Related papers: Propositional Equality for Gradual Dependently Typ…
We present Decalf, a directed, effectful cost-aware logical framework for studying quantitative aspects of functional programs with effects. Like Calf, the language is based on an internal phase distinction between the behavior of a program…
We prove a conservativity result for extensional type theories over propositional ones, i.e. dependent type theories with propositional computation rules, or computation axioms, using insights from homotopy type theory. The argument…
Bidirectional typing is a discipline in which the typing judgment is decomposed explicitly into inference and checking modes, allowing to control the flow of type information in typing rules and to specify algorithmically how they should be…
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…
We describe a Martin-L\"of-style dependent type theory, called Cocon, that allows us to mix the intensional function space that is used to represent higher-order abstract syntax (HOAS) trees with the extensional function space that…
We present an extension to the $\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and…
There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…
Prompt programming treats large language model prompts as software components with typed interfaces. Based on a literature survey of 15 recent works from 2023 to 2025, we observe a consistent trend: type systems are central to emerging…
In ASPIC-style structured argumentation an argument can rebut another argument by attacking its conclusion. Two ways of formalizing rebuttal have been proposed: In restricted rebuttal, the attacked conclusion must have been arrived at with…
Type-and-effect systems help the programmer to organize data and computational effects in a program. While for traditional type systems expressive variants with sophisticated inference algorithms have been developed and widely used in…
Conformal prediction methods provide statistically rigorous marginal coverage guarantees for machine learning models, but such guarantees fail to account for algorithmic biases, thereby undermining fairness and trust. This paper introduces…
In recent years, languages like Haskell have seen a dramatic surge of new features that significantly extends the expressive power of their type systems. With these features, the challenge of kind inference for datatype declarations has…
Linear type systems have a long and storied history, but not a clear path forward to integrate with existing languages such as OCaml or Haskell. In this paper, we study a linear type system designed with two crucial properties in mind:…
Using a dependently typed host language, we give a well scoped-and-typed by construction presentation of a minimal two level simply typed calculus with a static and a dynamic stage. The staging function partially evaluating the part of a…
Type-free systems of logic are designed to consistently handle significant instances of self-reference. Some consistent type-free systems also have the feature of allowing the sort of general abstraction or comprehension principle that…
Much recent research has been devoted to modeling effects within type theory. Building on this work, we observe that effectful type theories can provide a foundation on which to build semantics for more complex programming constructs and…
Dynamically typed object-oriented languages enable programmers to write elegant, reusable and extensible programs. However, with the current methodology for program verification, the absence of static type information creates significant…
Transient gradual typing imposes run-time type tests that typically cause a linear slowdown in programs' performance. This performance impact discourages the use of type annotations because adding types to a program makes the program…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
Large language and music models are increasingly used for constrained generation: rhyming lines, fixed meter, inpainting or infilling, positional endings, and other global form requirements. These systems often perform strikingly well, but…