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Sequentiality in orthogonal term rewriting systems

Jan Willem Klop, Aart Middeldorp
1991 Journal of symbolic computation  
A strongly sequential orthogonal term rewriting system admits an efficiently computable normalizing one-step reduction strategy. As shown by Huet and I.  ...  In this paper we present an alternative analysis of strongly sequential term rewriting systems, leading to two simplified proofs of the decidability of this property.  ...  Every left sequential constructor system is strongly sequential. PROOF. Let R be a left sequential constructor system.  ... 
doi:10.1016/s0747-7171(08)80124-1 fatcat:xgkaa5k7njdhdcc6lmt5uwqfb4

Free sequentially in orthogonal order-sorted rewriting systems with constructors [chapter]

Delia Kesner
1992 Lecture Notes in Computer Science  
We de ne free sequentiality for the class of orthogonal systems with constructors, a notion which does not impose conditions over the signature.  ...  We introduce the notions of sequentiality and strong sequentiality in ordersorted rewriting systems, both closely related to the subsort order and to the form of declarations of the signature.  ...  While strong sequentiality is equivalent to optimal computations in orthogonal untyped rewriting systems with constructors, a combination of sequential matching (strongly sequential bases) and sequential  ... 
doi:10.1007/3-540-55602-8_195 fatcat:ug6yq4cq3ff6vmzd3355k5ehja

Programming in Equational Logic: Beyond Strong Sequentiality

R.C. Sekar, I.V. Ramakrishnan
1993 Information and Computation  
Orthogonal term rewriting systems (also known as regular systems) provide an elegant framework for programming in equational logic.  ...  However, this algorithm required the input programs to be restricted to the subclass of strongly sequential systems.  ...  (This de nition is adapted from the de nition of strongly sequential systems in KM89], wherein it is also established that the notions of strong sequentiality and strong sequentiality are equivalent.  ... 
doi:10.1006/inco.1993.1026 fatcat:fgjmffkbpngjvbvpfxy2yfuj44

Polymorphic Iterable Sequential Effect Systems [article]

Colin S. Gordon
2020 arXiv   pre-print
Effect systems are lightweight extensions to type systems that can verify a wide range of important properties with modest developer burden.  ...  Understanding such systems in terms of a semilattice of effects grounds understanding of the essential issues, and provides guidance when designing new effect systems.  ...  Rewriting these traditional sequential effect judgments in a form closer to the traditional commutative form reveals some subtleties of sequential effect systems: Γ, : ⊢ : ′ | (Υ Υ ′ ) ⊗ Γ ⊢ ( . ) : (Υ  ... 
arXiv:1808.02010v5 fatcat:bkel27dtkffujjumvlnfkcwway

A refinement of strong sequentiality for term rewriting with constructors

Satish Thatte
1987 Information and Computation  
A much simpler and more direct proof of the sufliciency of strict sequentiality for the existence of such an algorithm in the case of constructor systems can be found in (Thatte, 1984) .  ...  Second, there is no algorithm which is safe for aZ1 systems based on a set of left-hand sides if that set is not left sequential, or, equivalently, not strongly sequential.  ... 
doi:10.1016/0890-5401(87)90050-2 fatcat:xswelfv72ba7xa5w7bvzu5slgu

Compositional Properties of Sequential Processes

Naijun Zhan
2005 Electronical Notes in Theoretical Computer Science  
It is widely agreed that the modular method is one of the most effective methods to specify and verify complex systems in order to avoid combinatorial explosion.  ...  In this paper, we study the compositionality of FLC, namely, to investigate the connection between the connectives of the logic and the constructors of programs.  ...  Acknowledgement Special thanks are due to Prof. Mila Majster-Cederbaum for her supervision and many fruitful discussions on the topic related to this paper.  ... 
doi:10.1016/j.entcs.2004.12.018 fatcat:i5eb4sltezfhjoc44dggfoou4e

Sequential and Concurrent Abstract Machines for Interaction Nets [chapter]

Jorge Sousa Pinto
2000 Lecture Notes in Computer Science  
This paper is a formal study of how to implement interaction nets, filling an important gap in the work on this graphical rewriting formalism, very promising for the implementation of languages based on  ...  As a natural extension of this, we then give a concurrent shared-memory abstract machine, and show how to implement it, resulting in the first parallel implementation of interaction nets.  ...  A standard result of (abstract) rewrite systems also yields, as a consequence of strong confluence: Lemma 1. Any normalizing interaction net is strongly normalizing. Remarks.  ... 
doi:10.1007/3-540-46432-8_18 fatcat:fyz4zukhdzf5lfrnojrmpwbub4

Page 6951 of Mathematical Reviews Vol. , Issue 95k [page]

1995 Mathematical Reviews  
{For the entire collection see MR 95j:68012.} 95k:68093 68Q42 Durand, Iréne (F-BORD-LB; Talence) ; Salinier, Bruno (F-BORD-LB; Talence) Constructor equivalent term rewriting systems are strongly sequential  ...  : a direct proof.  ... 

Compositional verification of sequential programs with procedures

Dilian Gurov, Marieke Huisman, Christoph Sprenger
2008 Information and Computation  
We present a method for algorithmic, compositional verification of control-flow-based safety properties of sequential programs with procedures.  ...  sequential procedural language.  ...  w in α M (A) form (together with w) a strongly connected component and are equivalent with respect to structural simulation.  ... 
doi:10.1016/j.ic.2008.03.003 fatcat:i2bb4ckl5ngp3aa6ezxzhpqt4a

Lifting Sequential Effects to Control Operators

Colin S. Gordon, Tobias Pape, Robert Hirschfeld
2020 European Conference on Object-Oriented Programming  
Sequential effect systems are a class of effect system that exploits information about program order, rather than discarding it as traditional commutative effect systems do.  ...  We give an effect system for a subset of Racket's tagged delimited control operators, as a lifting of an effect system for a language without direct control operators.  ...  Conclusions We have given the first general approach to integrating arbitrary sequential effect systems with tagged delimited control operators, which allows lifting existing sequential effect systems  ... 
doi:10.4230/lipics.ecoop.2020.23 dblp:conf/ecoop/Gordon19a fatcat:auadqh6nk5ga3eunegxv4z6bde

Page 5759 of Mathematical Reviews Vol. , Issue 97I [page]

1997 Mathematical Reviews  
Summary: “Strongly sequential constructor systems admit a very efficient algorithm to compute normal forms.  ...  “In this article, we present a new transformation which trans- forms any forward-branching system into a strongly sequential constructor system.  ... 

Separation logic for sequential programs (functional pearl)

Arthur Charguéraud
2020 Proceedings of the ACM on Programming Languages (PACMPL)  
This paper presents a simple mechanized formalization of Separation Logic for sequential programs.  ...  The formalization serves as support for a course that follows the style of the successful Software Foundations series, with all the statement and proofs formalized in Coq.  ...  The third one asserts that several copies of ⊤ ⊤ are equivalent to a single ⊤ ⊤.  ... 
doi:10.1145/3408998 fatcat:do7vjcwo2rc4pmqpdcnq6leshy

Lazy productivity via termination

Jörg Endrullis, Dimitri Hendriks
2011 Theoretical Computer Science  
We present a procedure for transforming strongly sequential constructor-based term rewriting systems (TRSs) into context-sensitive TRSs in such a way that productivity of the input system is equivalent  ...  A TRS is called productive if all its finite ground terms are constructor normalizing, and all 'inductive constructor paths' through the resulting (possibly non-wellfounded) constructor normal form are  ...  These systems can be rendered as strongly sequential term rewriting systems [23, 30] . For constructor TRSs it is known that strong sequentiality coincides with inductive sequentiality, see [21] .  ... 
doi:10.1016/j.tcs.2011.03.024 fatcat:akkabcwbt5cxdefk5voryqi5ca

The revised report on the syntactic theories of sequential control and state

Matthias Felleisen, Robert Hieb
1992 Theoretical Computer Science  
Hieb, The revised report on the syntactic theories of sequential control and state, Theoretical Computer Science 103 (1992) 235-271.  ...  Mason and Talcott's equational proof systems are essentially ad hoc approximations to the operational equivalences of the respective languages.  ...  For the simulation of these in a term rewriting system, we define the following computation rules: Notice that (ax.e)v is a redex for the reduction relations but not for the computation relations: in A  ... 
doi:10.1016/0304-3975(92)90014-7 fatcat:kpuhyvpsgfa6ngy2dotv446osi

Efficient Simulation of Forward-Branching Systems with Constructor Systems

1996 Journal of symbolic computation  
Strongly sequential constructor systems admit a very e cient algorithm to compute normal forms.  ...  In this article, we present a new transformation which transforms any forward-branching system into a strongly sequential constructor system.  ...  The class of strongly sequential term rewriting systems (SS) was de ned by Huet and L vy (1991) .  ... 
doi:10.1006/jsco.1996.0058 fatcat:kvut4jkrpzfofdl6y4zx2iazmq
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