8,340 research outputs found
Strict Ideal Completions of the Lambda Calculus
Full text linkThe infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of strictness. To obtain infinitary normalisation and infinitary confluence properties for these calculi, Kennaway et al. extend beta-reduction with infinitely many `bot-rules', which contract meaningless terms directly to bot. Three of the resulting Böhm reduction calculi have unique infinitary normal forms corresponding to Böhm-like trees.
In this paper we develop a corresponding theory of infinitary lambda calculi based on ideal completion instead of metric completion. We show that each of our calculi conservatively extends the corresponding metric-based calculus. Three of our calculi are infinitarily normalising and confluent; their unique infinitary normal forms are exactly the Böhm-like trees of the corresponding metric-based calculi. Our calculi dispense with the infinitely many bot-rules of the metric-based calculi. The fully non-strict calculus (called 111) consists of only beta-reduction, while the other two calculi (called 001 and 101) require two additional rules that precisely state their strictness properties: lambda x.bot -> bot (for 001) and bot M -> bot (for 001 and 101)
Infinitary Term Graph Rewriting is Simple, Sound and Complete
Full text linkBased on a simple metric and a simple partial order on term graphs, we develop two infinitary calculi of term graph rewriting. We show
that, similarly to infinitary term rewriting, the partial order formalisation yields a conservative extension of the metric formalisation of the calculus. By showing that the resulting calculi
simulate the corresponding well-established infinitary calculi of term rewriting in a sound and complete manner, we argue for the appropriateness of our approach to capture the notion of infinitary term graph rewriting
Böhm Reduction in Infinitary Term Graph Rewriting Systems
Full text linkThe confluence properties of lambda calculus and orthogonal term rewriting do not generalise to the corresponding infinitary calculi. In order to recover the confluence property in a meaningful way, Kennaway et al. introduced Böhm reduction, which extends the ordinary reduction relation so that "meaningless terms" can be contracted to a fresh constant "bottom". In previous work, we have established that Böhm reduction can be instead characterised by a different mode of convergences of transfinite reductions that is based on a partial order structure instead of a metric space.
In this paper, we develop a corresponding theory of Böhm reduction for term graphs. Our main result is that partial order convergence in a term graph rewriting system can be truthfully and faithfully simulated by metric convergence in the Böhm extension of the system. To prove this result we generalise the notion of residuals and projections to the setting of infinitary term graph rewriting. As ancillary results we prove the infinitary strip lemma and the compression property, both for partial order and metric convergence
Abstract Models of Transfinite Reductions
Full text linkWe investigate transfinite reductions in abstract reduction
systems. To this end, we study two abstract models for transfinite
reductions: a metric model generalising the usual metric approach to
infinitary term rewriting and a novel partial order model. For both
models we distinguish between a weak and a strong variant of
convergence as known from infinitary term rewriting. Furthermore, we
introduce an axiomatic model of reductions that is general enough to
cover all of these models of transfinite reductions as well as the
ordinary model of finite reductions. It is shown that, in this
unifying axiomatic model, many basic relations between termination and
confluence properties known from finite reductions still hold. The
introduced models are applied to term rewriting but also to term graph
rewriting. We can show that for both term rewriting as well as for
term graph rewriting the partial order model forms a conservative
extension to the metric model
Partial order infinitary term rewriting and böhm trees
Full text linkVol. 10(2:6)2014, pp. 1–52 www.lmcs-online.or
Modes of Convergence for Term Graph Rewriting
Full text linkTerm graph rewriting provides a simple mechanism to
finitely represent restricted forms of infinitary term
rewriting. The correspondence between infinitary term rewriting and
term graph rewriting has been studied to some extent. However, this
endeavour is impaired by the lack of an appropriate counterpart of
infinitary rewriting on the side of term graphs. We aim to fill this
gap by devising two modes of convergence based on a partial order
resp. a metric on term graphs. The thus obtained structures
generalise corresponding modes of convergence that are usually
studied in infinitary term rewriting. We argue that this yields a
common framework in which both term rewriting and term graph
rewriting can be studied. In order to substantiate our claim, we
compare convergence on term graphs and on terms. In particular, we
show that the resulting infinitary calculi of term graph rewriting
exhibit the same correspondence as we know it from term rewriting:
Convergence via the partial order is a conservative extension of the
metric convergence
Art, Biography, Sexuality: Patrick Procktor and Keith Vaughan
No full textThis critical review forms a reflection on the research published within the following publications:
Patrick Procktor: Art and Life (Unicorn Press, 2010)
Keith Vaughan: The Mature Oils 1946-1977, (Sansom & Co., 2012)
The research is on two artists, Patrick Procktor (1936-2003), and Keith Vaughan (1912-1977). The monograph on Procktor – previously one of the least documented of the generation of artists who came to prominence in London in the Sixties – positions him in a history of art from which he had been notably absent. The research on Vaughan asserts a new reading of his work, one that is both deeper and more nuanced in its analysis of the ways in which personal experience and sexuality are encoded autobiographically within his work. Crucially, in both artists biography and work are symbiotically linked; the research therefore examines the links between life and art.
Revisionary in intent, the work examines trajectories of experience of gay British (or rather, English) artists in the twentieth century, artists who sought to express themselves and forge careers within the constraints of a heteronormative society, albeit one in which attitudes to sexuality were undergoing change. As gay men, both were constrained by the social mores of their times, and each used painting as a means to affirm personal and sexual identities. A key research interest is in the ways in which sexuality and persona are reflected in critical responses to the artist’s work: in Vaughan, Procktor and other gay male artists of the period. The writing on both Procktor and Vaughan examines the relationship between their personal and professional/artistic lives, framed within a broader socio-political and art historical context. It asserts the place of biography as a means to understand and form new readings of the work. The work adds substantially to the literature and wider discourse on post-war British painting and social history
Patrick Chamoiseau Recovering Memory
No full textThis timely new book skillfully examines the work of the award-winning writer Patrick Chamoiseau. Considered by many as one of the most innovative writers to hit the French literary scene in over 40 years, Chamoiseau made his name with his book Texaco (published in 1992 and winner of the highest literary prize in France, the Prix Goncourt). His books have gone on to sell millions and his work has been translated by a number of academic presses. McCusker sets the author in context, providing a valuable contribution to 'memory studies' by looking at literary representation of memory in Martinique, a society founded on slavery but now politically assimilated to the metropolitan centre, France.Title Page -- Contents -- Introduction -- 1: Beginnings: The Enigma of Origin -- 2: 'Une tracée de survie': Autobiographical Memory -- 3: Memory Re-collected: Witnesses and Words -- 4: Memory Materialized: Traces of the Past -- 5: Flesh Made Word: Traumatic Memory in Biblique des derniers gestes -- Afterword -- Notes -- Bibliography -- IndexThis timely new book skillfully examines the work of the award-winning writer Patrick Chamoiseau. Considered by many as one of the most innovative writers to hit the French literary scene in over 40 years, Chamoiseau made his name with his book Texaco (published in 1992 and winner of the highest literary prize in France, the Prix Goncourt). His books have gone on to sell millions and his work has been translated by a number of academic presses. McCusker sets the author in context, providing a valuable contribution to 'memory studies' by looking at literary representation of memory in Martinique, a society founded on slavery but now politically assimilated to the metropolitan centre, France.Description based on publisher supplied metadata and other sources.Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, YYYY. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries
Musikstädte as real and imaginary soundscapes: urban musical images as literary motifs in twentieth-century German modernism
No full textPhDThis study examines German literary images of musical life as part of the wider sound identity of the modern German city at the turn of the twentieth century. Focussing on a forty-year period from 1890 to 1930, synonymous with the emergence of the modern German metropolis as an aesthetic object, the project assesses, compares and contrasts how musical life in the Musikstädte was perceived and portrayed by writers in an increasingly noisy urban environment. How does urban musical life influence and condition city writings? What are the differences and similarities between the writings on various musical cities? Can an urban textual sound identity be derived from these differences and similarities? The approach employed to answer these questions is a new, cross-disciplinary one to urban sound in literature, moving beyond reading the key sounds of the urban soundscape using urban musicology, sensorial anthropology and cultural poetics towards a literary contextualisation of the urban aural experience.
The literary motifs of the symphony, the gramophone and urban noise are put under the spotlight through the analysis of a wide range of modernist works by authors who have a special relationship with music. At the centre of this analysis are the Kaffeehausliteratur authors Hermann Bahr, Alfred Polgar and Peter Altenberg, the then Munich-based author Thomas Mann and the lesser known René Schickele. The analysis of these particular works is framed in the music-geographical context of the Musikstadt and literary underpinnings of this topos, ranging from Ingeborg Bachmann to Hans Mayer and, once again, Thomas Mann. In analysing these texts, the methodological approach devised by Strohm, who identifies the blending of a range of urban sounds as a definition of urban space and identity, is applied. His ideas combine historical literary
analysis, musical history and urban sociology. They are rarely used in the analysis of the auditory environment.Arts and Humanities Research Council
Westfield TrustWestfield Trust Studentship
Arts and Humanities Reseach Council (AHRC
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