Related papers: Native Type Theory
We prove a conjecture about the constructibility of coinductive types - in the principled form of indexed M-types - in Homotopy Type Theory. The conjecture says that in the presence of inductive types, coinductive types are derivable.…
Large language models (LLMs) have proven to be highly effective for solving complex reasoning tasks. Surprisingly, their capabilities can often be improved by iterating on previously generated solutions. In this context, a reasoning plan…
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…
Dependency parsing is a fundamental task in natural language processing (NLP), aiming to identify syntactic dependencies and construct a syntactic tree for a given sentence. Traditional dependency parsing models typically construct…
We present an approach to develop folds for nested data types using dependent types. We call such folds $\textit{dependently typed folds}$, they have the following properties. (1) Dependently typed folds are defined by well-founded…
Tableaux originate as a decision method for a logical language. They can also be extended to obtain a structure that spells out all the information in a set of sentences in terms of truth value assignments to atomic formulas that appear 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…
Game theory is used by all behavioral sciences, but its development has long centered around tools for relatively simple games and toy systems, such as the economic interpretation of equilibrium outcomes. Our contribution, compositional…
Language Generation Models produce words based on the previous context. Although existing methods offer input attributions as explanations for a model's prediction, it is still unclear how prior words affect the model's decision throughout…
Syntactic structures used to play a vital role in natural language processing (NLP), but since the deep learning revolution, NLP has been gradually dominated by neural models that do not consider syntactic structures in their design. One…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
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…
Ambiguity is an critical component of language that allows for more effective communication between speakers, but is often ignored in NLP. Recent work suggests that NLP systems may struggle to grasp certain elements of human language…
We describe a type system for a platform called the General Intensional Programming System (GIPSY), designed to support intensional programming languages built upon intensional logic and their imperative counter-parts for the intensional…
Existential rules, a.k.a. dependencies in databases, and Datalog+/- in knowledge representation and reasoning recently, are a family of important logical languages widely used in computer science and artificial intelligence. Towards a deep…
We study the problem of building generative models of natural source code (NSC); that is, source code written and understood by humans. Our primary contribution is to describe a family of generative models for NSC that have three key…
The emergence of large language models (LLMs) has demonstrated that systems trained solely on text can acquire extensive world knowledge, develop reasoning capabilities, and internalize abstract semantic concepts--showcasing properties that…
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,…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
Graphs are a generalized concept that encompasses more complex data structures than trees, such as difference lists, doubly-linked lists, skip lists, and leaf-linked trees. Normally, these structures are handled with destructive assignments…