Related papers: Mirroring Call-by-Need, or Values Acting Silly
We introduce Semantic Recall, a novel metric to assess the quality of approximate nearest neighbor search algorithms by considering only semantically relevant objects that are theoretically retrievable via exact nearest neighbor search.…
This paper studies normalisation by evaluation for typed lambda calculus from a categorical and algebraic viewpoint. The first part of the paper analyses the lambda definability result of Jung and Tiuryn via Kripke logical relations and…
We provide a computational definition of the notions of vector space and bilinear functions. We use this result to introduce a minimal language combining higher-order computation and linear algebra. This language extends the Lambda-calculus…
The reasoning capabilities of the recent LLMs enable them to execute external function calls to overcome their inherent limitations, such as knowledge cutoffs, poor arithmetic skills, or lack of access to private data. This development has…
Mathematical reasoning benchmarks are vital for evaluating large language models (LLMs), but many are static and repeatedly exposed through public evaluation and training pipelines, making it difficult to separate genuine reasoning from…
This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…
Under the extension of Curry-Howard's correspondence to classical logic, Gentzen's NK and LK systems can be seen as syntax-directed systems of simple types respectively for Parigot's Lambda Mu Calculus and Curien-Herbelin's Lambda Bar Mu Mu…
Convertibility checking - determining whether two lambda-terms are equal up to reductions - is a crucial component of proof assistants and dependently-typed languages. Practical implementations often use heuristics to quickly conclude that…
Normal-form bisimilarity is a simple, easy-to-use behavioral equivalence that relates terms in $\lambda$-calculi by decomposing their normal forms into bisimilar subterms. Moreover, it typically allows for powerful up-to techniques, such as…
We present a unified framework for quantifying the similarity between representations through the lens of \textit{usable} information, offering a rigorous theoretical and empirical synthesis across three key dimensions. First, addressing…
We explore the integration of metaprogramming in a call-by-value linear lambda-calculus and sketch its extension to a session type system. We build on a model of contextual modal type theory with multi-level contexts, where contextual…
In ML-aided decision-making tasks, such as fraud detection or medical diagnosis, the human-in-the-loop, usually a domain-expert without technical ML knowledge, prefers high-level concept-based explanations instead of low-level explanations…
In this paper, we define a new realizability semantics for the simply typed lambda-mu-calculus. We show that if a term is typable, then it inhabits the interpretation of its type. We also prove a completeness result of our realizability…
Applied process calculi include advanced programming constructs such as type systems, communication with pattern matching, encryption primitives, concurrent constraints, nondeterminism, process creation, and dynamic connection topologies.…
Researchers and practitioners operating on a limited budget face the cost-performance trade-off dilemma. The challenging decision often centers on whether to use a large LLM with better performance or a smaller one with reduced costs. This…
This work gives some insights and results on standardisation for call-by-name pattern calculi. More precisely, we define standard reductions for a pattern calculus with constructor-based data terms and patterns. This notion is based on…
Recent advances in large language models (LLMs) have enabled autonomous agents with complex reasoning and task-fulfillment capabilities using a wide range of tools. However, effectively identifying the most relevant tools for a given task…
Semantic data fuels many different applications, but is still lacking proper integration into programming languages. Untyped access is error-prone while mapping approaches cannot fully capture the conceptualization of semantic data. In this…
When translating a term calculus into a graphical formalism many inessential details are abstracted away. In the case of $\lambda$-calculus translated to proof-nets, these inessential details are captured by a notion of equivalence on…
In this work we study randomised reduction strategies,a notion already known in the context of abstract reduction systems, for the $\lambda$-calculus. We develop a simple framework that allows us to prove a randomised strategy to be…