Related papers: Reduction Strategies in the Lambda Calculus and Th…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
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…
Large Language Models (LLMs) have demonstrated remarkable capabilities in handling long texts and have almost perfect performance in traditional retrieval tasks. However, their performance significantly degrades when it comes to numerical…
The task of inferring logical formulas from examples has garnered significant attention as a means to assist engineers in creating formal specifications used in the design, synthesis, and verification of computing systems. Among various…
This paper formalizes and proves correct a compilation scheme for mutually-recursive definitions in call-by-value functional languages. This scheme supports a wider range of recursive definitions than previous methods. We formalize our…
In this paper, we present a general realizability semantics for the simply typed $\lambda\mu$-calculus. Then, based on this semantics, we derive both weak and strong normalization results for two versions of the $\lambda\mu$-calculus…
Reasoning requires going beyond pattern matching or memorization of solutions to identify and implement "algorithmic procedures" that can be used to deduce answers to hard problems. Doing so requires realizing the most relevant primitives,…
A major challenge in the deployment of scientific software solutions is the adaptation of research prototypes to production-grade code. While high-level languages like MATLAB are useful for rapid prototyping, they lack the resource…
Large language models (LLMs) have rapidly progressed into general-purpose agents capable of solving a broad spectrum of tasks. However, current models remain inefficient at reasoning: they apply fixed inference-time compute regardless of…
Large Language Models (LLMs) have attracted extensive attention due to their remarkable performance across various tasks. However, the substantial computational and memory requirements of LLM inference pose challenges for deployment in…
Terms in the lambda-calculus can be represented as planar trees decorated with symbols for abstraction and application, and having variables as leaves. In this paper, we concentrate on the branches of such trees, rather than on the trees…
This paper presents the Relational Machine Calculus (RMC): a simple, foundational model of first-order relational programming. The RMC originates from the Functional Machine Calculus (FMC), which generalizes the lambda-calculus and its…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
We introduce a category-theoreticabstraction of a syntax with auxiliary functions, called an admissiblemonad morphism. Relying on an abstract form of structural recursion,we then design generic tools to construct admissible monad…
The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching a la ML into a case analysis on constants and a commutation rule between case and application…
Adapting large language models (LLMs) to specific domains often faces a critical bottleneck: the scarcity of high-quality, human-curated data. While large volumes of unchecked data are readily available, indiscriminately using them for…
Commutativity reasoning based on Lipton's movers is a powerful technique for verification of concurrent programs. The idea is to define a program transformation that preserves a subset of the initial set of interleavings, which is sound…
This paper presents Favalon, a functional programming language built on the premise of a lambda calculus for use as an interactive shell replacement. Favalon seamlessly integrates with typed versions of existing libraries and commands using…
Large language models (LLMs) significantly enhance the performance of various applications, but they are computationally intensive and energy-demanding. This makes it challenging to deploy them on devices with limited resources, such as…
We present some lambda calculus with explicit substitutions and named variables. The characteristic feature of this calculus is as follows: renaming of bound variables when performing substitutions is done using special reductions and may…