Related papers: A type assignment for lambda-calculus complete bot…
Dependent types provide a lightweight and modular means to integrate programming and formal program verification. In particular, the types of programs written in dependently typed programming languages (Agda, Idris, F*, etc.) can be used to…
We provide a proof of strong normalisation for lambda+, a recently introduced, explicitly typed, non-deterministic lambda-calculus where isomorphic propositions are identified. Such a proof is a non-trivial adaptation of the reducibility…
Mixed-typed languages enable programmers to link typed and untyped components in various ways. Some offer rich type systems to facilitate the smooth migration of untyped code to the typed world; others merely provide a convenient form of…
Dynamic languages (such as Python and JavaScript) offer flexibility and simplified type handling for programming, but this can also lead to an increase in type-related errors and additional overhead for compile-time type inference. As a…
Despite a growing body of work at the intersection of deep learning and formal languages, there has been relatively little systematic exploration of transformer models for reasoning about typed lambda calculi. This is an interesting area of…
A novel language system has given rise to promising alternatives to standard formal and processor network models of computation. An interstring linked with a abstract machine environment, shares sub-expressions, transfers data, and…
We advocate the use of de Bruijn's universal abstraction $\lambda^\infty$ for the quantification of schematic variables in the predicative setting and we present a typed $\lambda$-calculus featuring the quantifier $\lambda^\infty$…
Probabilistic programming is perfectly suited to reliable and transparent data science, as it allows the user to specify their models in a high-level language without worrying about the complexities of how to fit the models. Static analysis…
Languages with gradual information-flow control combine static and dynamic techniques to prevent security leaks. Gradual languages should satisfy the gradual guarantee: programs that only differ in the precision of their type annotations…
Dependency pairs constitute a series of very effective techniques for the termination analysis of term rewriting systems. In this paper, we adapt the static dependency pair framework to logically constrained simply-typed term rewriting…
We address the problem of analysing the complexity of concurrent programs written in Pi-calculus. We are interested in parallel complexity, or span, understood as the execution time in a model with maximal parallelism. A type system for…
Recent years have witnessed increasing interests in prompt-based learning in which models can be trained on only a few annotated instances, making them suitable in low-resource settings. When using prompt-based learning for text…
Motivated by algorithmic information theory, the problem of program discovery can help find candidates of underlying generative mechanisms of natural and artificial phenomena. The uncomputability of such inverse problem, however,…
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…
Phase transitions in combinatorial problems have recently been shown to be useful in locating "hard" instances of combinatorial problems. The connection between computational complexity and the existence of phase transitions has been…
Abstract dynamic programming models are used to analyze $\lambda$-policy iteration with randomization algorithms. Particularly, contractive models with infinite policies are considered and it is shown that well-posedness of the…
We provide an implicit characterization of polynomial time computation in terms of ordinary differential equations: we characterize the class $\operatorname{PTIME}$ of languages computable in polynomial time in terms of differential…
Extending Large Language Models (LLMs) to advanced applications requires reliable structured output generation. Existing methods which often rely on rigid JSON schemas, can lead to unreliable outputs, diminished reasoning capabilities, and…
Simulation plays a central role in scientific discovery. In many applications, the bottleneck is no longer running a simulator; it is choosing among large families of plausible simulators, each corresponding to different forward…
We study the strict type assignment for lambda-mu that is presented in [van Bakel'16]. We define a notion of approximants of lambda-mu-terms, show that it generates a semantics, and that for each typeable term there is an approximant that…