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.

Embryo transfer as a tool to disseminate k-casein BB genotype and improve milk clotting properties

Dairy industries are asked to be increasingly competitive and efficient. Despite the increasing trend in milk yield and protein content during the last decade genetic selection, milk coagulation ability has diminished and even if the absolute amount of cheese produced has increased, the relative cheese yield from a set amount of milk, has decreased. As casein content and variants, along with milk clotting properties (MCP) are determined to a large extent at DNA level, genetic selection and embryo transfer can provide efficacious tools to reverse this trend and achieve improvements. The aim of the proposed research was to determine how rapidly and to what extent milk coagulation properties could be improved by using embryo transfer (ET) as a tool to increase the frequency of k-casein BB genotype cattle and reducing A and E variants in an Italian Holstein herd with a low prevalence of the favourable genotype. In the effort to optimize superovulation protocols and results, synchronization of wave emergence was performed through manual transrectal ablation of the largest (dominant) ovarian follicle on days 7 or 8 of the cycle (estrus = day 0); different drugs and dosage for the superstimulation protocol were experimented trying to overcome the negative effects of stress and the perturbance of LH secretion in superovulated highly producing lactating cows and the use of SexedULTRA™ sex-sorted semen, for artificial insemination of superovulated cows was reported for the first time. The selection program carried out in this research, gave evidence and gathered empirical data of feasible genetic improvements in cheesemaking ability of milk by means of k-casein BB selection. In conclusion, in this project, selection of k-casein BB genotype markedly enhanced cheese-making properties of milk, providing an impetus to include milk coagulation traits in genetic selection and breeding programs for dairy cattle.