Related papers: Resource-Bounded Martin-L\"of Type Theory: Composi…
The first part of this dissertation defines "dependently typed algebraic theories", which are a strict subclass of the generalised algebraic theories (GATs) of Cartmell. We characterise dependently typed algebraic theories as finitary…
This is the fourth in a series of papers extending Martin-L\"of's meaning explanation of dependent type theory to higher-dimensional types. In this installment, we show how to define cubical type systems supporting a general schema of…
Martin-L\"of's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of well-founded relations is presented. Using primitive…
Type-preserving translations are effective rigorous tools in the study of core programming calculi. In this paper, we develop a new typed translation that connects sequential and concurrent calculi; it is governed by type systems that…
One may formulate the dependent product types of Martin-L\"of type theory either in terms of abstraction and application operators like those for the lambda-calculus; or in terms of introduction and elimination rules like those for the…
Type-based amortised resource analysis following Hofmann and Jost---where resources are associated with individual elements of data structures and doled out to the programmer under a linear typing discipline---have been successful in…
We propose a type-based resource usage analysis for the π-calculus extended with resource creation/access primitives. The goal of the resource usage analysis is to statically check that a program accesses resources such as files and…
Type refinements combine the compositionality of typechecking with the expressivity of program logics, offering a synergistic approach to program verification. In this paper we apply dependent type refinements to SAX, a futures-based…
Externalized reasoning is already exploited by transformer-based agents through chain-of-thought, but structured retrieval -- indexing over one's own reasoning state -- remains underexplored. We formalize the transformer context window as…
We combine dependent types with linear type systems that soundly and completely capture polynomial time computation. We explore two systems for capturing polynomial time: one system that disallows construction of iterable data, and one,…
In dependent type theory, being able to refer to a type universe as a term itself increases its expressive power, but requires mechanisms in place to prevent Girard's paradox from introducing logical inconsistency in the presence of…
First-order resolution has been used for type inference for many years, including in Hindley- Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show…
There exist many techniques for automatically deriving parametric resource (or cost) bounds by analyzing the source code of a program. These techniques work effectively for a large class of programs and language features. However, non-local…
A substantial amount of research has been carried out in developing machine learning algorithms that account for term dependence in text classification. These algorithms offer acceptable performance in most cases but they are associated…
Multinomial processing tree (MPT) models are tools for disentangling the contributions of latent cognitive processes in a given experimental paradigm. The present note analyzes MPT models subject to order constraints on subsets of its…
We construct a realizability model of linear dependent type theory from a linear combinatory algebra. Our model motivates a number of additions to the type theory. In particular, we add a universe with two decoding operations: one takes…
We introduce a novel resource analysis for typed term rewrite systems based on a potential-based type system. This type system gives rise to polynomial bounds on the innermost runtime complexity. We relate the thus obtained amortised…
Dependently typed languages are well known for having a problem with code reuse. Traditional non-indexed algebraic datatypes (e.g. lists) appear alongside a plethora of indexed variations (e.g. vectors). Functions are often rewritten for…
We study a cost-aware programming language for higher-order recursion dubbed $\textbf{PCF}_\mathsf{cost}$ in the setting of synthetic domain theory (SDT). Our main contribution relates the denotational cost semantics of…
In the current landscape of large language models (LLMs), the process of instruction tuning serves as an essential step. Considering the high computing power overhead, data-efficient instruction tuning was proposed to reduce the training…