Related papers: Geometry of Resource Interaction - A Minimalist Ap…
I present a model of universal parallel computation called $\Delta$-Nets, and a method to translate $\lambda$-terms into $\Delta$-nets and back. Together, the model and the method constitute an algorithm for optimal parallel…
In game semantics and related approaches to programming language semantics, programs are modelled by interaction dialogues. Such models have recently been used in the design of new compilation methods, e.g. for hardware synthesis or for…
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…
In this paper we introduce several quantitative methods for the lambda-calculus based on partial metrics, a well-studied variant of standard metric spaces that have been used to metrize non-Hausdorff topologies, like those arising from…
Randomized higher-order computation can be seen as being captured by a lambda calculus endowed with a single algebraic operation, namely a construct for binary probabilistic choice. What matters about such computations is the probability of…
In the first part of this paper, we define two resource aware typing systems for the {\lambda}{\mu}-calculus based on non-idempotent intersection and union types. The non-idempotent approach provides very simple combinatorial…
Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…
Just as the $\lambda$-calculus uses three primitives (abstraction, application, variable) as the foundation of functional programming, inheritance-calculus uses three primitives (record, definition, inheritance) as the foundation of…
We evaluate language models on their ability to explore interactive environments under a limited interaction budget. We introduce three parametric tasks with controllable exploration difficulty, spanning continuous and discrete…
In implementing evaluation strategies of the lambda-calculus, both correctness and efficiency of implementation are valid concerns. While the notion of correctness is determined by the evaluation strategy, regarding efficiency there is a…
We introduce a linear infinitary $\lambda$-calculus, called $\ell\Lambda_{\infty}$, in which two exponential modalities are available, the first one being the usual, finitary one, the other being the only construct interpreted…
A central question in cognitive science is whether conceptual representations converge onto a shared manifold to support generalization, or diverge into orthogonal subspaces to minimize task interference. While prior work has discovered…
We introduce a calculus of extensional resource terms. These are resource terms \`a la Ehrhard-Regnier, but in infinitely eta-long form. The calculus still retains a finite syntax and dynamics: in particular, we prove strong confluence and…
We study the interpretation of the lambda-calculus in a framework based on tropical mathematics, and we show that it provides a unifying framework for two well-developed quantitative approaches to program semantics: on the one hand program…
In implementing evaluation strategies of the lambda-calculus, both correctness and efficiency of implementation are valid concerns. While the notion of correctness is determined by the evaluation strategy, regarding efficiency there is a…
In this paper we introduce a typed, concurrent $\lambda$-calculus with references featuring explicit substitutions for variables and references. Alongside usual safety properties, we recover strong normalization. The proof is based on a…
In this work, we have studied classical and quantum systems in interaction by means of geometric reduction procedure. The main target is the description in these terms of fundamental interactions. We have shown that, to describe in a…
We prove the Stability Property for the call-by-value $\lambda$-calculus (CbV in the following). This result states necessary conditions under which the contexts of the CbV $\lambda$-calculus commute with intersections of approximants. This…
Linear typed $\lambda$-calculi are more delicate than their simply typed siblings when it comes to metatheoretic results like preservation of typing under renaming and substitution. Tracking the usage of variables in contexts places more…
Residual coherence is a graphical tool for selecting potential second-order interaction terms as functions of a single time series and its lags. This paper extends the notion of residual coherence to account for interaction terms of…