Inspired by a recent work of Mesnager, we present several new infinite families of quadratic ternary bent, near-bent and 2-plateaued functions from some known quadratic ternary bent functions. Meanwhile, the distribution of the Walsh spectrum of two class of 2-plateaued functions obtained in this paper is completely determined. Additionally, we construct the first class of p-ary bent functions ...

We show that function types which have only initial algebras for regular functors in the domains, i.e. first order function types, can be represented by terminal coalgebras for certain nested functors. The representation exploits properties of ω-limits and local ω-colimits.

Two general classes (constructions) of bent functions are derived from the notion of spread. The first class, PS, gives a useful framework for designing bent functions which are constant (except maybe at 0) on each of the m-dimensional subspaces of F22m belonging to a partial spread. Explicit expressions (which may be used for applications) of bent functions by means of the trace can be derived...

We present a proof procedure for functional first-order logic programs. The programs we consider allow first-order goals (including disjunctions, conjunctions, negations, and quantifications on elements of the domain). Atoms are either built-in statements or reduction statements of the form t → s, meaning that t is reducible to s. Call-time choices are used and the functions are non-determinist...

We prove the soundness of a polymorphic type system for a language with variables, assignments, and first-class functions. As a corollary, this proves the soundness of the Edinburgh LCF ML rules for typing variables and assignments, thereby settling a long-standing open problem.

The study of structure systems, an abstraction of the concept of firstorder structures, is continued. Structure systems have algebraic systems, rather than universal algebras, as their algebraic reducts. Moreover, their relational component consists of a collection of relation systems on the underlying functors, rather than simply a system of relations on a single set. A variety of operators on...

We study the expressive power of fragments of inclusion and independence logic defined either by restricting the number of universal quantifiers or the arity of inclusion and independence atoms in formulas. Assuming the so-called lax semantics for these logics, we relate these fragments of inclusion and independence logic to familiar sublogics of existential second-order logic. We also show tha...