Normalisation for higher-order calculi with explicit substitutions

Explicit substitutions (ES) were introduced as a bridge between the theory of rewrite systems with binders and substitution, such as the λ-calculus, and their implementation. In a seminal paper Melliès observed that the dynamical properties of a rewrite system and its ES-based implementation may not coincide: he showed that a strongly normalising term (i.e. one which does not admit infinite derivations) in the λ-calculus may lose this status in its ES-based implementation. This paper studies normalisation for the latter systems in the general setting of higher-order rewriting: Based on recent work extending the theory of needed strategies to non-orthogonal rewrite systems we show that needed strategies normalise in the ES-based implementation of any orthogonal pattern higher-order rewrite system.Facultad de Informátic

Normalisation for higher-order calculi with explicit substitutions

Explicit substitutions (ES) were introduced as a bridge between the theory of rewrite systems with binders and substitution, such as the λ-calculus, and their implementation. In a seminal paper Melliès observed that the dynamical properties of a rewrite system and its ES-based implementation may not coincide: he showed that a strongly normalising term (i.e. one which does not admit infinite derivations) in the λ-calculus may lose this status in its ES-based implementation. This paper studies normalisation for the latter systems in the general setting of higher-order rewriting: Based on recent work extending the theory of needed strategies to non-orthogonal rewrite systems we show that needed strategies normalise in the ES-based implementation of any orthogonal pattern higher-order rewrite system.Facultad de Informátic

Braids via term rewriting

We present a brief introduction to braids, in particular simple positive braids, with a double emphasis: first, we focus on term rewriting techniques, in particular, reduction diagrams and decreasing diagrams. The second focus is our employment of the colored braid notation next to the more familiar Artin notation. Whereas the latter is a relative, position dependent, notation, the former is an absolute notation that seems more suitable for term rewriting techniques such as symbol tracing. Artin's equations translate in this notation to simple word inversions. With these points of departure we treat several basic properties of positive braids, in particular related to the word problem, confluence property, projection equivalence, and the congruence property. In our introduction the beautiful diamond known as the permutohedron plays a decisive role

Proof pearl: abella formalization of lambda-calculus cube property

International audienceIn 1994 Gerard Huet formalized in Coq the cube property of lambda-calculus residuals. His development is based on a clever idea, a beautiful inductive definition of residuals. However, in his formalization there is a lot of noise concerning the representation of terms with binders. We re-interpret his work in Abella, a recent proof assistant based on higher-order abstract syntax and provided with a nominal quantifier. By revisiting Huet's approach and exploiting the features of Abella, we get a strikingly compact and natural development, which makes Huet's idea really shine

Normalisation for higher-order calculi with explicit substitutions

Explicit substitutions (ES) were introduced as a bridge between the theory of rewrite systems with binders and substitution, such as the λ-calculus, and their implementation. In a seminal paper Melliès observed that the dynamical properties of a rewrite system and its ES-based implementation may not coincide: he showed that a strongly normalising term (i.e. one which does not admit infinite derivations) in the λ-calculus may lose this status in its ES-based implementation. This paper studies normalisation for the latter systems in the general setting of higher-order rewriting: Based on recent work extending the theory of needed strategies to non-orthogonal rewrite systems we show that needed strategies normalise in the ES-based implementation of any orthogonal pattern higher-order rewrite system.Facultad de Informátic

Homological Computations for Term Rewriting Systems

An important problem in universal algebra consists in finding presentations of algebraic theories by generators and relations, which are as small as possible. Exhibiting lower bounds on the number of those generators and relations for a given theory is a difficult task because it a priori requires considering all possible sets of generators for a theory and no general method exists. In this article, we explain how homological computations can provide such lower bounds, in a systematic way, and show how to actually compute those in the case where a presentation of the theory by a convergent rewriting system is known. We also introduce the notion of coherent presentation of a theory in order to consider finer homotopical invariants. In some aspects, this work generalizes, to term rewriting systems, Squier\u27s celebrated homological and homotopical invariants for string rewriting systems

Film adaptation of the post-apartheid South African novel: re-examining the aesthetics of creation of disgrace

While many scholarships of the film adaptation of Disgrace have championed the fidelity rhetoric of the film with respect to J.M. Coetzee's novel, and in so doing, have advocated the axiomatic hierarchy of literature over cinema, this dissertation challenges the fidelity discourse about the film and proposes new tropes for adaptation criticism beyond the classical paradigm. Central to the thesis is the argument that a re-examination of Steve Jacobs's feature film Disgrace unveils the inconsistency and inadequacy of the fidelity rhetoric as a language for adaptation criticism, positions the film as an independent genre with its specificity and poeticity, and allows for an intertextual dialogue with other post-apartheid South African and postcolonial African cinematic productions as a means of promoting adaptation criticism beyond the fidelity model. While cementing the film's independent status vis-à-vis the novel, the intertextual critique also allows for a rewriting of Jacobs's Disgrace that addresses its shortcomings and controversies. Hence, drawing upon structural narratologists such as Gerard Genette, postcolonial scholars such as Gayatri Spivak and Frantz Fanon, and adaptation critics including Linda Hutcheon, Robert Stam, Alexie Tcheuyap, and Lindiwe Dovey, the dissertation explores at a time formal and thematic aesthetics of the film adaptation to diversify its critical avenues not only but also to bridge epistemological gaps left by previous studies which are limited to thematic hermeneutics