Maximal Sharing in the Lambda Calculus with letrec

Increasing sharing in programs is desirable to compactify the code, and to avoid duplication of reduction work at run-time, thereby speeding up execution. We show how a maximal degree of sharing can be obtained for programs expressed as terms in the lambda calculus with letrec. We introduce a notion of `maximal compactness' for lambda-letrec-terms among all terms with the same infinite unfolding. Instead of defined purely syntactically, this notion is based on a graph semantics. lambda-letrec-terms are interpreted as first-order term graphs so that unfolding equivalence between terms is preserved and reflected through bisimilarity of the term graph interpretations. Compactness of the term graphs can then be compared via functional bisimulation. We describe practical and efficient methods for the following two problems: transforming a lambda-letrec-term into a maximally compact form; and deciding whether two lambda-letrec-terms are unfolding-equivalent. The transformation of a lambda-letrec-term $L$ into maximally compact form $L_0$ proceeds in three steps: (i) translate L into its term graph $G = [[ L ]]$; (ii) compute the maximally shared form of $G$ as its bisimulation collapse $G_0$; (iii) read back a lambda-letrec-term $L_0$ from the term graph $G_0$ with the property $[[ L_0 ]] = G_0$. This guarantees that $L_0$ and $L$ have the same unfolding, and that $L_0$ exhibits maximal sharing. The procedure for deciding whether two given lambda-letrec-terms $L_1$ and $L_2$ are unfolding-equivalent computes their term graph interpretations $[[ L_1 ]]$ and $[[ L_2 ]]$, and checks whether these term graphs are bisimilar. For illustration, we also provide a readily usable implementation.Comment: 18 pages, plus 19 pages appendi

Hierarchical Graph Transformation

If systems are specified by graph transformation, large graphs should be structured in order to be comprehensible. In this paper, we present an approach for the rule-based transformation of hierarchically structured (hyper)graphs. In these graphs, distinguished hyperedges contain graphs that can be hierarchical again. Our framework extends the well-known double-pushout approach from at to hierarchical graphs. In particular, we show how pushouts and pushout complements of hierarchical graphs and graph morphisms can be constructed recursively. Moreover, we make rules more expressive by introducing variables which allow to copy and to remove hierarchical subgraphs in a single rule application

Rewriting modulo symmetric monoidal structure

String diagrams are a powerful and intuitive graphical syntax for terms of symmetric monoidal categories (SMCs). They find many applications in computer science and are becoming increasingly relevant in other fields such as physics and control theory.An important role in many such approaches is played by equational theories of diagrams, typically oriented and applied as rewrite rules. This paper lays a comprehensive foundation for this form of rewriting. We interpret diagrams combinatorially as typed hypergraphs and establish the precise correspondence between diagram rewriting modulo the laws of SMCs on the one hand and double pushout (DPO) rewriting of hypergraphs, subject to a soundness condition called convexity, on the other. This result rests on a more general characterisation theorem in which we show that typed hypergraph DPO rewriting amounts to diagram rewriting modulo the laws of SMCs with a chosen special Frobenius structure.We illustrate our approach with a proof of termination for the theory of non-commutative bimonoids

Rewriting Systems for Reachability in Vector Addition Systems with Pairs

15 pagesInternational audienceWe adapt hypergraph rewriting system to a generalization of Vector Addition Systems with States (VASS) that we call vector addition systems with pairs (VASP). We give rewriting systems and strategies, that allow us to obtain reachability equivalence results between some classes of VASP and VASS. Reachability for the later is well known be equivalent to reachability in Petri nets. VASP generalize also Branching Extension of VASS (BVASS) for which it is unknown if they are more expressive than VASS. We consider here a more restricted notion of reachability for VASP than that for BVASS. However the reachability decision problem corresponding is already equivalent to decidability of the provability in Multiplicative and Exponential Linear Logic (MELL), a question left open for more than 20 years

Disability, Personalisation and Community Arts:exploring the spatial dynamics of children with disabilities participating in inclusive music classes

This paper uses personalisation and the capabilities approach to explore inclusive music classes for children with disabilities in Scotland. It provides a unique insight into the impact of participation through the voices of the disabled young musicians, their parents and tutors. The study highlights the power of inclusive spaces to transform lives, to build confidence and intersectional identities. It engages in the spatial dynamic of opening up inclusive spaces, as well as exposing emerging tensions in the liminal space that is created through movement between safe and supported spaces and the antithesis, spaces that disempower and marginalise. The findings suggest good practice around personalisation, when conceived of from a social justice perspective, as a template for working with other marginalised groups and in other professional settings

Confluence up to Garbage

No abstract available

Synaptic and transcriptionally downregulated genes are associated with cortical thickness differences in autism.

Differences in cortical morphology-in particular, cortical volume, thickness and surface area-have been reported in individuals with autism. However, it is unclear what aspects of genetic and transcriptomic variation are associated with these differences. Here we investigate the genetic correlates of global cortical thickness differences (ΔCT) in children with autism. We used Partial Least Squares Regression (PLSR) on structural MRI data from 548 children (166 with autism, 295 neurotypical children and 87 children with ADHD) and cortical gene expression data from the Allen Institute for Brain Science to identify genetic correlates of ΔCT in autism. We identify that these genes are enriched for synaptic transmission pathways and explain significant variation in ΔCT. These genes are also significantly enriched for genes dysregulated in the autism post-mortem cortex (Odd Ratio (OR) = 1.11, Pcorrected  10-14), driven entirely by downregulated genes (OR = 1.87, Pcorrected  10-15). We validated the enrichment for downregulated genes in two independent data sets: Validation 1 (OR = 1.44, Pcorrected = 0.004) and Validation 2 (OR = 1.30; Pcorrected = 0.001). We conclude that transcriptionally downregulated genes implicated in autism are robustly associated with global changes in cortical thickness variability in children with autism