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The reduction algorithm is used to compute reduced ideals of a number field. However, there are reduced ideals that can never be obtained from this algorithm. In this paper, we will show that these ideals have inverses of larger norms among…
Coverage Types provide a suitable type mechanism that integrates under-approximation logic to support Property-Based Testing. They are used to type the return value of a function that represents an input test generator. This allows us to…
A choice of optimization objective is immensely pivotal in the design of a recommender system as it affects the general modeling process of a user's intent from previous interactions. Existing approaches mainly adhere to three categories of…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
Feature attribution methods, proposed recently, help users interpret the predictions of complex models. Our approach integrates feature attributions into the objective function to allow machine learning practitioners to incorporate priors…
The framework Pure Type System (PTS) offers a simple and general approach to designing and formalizing type systems. However, in the presence of dependent types, there often exist certain acute problems that make it difficult for PTS to…
In dependently typed programming, proofs of basic, structural properties can be embedded implicitly into programs and do not need to be written explicitly. Besides saving the effort of writing separate proofs, a most distinguishing and…
We define a compilation scheme for a constructor-based, strongly-sequential, graph rewriting system which shortcuts some needed steps. The object code is another constructor-based graph rewriting system. This system is normalizing for the…
Optimization methods have been broadly applied to two classes of objects viz. (i) modeling and description of data and (ii) the determination of the stationary points of functions. Here, a theoretical basis is developed that optimizes an…
We introduce two-sided type systems, which are sequent calculi for typing formulas. Two-sided type systems allow for hypothetical reasoning over the typing of compound program expressions, and the refutation of typing formulas. By…
Many semantical aspects of programming languages, such as their operational semantics and their type assignment calculi, are specified by describing appropriate proof systems. Recent research has identified two proof-theoretic features that…
Automated unit test generation is an established research field that has so far focused on statically-typed programming languages. The lack of type information in dynamically-typed programming languages, such as Python, inhibits test…
The inclusion of universal quantification and a form of implication in goals in logic programming is considered. These additions provide a logical basis for scoping but they also raise new implementation problems. When universal and…
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
In multi-objective optimization problems, there might exist hidden objectives that are important to the decision-maker but are not being optimized. On the other hand, there might also exist irrelevant objectives that are being optimized but…
In this monograph, nonstandard characteristics for many notions from real analysis are obtained and applied. However, only two simple types of atomic formula are used and almost all of the characteristics are shown to hold for a simple…
Feature selection is popular for obtaining small, interpretable, yet highly accurate prediction models. Conventional feature-selection methods typically yield one feature set only, which might not suffice in some scenarios. For example,…
Genetic Algorithms have established their capability for solving many complex optimization problems. Even as good solutions are produced, the user's understanding of a problem is not necessarily improved, which can lead to a lack of…
In this paper, we argue that type inferencing incorrectly implements appropriateness specifications for typed feature structures, promote a combination of type resolution and unfilling as a correct and efficient alternative, and consider…