Related papers: Reduction Strategies in the Lambda Calculus and Th…
The technique of abstracting abstract machines (AAM) provides a systematic approach for deriving computable approximations of evaluators that are easily proved sound. This article contributes a complementary step-by-step process for…
We present a system to translate natural language sentences to formulas in a formal or a knowledge representation language. Our system uses two inverse lambda-calculus operators and using them can take as input the semantic representation…
Large Language Models (LLMs) have shown impressive abilities in solving various natural language processing tasks and are now widely offered as services. LLM services enable users to accomplish tasks without requiring specialized knowledge,…
In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit…
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…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
Prompt programming treats large language model prompts as software components with typed interfaces. Based on a literature survey of 15 recent works from 2023 to 2025, we observe a consistent trend: type systems are central to emerging…
This note is about a reasonable abstract machine, called Maximal MAM, implementing the maximal strategy of the lambda-calculus, that is, the strategy that always produces a longest evaluation sequence.
Landauer's embeddings enable the reversibility of computations for non-reversible programming languages, augmenting each intermediate state with enough data to reconstruct the previous state. An interesting research question is therefore to…
This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order,…
We introduce the structural resource lambda-calculus, a new formalism in which strongly normalizing terms of the lambda-calculus can naturally be represented, and at the same time any type derivation can be internally rewritten to its…
We investigate the possibility of a semantic account of the execution time (i.e. the number of beta-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value lambda-calculus. For this…
Static program analysis is a valuable tool for any programming language that people write programs in. The prevalence of scripting languages in the world suggests programming language interpreters are relatively easy to write. Users of…
The strength of a dynamic language is also its weakness: run-time flexibility comes at the cost of compile-time predictability. Many of the hallmarks of dynamic languages such as closures, continuations, various forms of reflection, and a…
Differential lambda-calculus was first introduced by Thomas Ehrhard and Laurent Regnier in 2003. Despite more than 15 years of history, little work has been done on a differential calculus with integration. In this paper, we shall propose a…
We investigate the possibility of a semantic account of the execution time (i.e. the number of \beta_v-steps leading to the normal form, if any) for the shuffling calculus, an extension of Plotkin's call-by-value {\lambda}-calculus. For…
This thesis is devoted to the study of a calculus that describes the application of conditional rewriting rules and the obtained results at the same level of representation. We introduce the rewriting calculus, also called the rho-calculus,…
If the result of an expensive computation is invalidated by a small change to the input, the old result should be updated incrementally instead of reexecuting the whole computation. We incrementalize programs through their derivative. A…
Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we…
This paper introduces a new machine architecture for evaluating lambda expressions using the normal-order reduction, which guarantees that every lambda expression will be evaluated if the expression has its normal form and the system has…