Related papers: Generic bidirectional typing for dependent type th…
Type inference refers to the task of inferring the data type of a given column of data. Current approaches often fail when data contains missing data and anomalies, which are found commonly in real-world data sets. In this paper, we propose…
Refinement types enrich a language's type system with logical predicates that circumscribe the set of values described by the type, thereby providing software developers a tunable knob with which to inform the type system about what…
In this paper, we describe our experience incorporating gradual types in a statically typed functional language with Hindley-Milner style type inference. Where most gradually typed systems aim to improve static checking in a dynamically…
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of…
Recent years have seen growing interest in the retrofitting of type systems onto dynamically-typed programming languages, in order to improve type safety, programmer productivity, or performance. In such cases, type system developers must…
We consider a general prescriptive type system with parametric polymorphism and subtyping for logic programs. The property of subject reduction expresses the consistency of the type system w.r.t. the execution model: if a program is…
Bilinear maps and their classifying tensor products are well-known in the theory of linear algebra, and their generalization to algebras of commutative monads is a classical result of monad theory. Motivated by constructions needed in…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
This work initiates a systematic investigation of testing high-dimensional structured distributions by focusing on testing Bayesian networks -- the prototypical family of directed graphical models. A Bayesian network is defined by a…
We present a type checking algorithm for establishing a session-based discipline in the pi calculus of Milner, Parrow and Walker. Our session types are qualified as linear or unrestricted. Linearly typed communication channels are…
Dependently typed proof assistant rely crucially on definitional equality, which relates types and terms that are automatically identified in the underlying type theory. This paper extends type theory with definitional functor laws,…
In functional programming languages, generalized algebraic data types (GADTs) are very useful as the unnecessary pattern matching over them can be ruled out by the failure of unification of type arguments. In dependent type systems, this is…
This paper introduces a simple type system for combinatory logic in which combinators have at most one type, whose polymorphism is revealed by application. The combinatory types exactly describe the structure of their values, which may be…
Intersection types are an essential tool in the analysis of operational and denotational properties of lambda-terms and functional programs. Among them, non-idempotent intersection types provide precise quantitative information about the…
Gradual typing combines static and dynamic typing in the same language, offering the benefits of both to programmers. Static typing provides error detection and strong guarantees while dynamic typing enables rapid prototyping and flexible…
We introduce $\infty$-type theories as an $\infty$-categorical generalization of the categorical definition of type theories introduced by the second named author. We establish analogous results to the previous work including the…
Reasoning about the sensitivity of functions with respect to their inputs has interesting applications in various areas, such as differential privacy. In order to check and enforce sensitivity, several approaches have been developed,…
We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We…
A typed model of strategic term rewriting is developed. The key innovation is that generic traversal is covered. To this end, we define a typed rewriting calculus S'_{gamma}. The calculus employs a many-sorted type system extended by…
A prediction makes a claim about a system's future given knowledge of its past. A retrodiction makes a claim about its past given knowledge of its future. The bidirectional machine is an ambidextrous hidden Markov chain that does both…