Related papers: A graded dependent type system with a usage-aware …
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
Automated industrial optimization modeling requires reliable translation of natural-language requirements into solver-executable code. However, large language models often generate non-compilable models due to missing declarations, type…
Deductive verification techniques based on program logics (i.e., the family of Floyd-Hoare logics) are a powerful approach for program reasoning. Recently, there has been a trend of increasing the expressive power of such logics by…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Reasoning over knowledge graphs is traditionally built upon a hierarchy of languages in the Semantic Web Stack. Starting from the Resource Description Framework (RDF) for knowledge graphs, more advanced constructs have been introduced…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
Dependent Object Types (DOT) is intended to be a core calculus for modelling Scala. Its distinguishing feature is abstract type members, fields in objects that hold types rather than values. Proving soundness of DOT has been surprisingly…
We develop a dependent type theory that is based purely on inductive and coinductive types, and the corresponding recursion and corecursion principles. This results in a type theory with a small set of rules, while still being fairly…
In automated complexity analysis, noninterference-based type systems statically guarantee, via soundness, the property that well-typed programs compute functions of a given complexity class, e.g., the class FP of functions computable in…
Constructive type theory combines logic and programming in one language. This is useful both for reasoning about programs written in type theory, as well as for reasoning about other programming languages inside type theory. It is…
Tree-based Long short term memory (LSTM) network has become state-of-the-art for modeling the meaning of language texts as they can effectively exploit the grammatical syntax and thereby non-linear dependencies among words of the sentence.…
Targeted sentiment classification predicts the sentiment polarity on given target mentions in input texts. Dominant methods employ neural networks for encoding the input sentence and extracting relations between target mentions and their…
We present a general and user-extensible equality checking algorithm that is applicable to a large class of type theories. The algorithm has a type-directed phase for applying extensionality rules and a normalization phase based on…
We present {\lambda}ert, a type theory supporting refinement types with explicit proofs. Instead of solving refinement constraints with an SMT solver like DML and Liquid Haskell, our system requires and permits programmers to embed proofs…
Dependent type theory gives an expressive type system facilitating succinct formalizations of mathematical concepts. In practice, it is mainly used for interactive theorem proving with intensional type theories, with PVS being a notable…
We use type-theoretic techniques to present an algebraic theory of $\infty$-categories with strict units. Starting with a known type-theoretic presentation of fully weak $\infty$-categories, in which terms denote valid operations, we extend…
We propose a novel dependency-based hybrid tree model for semantic parsing, which converts natural language utterance into machine interpretable meaning representations. Unlike previous state-of-the-art models, the semantic information is…
Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type…
The categorical compositional distributional model of natural language provides a conceptually motivated procedure to compute the meaning of sentences, given grammatical structure and the meanings of its words. This approach has…
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…