Related papers: The Functional Machine Calculus
Contrary to several other families of lambda terms, no closed formula or generating function is known and none of the sophisticated techniques devised in analytic combinatorics can currently help with counting or generating the set of {\em…
We introduce two extensions of the $\lambda$-calculus with a probabilistic choice operator, $\Lambda_\oplus^{cbv}$ and $\Lambda_\oplus^{cbn}$, modeling respectively call-by-value and call-by-name probabilistic computation. We prove that…
We study quantum mechanics in the stochastic formulation, using the functional integral approach. The noise term enters the classical action as a local contribution of anticommuting fields. The partition function is not invariant under…
Estimators based on influence functions (IFs) have been shown to be effective in many settings, especially when combined with machine learning techniques. By focusing on estimating a specific target of interest (e.g., the average effect of…
The higher-dimensional modal mu-calculus is an extension of the mu-calculus in which formulas are interpreted in tuples of states of a labeled transition system. Every property that can be expressed in this logic can be checked in…
We combine high-dimensional factor models with fractional integration methods and derive models where nonstationary, potentially cointegrated data of different persistence is modelled as a function of common fractionally integrated factors.…
In this paper, we present an extension of $\lambda\mu$-calculus called $\lambda\mu^{++}$-calculus which has the following properties: subject reduction, strong normalization, unicity of the representation of data and thus confluence only on…
Machine learning (ML) has seen significant growth in both popularity and importance. The high prediction accuracy of ML models is often achieved through complex black-box architectures that are difficult to interpret. This interpretability…
We propose a method to adapt functional logic programming to deal with reasoning on coinductively interpreted programs as well as on inductively interpreted programs. In order to do so, we consider a class of objects interesting for this…
Probabilistic programming languages, which exist in abundance, are languages that allow users to calculate probability distributions defined by probabilistic programs, by using inference algorithms. However, the underlying inference…
LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call-by-name and call-by-value…
Functional data analysis in a mixed-effects model framework is done using operator calculus. In this approach the functional parameters are treated as serially correlated effects giving an alternative to the penalized likelihood approach,…
Addressing machines have been introduced as a formalism to construct models of the pure, untyped lambda-calculus. We extend the syntax of their programs by adding instructions for executing arithmetic operations on natural numbers, and…
Some effects are considered to be higher-level than others. High-level effects provide expressive and succinct abstraction of programming concepts, while low-level effects allow more fine-grained control over program execution and…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
We consider the non-deterministic extension of the call-by-value lambda calculus, which corresponds to the additive fragment of the linear-algebraic lambda-calculus. We define a fine-grained type system, capturing the right linearity…
We explore the design and implementation of Frank, a strict functional programming language with a bidirectional effect type system designed from the ground up around a novel variant of Plotkin and Pretnar's effect handler abstraction.…
Reversible computing is motivated by both pragmatic and foundational considerations arising from a variety of disciplines. We take a particular path through the development of reversible computation, emphasizing compositional reversible…