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The lambda-Pi-calculus allows to express proofs of minimal predicate logic. It can be extended, in a very simple way, by adding computation rules. This leads to the lambda-Pi-calculus modulo. We show in this paper that this simple extension…
Ludics is a logical framework in which types/formulas are modelled by sets of terms with the same computational behaviour. This paper investigates the representation of inductive data types and functional types in ludics. We study their…
Many machine learning tasks can be formulated in terms of predicting structured outputs. In frameworks such as the structured support vector machine (SVM-Struct) and the structured perceptron, discriminative functions are learned by…
The lambda calculus since more than half a century is a model and foundation of functional programming languages. However, lambda expressions can be evaluated with different reduction strategies and thus, there is no fixed cost model nor…
In Constructive Type Theory, recursive and corecursive definitions are subject to syntactic restrictions which guarantee termination for recursive functions and productivity for corecursive functions. However, many terminating and…
We present a compilation framework in which dimensional type annotations persist through multi-stage MLIR lowering, enabling the compiler to jointly resolve numeric representation selection and deterministic memory management as coeffect…
Diffusion language models (DLMs) are an attractive alternative to autoregressive models because they promise sublinear-time, parallel generation, yet practical gains remain elusive as high-quality samples still demand hundreds of refinement…
The lambda calculus is a widely accepted computational model of higher-order functional pro- grams, yet there is not any direct and universally accepted cost model for it. As a consequence, the computational difficulty of reducing lambda…
The vector field of a controlled differential equation (CDE) describes the relationship between a control path and the evolution of a solution path. Neural CDEs (NCDEs) treat time series data as observations from a control path,…
Recent advancements in transformer-based models have greatly improved time series analysis, providing robust solutions for tasks such as forecasting, anomaly detection, and classification. A crucial element of these models is positional…
Prior works have demonstrated that implicit representations trained only for reconstruction tasks typically generate encodings that are not useful for semantic tasks. In this work, we propose a method that contextualises the encodings of…
Refinement types enable lightweight verification of functional programs. Algorithms for statically inferring refinement types typically work by reduction to solving systems of constrained Horn clauses extracted from typing derivations. An…
Efficient inference in large language models (LLMs) has become a critical focus as their scale and complexity grow. Traditional autoregressive decoding, while effective, suffers from computational inefficiencies due to its sequential token…
Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful…
A well-known problem in the theory of dependent types is how to handle so-called nested data types. These data types are difficult to program and to reason about in total dependently typed languages such as Agda and Coq. In particular, it…
We introduce a new compile-time notion of type subsumption based on type simulation. We show how to apply this static subsumption relation to support a more intuitive, object oriented approach to generic programming of reusable, high…
We extend Levy's call-by-push-value (CBPV) analysis from simple to dependent type theory (DTT) in order to study the interaction between computational effects and dependent types. We define the naive system of dependently typed CBPV,…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
In this paper, we present an explicit substitution calculus which distinguishes between ordinary bound variables and meta-variables. Its typing discipline is derived from contextual modal type theory. We first present a dependently typed…
The benchmark for computation is typically given as Turing computability; the ability for a computation to be performed by a Turing Machine. Many languages exploit (indirect) encodings of Turing Machines to demonstrate their ability to…