Constraint handling rules. Compositional semantics and program transformation

This thesis intends to investigate two aspects of Constraint Handling Rules (CHR). It proposes a compositional semantics and a technique for program transformation. CHR is a concurrent committed-choice constraint logic programming language consisting of guarded rules, which transform multi-sets of atomic formulas (constraints) into simpler ones until exhaustion [Frü06] and it belongs to the declarative languages family. It was initially designed for writing constraint solvers but it has recently also proven to be a general purpose language, being as it is Turing equivalent [SSD05a]. Compositionality is the first CHR aspect to be considered. A trace based compositional semantics for CHR was previously defined in [DGM05]. The reference operational semantics for such a compositional model was the original operational semantics for CHR which, due to the propagation rule, admits trivial non-termination. In this thesis we extend the work of [DGM05] by introducing a more refined trace based compositional semantics which also includes the history. The use of history is a well-known technique in CHR which permits us to trace the application of propagation rules and consequently it permits trivial non-termination avoidance [Abd97, DSGdlBH04]. Naturally, the reference operational semantics, of our new compositional one, uses history to avoid trivial non-termination too. Program transformation is the second CHR aspect to be considered, with particular regard to the unfolding technique. Said technique is an appealing approach which allows us to optimize a given program and in more detail to improve run-time efficiency or spaceconsumption. Essentially it consists of a sequence of syntactic program manipulations which preserve a kind of semantic equivalence called qualified answer [Frü98], between the original program and the transformed ones. The unfolding technique is one of the basic operations which is used by most program transformation systems. It consists in the replacement of a procedure-call by its definition. In CHR every conjunction of constraints can be considered as a procedure-call, every CHR rule can be considered as a procedure and the body of said rule represents the definition of the call. While there is a large body of literature on transformation and unfolding of sequential programs, very few papers have addressed this issue for concurrent languages. We define an unfolding rule, show its correctness and discuss some conditions in which it can be used to delete an unfolded rule while preserving the meaning of the original program. Finally, confluence and termination maintenance between the original and transformed programs are shown. This thesis is organized in the following manner. Chapter 1 gives some general notion about CHR. Section 1.1 outlines the history of programming languages with particular attention to CHR and related languages. Then, Section 1.2 introduces CHR using examples. Section 1.3 gives some preliminaries which will be used during the thesis. Subsequentely, Section 1.4 introduces the syntax and the operational and declarative semantics for the first CHR language proposed. Finally, the methodologies to solve the problem of trivial non-termination related to propagation rules are discussed in Section 1.5. Chapter 2 introduces a compositional semantics for CHR where the propagation rules are considered. In particular, Section 2.1 contains the definition of the semantics. Hence, Section 2.2 presents the compositionality results. Afterwards Section 2.3 expounds upon the correctness results. Chapter 3 presents a particular program transformation known as unfolding. This transformation needs a particular syntax called annotated which is introduced in Section 3.1 and its related modified operational semantics !0t is presented in Section 3.2. Subsequently, Section 3.3 defines the unfolding rule and prove its correctness. Then, in Section 3.4 the problems related to the replacement of a rule by its unfolded version are discussed and this in turn gives a correctness condition which holds for a specific class of rules. Section 3.5 proves that confluence and termination are preserved by the program modifications introduced. Finally, Chapter 4 concludes by discussing related works and directions for future work.

Relationships between plant diversity and environmental heterogeneity in rupicolous grasslands on gypsum. The case study of Alysso-Sedion albi (Habitat 6110).

Plant communities on weathered rock and outcrops are characterized by high values in species richness (Dengler 2006) and often persist on small and fragmented surfaces. Yet very few studies have examined the relationships between heterogeneity and plant diversity at small scales, in particular in poor-nutrient and low productive environment (Shmida and Wilson 1985, Lundholm 2003). In order to assess these relationships both in space and time in relationship, two different approaches were employed in the present study, in two gypsum outcrops of Northern Apennine. Diachronic and synchronic samplings from April 2012 to March 2013 were performed. A 50x50 cm plot was used in both samplings such as the sampling unit base. The diachronic survey aims to investigate seasonal patterning of plant diversity by the use of images analysis techniques integrated with field data and considering also seasonal climatic trend, the substrate quality and its variation in time. The purpose of the further, synchronic sampling was to describe plant diversity pattern as a function of the environmental heterogeneity meaning in substrate typologies, soil depth and topographic features. Results showed that responses of diversity pattern depend both on the resources availability, environmental heterogeneity and the manner in which the different taxonomic group access to them during the year. Species richness and Shannon diversity were positively affected by increasing in substrate heterogeneity. Furthermore a good turnover in seasonal species occurrence was detected. This vegetation may be described by the coexistence of three groups of species which created a gradient from early colonization stages, characterized by greater slope and predominance of bare rock, gradually to situation of more developed soil.

The impact of intraclonal heterogeneity on the outcomes of Multiple Myeloma patients treated with new drugs

Understanding the biology of Multiple Myeloma (MM) is of primary importance in the struggle to achieve a cure for this yet incurable neoplasm. A better knowledge of the mechanism underlying the development of MM can guide us in the development of new treatment strategies. Studies both on solid and haematological tumours have shown that cancer comprises a collection of related but subtly different clones, a feature that has been termed “intra-clonal heterogeneity”. This intra-clonal heterogeneity is likely, from a “Darwinian” natural selection perspective, to be the essential substrate for cancer evolution, disease progression and relapse. In this context the critical mechanism for tumour progression is competition between individual clones (and cancer stem cells) for the same microenvironmental “niche”, combined with the process of adaptation and natural selection. The Darwinian behavioural characteristics of cancer stem cells are applicable to MM. The knowledge that intra-clonal heterogeneity is an important feature of tumours’ biology has changed our way to addressing cancer, now considered as a composite mixture of clones and not as a linear evolving disease. In this variable therapeutic landscape it is important for clinicians and researchers to consider the impact that evolutionary biology and intra-clonal heterogeneity have on the treatment of myeloma and the emergence of treatment resistance. It is clear that if we want to effectively cure myeloma it is of primarily importance to understand disease biology and evolution. Only by doing so will we be able to effectively use all of the new tools we have at our disposal to cure myeloma and to use treatment in the most effective way possible. The aim of the present research project was to investigate at different levels the presence of intra-clonal heterogeneity in MM patients, and to evaluate the impact of treatment on clonal evolution and on patients’ outcomes.