a proof theoretic manner by means of an inference system rather than just by a rewriting relation.  ...  (vi) M is a set of conditional memberships of the form (∀X) t : s if A 1 ∧ . . . ∧ A k with the A i as before. The inference system in Figure 2 defines the execution semantics of SCS-MCTRSs.  ... 
doi:10.1016/j.entcs.2009.07.062 fatcat:gf3lzx2eb5bl5glrlp7hfz26ia

Polynomials for Proving Termination of Context-Sensitive Rewriting [chapter]

Salvador Lucas
2004 Lecture Notes in Computer Science  
The latter is the case for context-sensitive rewriting (CSR), a simple restriction of rewriting which has been proved useful for describing the semantics of several programming languages (e.g., Maude)  ...  For instance, the dependency pairs method for proving termination of rewriting, and some restrictions of the rewrite relation which are not monotonic in all arguments of the function symbols, can benefit  ...  This provides a new technique for proving termination of rewriting (Example 5) and a basis for proving termination of CSR by means of very general polynomial interpretations which can be characterized  ... 
doi:10.1007/978-3-540-24727-2_23 fatcat:dgodjvwoeja3ndv2uqq74wrwvi
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