Related papers: Impredicative Encodings of (Higher) Inductive Type…
Homotopy Type Theory with a univalent universe $\,\mathcal{U}_0$ is interpreted at the strength of finite order arithmetic. We eliminate Grothendieck universes, avoid the axiom of replacement, and bound all uses of separation.
In the context of dependent type theory, we show that coinductive predicates have an equivalent topological counterpart in terms of coinductively generated positivity relations, introduced by G. Sambin to represent closed subsets in…
A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations,…
Inductive families provide a convenient way of programming with dependent types. Yet, when it comes to compilation, their default linked-tree runtime representations, as well as the need to convert between different indexed views of the…
Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
Using dependent type theory to formalise the syntax of dependent type theory is a very active topic of study and goes under the name of "type theory eating itself" or "type theory in type theory." Most approaches are at least loosely based…
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…
We investigate the class of models of a general dependent theory. We continue math.LO/0702292 in particular investigating so called "decomposition of types"; thesis is that what holds for stable theory and for Th(Q,<) hold for dependent…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…
When working in Homotopy Type Theory and Univalent Foundations, the traditional role of the category of sets, Set, is replaced by the category hSet of homotopy sets (h-sets); types with h-propositional identity types. Many of the properties…
Token representation strategies within large-scale neural architectures often rely on contextually refined embeddings, yet conventional approaches seldom encode structured relationships explicitly within token interactions. Self-attention…
Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Guarded recursion is a powerful modal approach to recursion that can be seen as an abstract form of step-indexing. It is currently used extensively in separation logic to model programming languages with advanced features by solving domain…
The problem of learning a minimal consistent model from a set of labeled sequences of symbols is addressed from a satisfiability modulo theories perspective. We present two encodings for deterministic finite automata and extend one of these…
A type theory is presented that combines (intuitionistic) linear types with type dependency, thus properly generalising both intuitionistic dependent type theory and full linear logic. A syntax and complete categorical semantics are…
We introduce a universe of regular datatypes with variable binding information, for which we define generic formation and elimination (i.e. induction /recursion) operators. We then define a generic alpha-equivalence relation over the types…
We define a class of higher inductive types that can be constructed in the category of sets under the assumptions of Zermelo-Fraenkel set theory without the axiom of choice or the existence of uncountable regular cardinals. This class…
This paper deals with Fountain codes, and especially with their encoding matrices, which are required here to be invertible. A result is stated that an encoding matrix induces a permutation. Also, a result is that encoding matrices form a…