Proof Terms for Infinitary Rewriting

Lombardi, Carlos; Ríos, Alejandro; Vrijer, Roel de

doi:10.1007/978-3-319-08918-8_21

Cited by 5 publications

(15 citation statements)

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“…The available energy makes possible dissociative channels, alternative to the minimum energy path, involving excited electronic states, yielding products with a large variety of energy distribution among translational and internal degrees of freedom. Our recent studies were devoted to the photodissociation dynamics of methyl formate [2][3][4][5] , the simplest of esters and considered archetypal of organic molecules, with interest in astrochemistry 6 and prebiotic chemistry. 7 (For characterization of potential surface of chiral molecules see references [8][9][10] and for molecular dynamics simulation of enantiomeric discrimination see reference [11]).…”

Section: Introductionmentioning

confidence: 99%

Rovibrationally Excited Molecules on the Verge of a Triple Breakdown: Molecular and Roaming Mechanisms in the Photodecomposition of Methyl Formate

et al. 2016

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Hexapole oriented 2-bromobutane is photodissociated and detected by a slice-ion-imaging technique at 234 nm. The laser wavelength corresponds to the C-Br bond breaking with emission of a Br atom fragment in two accessible fine-structure states: the ground state Br (2 P3/2) and the excited state Br (2 P1/2), both observable separately by resonance-enhanced multiphoton ionization (REMPI). Orientation is evaluated by time-of-flight measurements combined with slice-ion-imaging.

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Section: Introductionmentioning

confidence: 99%

Rovibrationally Excited Molecules on the Verge of a Triple Breakdown: Molecular and Roaming Mechanisms in the Photodecomposition of Methyl Formate

et al. 2016

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“…Projections of possibly infinite reductions are also defined in [8], and in a similar way, in [15], Chapter 12; our work proposes an alternative approach to that subject, via proof terms. Proof terms for term rewriting were introduced in [15], Chapter 8 and have been adapted to the infinitary setting in [12] and [11].…”

Section: Preliminariesmentioning

confidence: 99%

“…The initial stage in the definition of infinitary proof terms, as given in [11,12], is the set of infinitary multi-steps, i.e., the finite or infinite terms over the signature extended with rule symbols. Multi-steps with exactly one occurrence of a rule symbol denote single reduction steps, e.g.…”

Section: Preliminariesmentioning

confidence: 99%

“…Permutation equivalence (noted ≈ henceforth) relates the proof terms that denote the same reduction in different ways, regarding parallelism/nesting degree, sequential order, and/or localisation. This relation is defined, in [11,12], as the congruence generated by the following seven basic equivalences: . . , t m ) where µ : l → r, s i = src(ψ i ) and t i = tgt(ψ i ) in (InOut) and (OutIn), augmented with the following equational logic rules:…”

Section: Preliminariesmentioning

confidence: 99%

“…To this end, we use the representation of infinitary rewriting by means of proof terms given in [12], which extends that given for finitary, first-order, left-linear term rewriting in [15]. A proof term is an expression, namely a term, that describes a reduction.…”

Section: Introductionmentioning

confidence: 99%

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Projections for Infinitary Rewriting

Lombardi

Ríos

Vrijer

2017

Electronic Notes in Theoretical Computer Science

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Proof terms in term rewriting are a representation means for reduction sequences, and more in general for contraction activity, allowing to distinguish e.g. simultaneous from sequential reduction. Proof terms for finitary, first-order, left-linear term rewriting are described in [15], ch. 8. In a previous work [12] we defined an extension of the finitary proof-term formalism, that allows to describe contractions in infinitary first-order term rewriting, and gave a characterisation of permutation equivalence. In this work, we discuss how projections of possibly infinite rewrite sequences can be modeled using proof terms. Again, the foundation is a characterisation of projections for finitary rewriting described in [15], Sec. 8.7. We extend this characterisation to infinitary rewriting and also refine it, by describing precisely the role that structural equivalence plays in the development of the notion of projection. The characterisation we propose yields a definite expression, i.e. a proof term, that describes the projection of an infinitary reduction over another. To illustrate the working of projections, we show how a common reduct of a (possibly infinite) reduction and a single step that makes part of it can be obtained via their respective projections. We show, by means of several examples, that the proposed definition yields the expected behavior also in cases beyond those covered by this result. Finally, we discuss how the notion of limit is used in our definition of projection for infinite reduction.

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Coinductive Foundations of Infinitary Rewriting and Infinitary Equational Logic

Endrullis¹,

Hansen

Hendriks³

et al. 2018

Logical Methods in Computer Science ; Volume 14

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We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform way. We define ∞ =, the infinitary extension of a given equational theory =R, and → ∞ , the standard notion of infinitary rewriting associated to a reduction relation →R, as follows:Here µ and ν are the least and greatest fixed-point operators, respectively, andThe setup captures rewrite sequences of arbitrary ordinal length, but it has neither the need for ordinals nor for metric convergence. This makes the framework especially suitable for formalizations in theorem provers.

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Proof Terms for Infinitary Rewriting

Cited by 5 publications

References 4 publications

Rovibrationally Excited Molecules on the Verge of a Triple Breakdown: Molecular and Roaming Mechanisms in the Photodecomposition of Methyl Formate

Rovibrationally Excited Molecules on the Verge of a Triple Breakdown: Molecular and Roaming Mechanisms in the Photodecomposition of Methyl Formate

Projections for Infinitary Rewriting

Coinductive Foundations of Infinitary Rewriting and Infinitary Equational Logic

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