Related papers: Reduction Strategies in the Lambda Calculus and Th…
The application of automatic transformation processes during the formal development and optimization of programs can introduce encumbrances in the generated code that programmers usually (or presumably) do not write. An example is the…
Call-by-need evaluation for the lambda-calculus can be seen as merging the best of call-by-name and call-by-value, namely the wise erasing behaviour of the former and the wise duplicating behaviour of the latter. To better understand how…
We present counting reward automata-a finite state machine variant capable of modelling any reward function expressible as a formal language. Unlike previous approaches, which are limited to the expression of tasks as regular languages, our…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
Turing machines and register machines have been used for decades in theoretical computer science as abstract models of computation. Also the $\lambda$-calculus has played a central role in this domain as it allows to focus on the notion of…
There is still a lot of confusion about "optimal" sharing in the lambda calculus, and its actual efficiency. In this article, we shall try to clarify some of these issues.
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
We introduce LArge Model Based Data Agent (LAMBDA), a novel open-source, code-free multi-agent data analysis system that leverages the power of large language models. LAMBDA is designed to address data analysis challenges in data-driven…
We review the close relationship between abstract machines for (call-by-name or call-by-value) lambda-calculi (extended with Felleisen's C) and sequent calculus, reintroducing on the way Curien-Herbelin's syntactic kit expressing the…
The Algebraic lambda-calculus and the Linear-Algebraic lambda-calculus extend the lambda-calculus with the possibility of making arbitrary linear combinations of terms. In this paper we provide a fine-grained, System F-like type system for…
Soft linear logic ([Lafont02]) is a subsystem of linear logic characterizing the class PTIME. We introduce Soft lambda-calculus as a calculus typable in the intuitionistic and affine variant of this logic. We prove that the (untyped) terms…
Superdeduction is a method specially designed to ease the use of first-order theories in predicate logic. The theory is used to enrich the deduction system with new deduction rules in a systematic, correct and complete way. A proof-term…
While transistor density is still increasing, clock speeds are not, motivating the search for new parallel architectures. One approach is to completely abandon the concept of CPU -- and thus serial imperative programming -- and instead to…
Final-answer-based metrics are commonly used for evaluating large language models (LLMs) on math word problems, often taken as proxies for reasoning ability. However, such metrics conflate two distinct sub-skills: abstract formulation…
Prompting is a mainstream paradigm for adapting large language models to specific natural language processing tasks without modifying internal parameters. Therefore, detailed supplementary knowledge needs to be integrated into external…
Recently, Miller and Wu introduced the positive $\lambda$-calculus, a call-by-value $\lambda$-calculus with sharing obtained by assigning proof terms to the positively polarized focused proofs for minimal intuitionistic logic. The positive…
This paper explores the semantics of a combinatory fragment of reFLect, the lambda-calculus underlying a functional language used by Intel Corporation for hardware design and verification. ReFLect is similar to ML, but has a primitive data…
Lambda-calculi come with no fixed evaluation strategy. Different strategies may then be considered, and it is important that they satisfy some abstract rewriting property, such as factorization or normalization theorems. In this paper we…
We build on a fine-grained analysis of session-based interaction as provided by the linear logic typing disciplines to introduce the SAM, an abstract machine for mechanically executing session-typed processes. A remarkable feature of the…
We formally verify an abstract machine for a call-by-value lambda-calculus with de Bruijn terms, simple substitution, and small-step semantics. We follow a stepwise refinement approach starting with a naive stack machine with substitution.…