Related papers: Nominal Type Theory by Nullary Internal Parametric…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
We propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…
We investigate formal power series ideals and their relationship to topological rewriting theory. Since commutative formal power series algebras are Zariski rings, their ideals are closed for the adic topology defined by the maximal ideal…
We define a model of predicate logic in which every term and predicate, open or closed, has an absolute denotation independently of a valuation of the variables. For each variable a, the domain of the model contains an element [[a]] which…
Software development depends on the use of libraries whose public specifications inform client code and impose obligations on private implementations; it follows that verification at scale must also be modular, preserving such abstraction.…
This paper introduces a new family of models of intensional Martin-L\"of type theory. We use constructive ordered algebra in toposes. Identity types in the models are given by a notion of Moore path. By considering a particular gros topos,…
We investigate completeness and parametricity for a general class of realizability semantics for System F defined in terms of closure operators over sets of $\lambda$-terms. This class includes most semantics used for normalization…
A type description is a succinct noun compound which helps human and machines to quickly grasp the informative and distinctive information of an entity. Entities in most knowledge graphs (KGs) still lack such descriptions, thus calling for…
Type systems certify program properties in a compositional way. From a bigger program one can abstract out a part and certify the properties of the resulting abstract program by just using the type of the part that was abstracted away.…
Modal types -- types that are derived from proof systems of modal logic -- have been studied as theoretical foundations of metaprogramming, where program code is manipulated as first-class values. In modal type systems, modality corresponds…
We develop formal theories of conversion for Church-style lambda-terms with Pi-types in first-order syntax using one-sorted variables names and Stoughton's multiple substitutions. We then formalize the Pure Type Systems along some…
We adapt the technique of type-generic programming via descriptions pointing into a universe to the domain of typed languages with binders and variables, implementing a notion of "syntax-generic programming" in a dependently typed…
We present a type-theoretic framework for reasoning about incorrectness in functional programs that interact with effectful, opaque library APIs. Our approach centers on traces -- temporally-ordered sequences of library API invocations --…
Words in some natural languages can have a composite structure. Elements of this structure include the root (that could also be composite), prefixes and suffixes with which various nuances and relations to other words can be expressed.…
A data-centric approach with Natural Language Processing (NLP) to predict personality types based on the MBTI (an introspective self-assessment questionnaire that indicates different psychological preferences about how people perceive the…
The depth-bounded fragment of the pi-calculus is an expressive class of systems enjoying decidability of some important verification problems. Unfortunately membership of the fragment is undecidable. We propose a novel type system,…
Natural language contexts display logical regularities with respect to substitutions of related concepts: these are captured in a functional order-theoretic property called monotonicity. For a certain class of NLI problems where the…
We present the system $\mathtt{d}$, an extended type system with lambda-typed lambda-expressions. It is related to type systems originating from the Automath project. $\mathtt{d}$ extends existing lambda-typed systems by an existential…
With the rising popularity of interdisciplinary work and increasing institutional incentives in this direction, there is a growing need to understand how resulting publications incorporate ideas from multiple disciplines. Existing…
This paper proposes a modal typing system that enables us to handle self-referential formulae, including ones with negative self-references, which on one hand, would introduce a logical contradiction, namely Russell's paradox, in the…