We study a programming language with a built-in ground type for real numbers. In order for the language to be sufficiently expressive but still sequential, we consider a construction proposed by Boehm and Cartwright. The nondeterministic nature of the construction suggests the use of powerdomains in order to obtain a denotational semantics for the language. We show that the construction cannot be modelled by the Plotkin or Smyth powerdomains, but that the Hoare powerdomain gives a computationally adequate semantics. As is well known, Hoare semantics can be used in order to establish partial correctness only. Since computations on the reals are infinite, one cannot decompose total correctness into the conjunction of partial correctness and termination as it is traditionally done. We instead introduce a suitable operational notion of strong convergence and show that total correctness can be proved by establishing partial correctness (using denotational methods) and strong convergence (using operational methods). We illustrate the technique with a representative example.then non-trivial predicates are obtained, and this together with the parallel conditional allow us to define non-trivial total functions [6].This phenomenon had been anticipated by Boehm and Cartwright [3], who also proposed a solution to this problem. In this paper, we develop the proposed solution and study its operational and denotational semantics. The idea is based on the following observations. In classical mathematics, the trichotomy law "

We study a programming language with a built-in ground type for real numbers

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Class overlap and class imbalance are two data complexities that challenge the design of effective classifiers in Pattern Recognition and Data Mining as they may cause a significant loss in performance. Several solutions have been proposed to face both data difficulties, but most of these approaches tackle each problem separately. In this paper, we propose a two-stage under-sampling technique that combines the DBSCAN clustering algorithm to remove noisy samples and clean the decision boundary with a minimum spanning tree algorithm to face the class imbalance, thus handling class overlap and imbalance simultaneously with the aim of improving the performance of classifiers. An extensive experimental study shows a significantly better behavior of the new algorithm as compared to 12 state-of-the-art under-sampling methods using three standard classification models (nearest neighbor rule, J48 decision tree, and support vector machine with a linear kernel) on both real-life and synthetic databases.