Related papers: Denotational semantics for guarded dependent type …
Homotopy Type Theory is a new field of mathematics based on the surprising and elegant correspondence between Martin-Lofs constructive type theory and abstract homotopy theory. We have a powerful interplay between these disciplines - we can…
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…
In Constructive Type Theory, recursive and corecursive definitions are subject to syntactic restrictions which guarantee termination for recursive functions and productivity for corecursive functions. However, many terminating and…
State of the art optimisation passes for dependently typed languages can help erase the redundant information typical of invariant-rich data structures and programs. These automated processes do not dramatically change the structure of the…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
Temporal gates play a significant role in modern recurrent-based neural encoders, enabling fine-grained control over recursive compositional operations over time. In recurrent models such as the long short-term memory (LSTM), temporal gates…
Featherweight Generic Go (FGG) is a minimal core calculus modeling the essential features of the programming language Go. It includes support for overloaded methods, interface types, structural subtyping and generics. The most…
We introduce a temporal model for reasoning on disjunctive metric constraints on intervals and time points in temporal contexts. This temporal model is composed of a labeled temporal algebra and its reasoning algorithms. The labeled…
We extend resource-bounded type theory to Martin-Lof type theory (MLTT) with dependent types, enabling size-indexed cost bounds for programs over inductive families. We introduce a resource-indexed universe hierarchy U_r where r is an…
Time series graphical models have recently received considerable attention for characterizing (conditional) dependence structures in multivariate time series. In many applications, the multivariate series exhibit variable-partitioned…
Like the notion of computation via (strong) monads serves to classify various flavours of impurity, including exceptions, non-determinism, probability, local and global store, the notion of guardedness classifies well-behavedness of cycles…
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…
Recurrent Neural Networks (RNNs) with attention mechanisms have obtained state-of-the-art results for many sequence processing tasks. Most of these models use a simple form of encoder with attention that looks over the entire sequence and…
This paper presents a computationally efficient robust model predictive control law for discrete linear time invariant systems subject to additive disturbances that may depend on the state and/or input norms. Despite the dependency being…
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
The chase algorithm is a fundamental tool for query evaluation and query containment under constraints, where the constraints are (sub-classes of) tuple-generating dependencies (TGDs) and equality generating depencies (EGDs). So far, most…
Type classes in Haskell are used to implement ad-hoc polymorphism, i.e. a way to ensure both to the programmer and the compiler that a set of functions are defined for a specific data type. All instances of such type classes are expected to…
Motivated by applications in movement ecology, in this paper I propose a new class of integrated continuous-time hidden Markov models in which each observation depends on the underlying state of the process over the whole interval since the…
Most categorical models for dependent types have traditionally been heavily set based: contexts form a category, and for each we have a set of types in said context -- and for each type a set of terms of said type. This is the case for…
Inspired by the trend on unifying theories of programming, this paper shows how the algebraic treatment of standard data dependency theory equips relational data with functional types and an associated type system which is useful for type…