Related papers: Relating Church-Style and Curry-Style Subtyping
Typed operational semantics is a method developed by H. Goguen to prove meta-theoretic properties of type systems. This paper studies the metatheory of a type system with dependent record types, using the approach of typed operational…
Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in…
Semantic subtyping enables simple, set-theoretical reasoning about types by interpreting a type as the set of its values. Previously, semantic subtyping has been studied primarily in the context of statically typed languages with structural…
We present the first definition of strictly associative and unital $\infty$-category. Our proposal takes the form of a type theory whose terms describe the operations of such structures, and whose definitional equality relation enforces…
In type theory, we can express many practical ideas by attributing some additional data to expressions we operate on during compilation. For instance, some substructural type theories augment variables' typing judgments with the information…
In this paper, we explore a connection between type universes and memory allocation. Type universe hierarchies are used in dependent type theories to ensure consistency, by forbidding a type from quantifying over all types. Instead, the…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…
We present a novel dependent linear type theory in which the multiplicity of some variable-i.e., the number of times the variable can be used in a program-can depend on other variables. This allows us to give precise resource annotations to…
Functional logic languages can solve equations over user-defined data and functions. Thus, the definition of an appropriate meaning of equality has a long history in these languages, ranging from reflexive equality in early equational logic…
Date and Darwen have proposed a theory of types, the latter forms the basis of a detailed presentation of a panoply of simple and complex types. However, this proposal has not been structured in a formal system. Specifically, Date and…
The computer-mechanization of an ambitious explicit ethical theory, Gewirth's Principle of Generic Consistency, is used to showcase an approach for representing and reasoning with ethical theories exhibiting complex logical features like…
We show that if a context-free grammar generates a language whose lexicographic ordering is well-ordered of type less than $\omega^2$, then its order type is effectively computable.
This paper presents and extends our type theoretical framework for a compositional treatment of natural language semantics with some lexical features like coercions (e.g. of a town into a football club) and copredication (e.g. on a town as…
Type systems hide data that is captured by function closures in function types. In most cases this is a beneficial design that favors simplicity and compositionality. However, some applications require explicit information about the data…
Finster and Mimram have defined a dependent type theory called CaTT, which describes the structure of omega-categories. Types in homotopy type theory with their higher identity types form weak omega-groupoids, so they are in particular weak…
We develop semantics and syntax for bicategorical type theory. Bicategorical type theory features contexts, types, terms, and directed reductions between terms. This type theory is naturally interpreted in a class of structured…
Session types, types for structuring communication between endpoints in distributed systems, are recently being integrated into mainstream programming languages. In practice, a very important notion for dealing with such types is that of…
This is a study of the computing power of the subtyping machine behind Kennedy and Pierce's nominal subtyping with variance. We depict the lattice of fragments of Kennedy and Pierce's type system and characterize their computing power in…
Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry…
For many compiled languages, source-level types are erased very early in the compilation process. As a result, further compiler passes may convert type-safe source into type-unsafe machine code. Type-unsafe idioms in the original source and…