Confluence of Curried Term-Rewriting Systems

Kahrs, Stefan

doi:10.1006/jsco.1995.1035

Cited by 10 publications

(16 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now let R be a TRS satisfying UN. Kahrs (1995) has proved preservation of CR, and R CR is CR, therefore PP(R CR ) is CR. We will prove that PP(R) and PP(R CR ) stand in the same relation as do R and R CR .…”

Section: Preservation Of Wcr By Currying Theorem If R Is Wcr Then Ppmentioning

confidence: 95%

“…We also explore connections between currying and modular properties. Kahrs (1995) has recently shown that the Church-Rosser property (CR) is preserved by currying for all rewrite systems. This corrects an error in an earlier version of this paper, which proved preservation of CR for left-linear systems, but claimed a counterexample for non-left linear systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Comparing Curried and Uncurried Rewriting

Kennaway

Klop

Sleep

et al. 1996

Journal of Symbolic Computation

View full text Add to dashboard Cite

Currying is a transformation of term rewrite systems which may contain symbols of arbitrary arity into systems which contain only nullary symbols, together with a single binary symbol called application. We show that for all term rewrite systems (whether orthogonal or not) the following properties are preserved by this transformation: strong normalization, weak normalization, weak Church-Rosser, completeness, semi-completeness, and the non-convertibility of distinct normal forms. Under the condition of leftlinearity we show preservation of the properties NF (if a term is reducible to a normal form, then its reducts are all reducible to the same normal form) and UN → (a term is reducible to at most one normal form). We exhibit counterexamples to the preservation of NF and UN → for non-left-linear systems. The results extend to partial currying (where some subset of the symbols are curried), and imply some modularity properties for unions of applicative systems.

show abstract

Section: Preservation Of Wcr By Currying Theorem If R Is Wcr Then Ppmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Comparing Curried and Uncurried Rewriting

Kennaway

Klop

Sleep

et al. 1996

Journal of Symbolic Computation

View full text Add to dashboard Cite

show abstract

“…That is, we first introduce an explicit program symbol app to denote application and use the symbols S and F solely as constructors. Secondly we stratify the combinators C ∈ {S, F} into sets {C 0 , C 1 , C 2 } of constructors, each of which represent successive partial applications of their underlying combinator C. Although this 'currying' process is well-known from the world of functional programming, the reader may refer to [20,3] for a formal definition of this process in the context of general term rewriting.…”

Section: Encoding the Factorisation Calculusmentioning

confidence: 99%

Encoding the Factorisation Calculus

Rowe

2015

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

Jay and Given-Wilson have recently introduced the Factorisation (or SF-) calculus as a minimal fundamental model of intensional computation. It is a combinatory calculus containing a special combinator, F, which is able to examine the internal structure of its first argument. The calculus is significant in that as well as being combinatorially complete it also exhibits the property of structural completeness, i.e. it is able to represent any function on terms definable using pattern matching on arbitrary normal forms. In particular, it admits a term that can decide the structural equality of any two arbitrary normal forms. Since SF-calculus is combinatorially complete, it is clearly at least as powerful as the more familiar and paradigmatic Turing-powerful computational models of Lambda Calculus and Combinatory Logic. Its relationship to these models in the converse direction is less obvious, however. Jay and Given-Wilson have suggested that SF-calculus is strictly more powerful than the aforementioned models, but a detailed study of the connections between these models is yet to be undertaken. This paper begins to bridge that gap by presenting a faithful encoding of the Factorisation Calculus into the Lambda Calculus preserving both reduction and strong normalisation. The existence of such an encoding is a new result. It also suggests that there is, in some sense, an equivalence between the former model and the latter. We discuss to what extent our result constitutes an equivalence by considering it in the context of some previously defined frameworks for comparing computational power and expressiveness.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.0634

show abstract

“…In first-order rewriting, the question whether properties such as confluence and termination are preserved under currying or uncurrying is studied in [5,6,2]. In [6] a currying transformation from (functional) term rewriting systems (TRSs) into applicative term rewriting systems (ATRSs) is defined; a TRS is terminating if and only if its curried form is.…”

Section: Theorem 5 ⇒ R Is Well-founded On Terms Over F If and Only Ifmentioning

confidence: 99%

Simplifying Algebraic Functional Systems

Kop¹

2011

Algebraic Informatics

View full text Add to dashboard Cite

Abstract.A popular formalism of higher order rewriting, especially in the light of termination research, are the Algebraic Functional Systems (AFSs) defined by Jouannaud and Okada. However, the formalism is very permissive, which makes it hard to obtain results; consequently, techniques are often restricted to a subclass. In this paper we study termination-preserving transformations to make AFS-programs adhere to a number of standard properties. This makes it significantly easier to obtain general termination results.

show abstract

Confluence of Curried Term-Rewriting Systems

Abstract: The version in the Kent Academic Repository may differ from the final published version. Users are advised to check http://kar.kent.ac.uk for the status of the paper. Users should always cite the published version of record.

Cited by 10 publications

References 11 publications

Comparing Curried and Uncurried Rewriting

Comparing Curried and Uncurried Rewriting

Encoding the Factorisation Calculus

Simplifying Algebraic Functional Systems

Contact Info

Product

Resources

About