Related papers: The computability path ordering
Usual termination proofs for a functional program require to check all the possible reduction paths. Due to an exponential gap between the height and size of such the reduction tree, no naive formalization of termination proofs yields a…
Direct Preference Optimization (DPO) is an effective framework for aligning large language models with human preferences, but it struggles with complex reasoning tasks. DPO optimizes for the likelihood of generating preferred over…
We consider different classes of combinatory structures related to Krivine realizability. We show, in the precise sense that they give rise to the same class of triposes, that they are equivalent for the purpose of modeling higher-order…
We address the problem of complementing higher-order patterns without repetitions of existential variables. Differently from the first-order case, the complement of a pattern cannot, in general, be described by a pattern, or even by a…
Multimodal Large Reasoning Models introduce the reasoning paradigm, demonstrating strong capabilities on complex vision-language tasks. However, they still suffer from severe hallucinations. Existing training-based methods typically…
We classify programming languages according to evaluation order: each language fixes one evaluation order as the default, making it transparent to program in that evaluation order, and troublesome to program in the other. This paper…
We introduce ordered transfer hyperparameter optimisation (OTHPO), a version of transfer learning for hyperparameter optimisation (HPO) where the tasks follow a sequential order. Unlike for state-of-the-art transfer HPO, the assumption is…
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 propose a simple calculus for processing data streams (infinite flows of data series), represented by finite sets of equations built on stream operators. Furthermore, functions defining streams are regularly corecursive, that is, cyclic…
Contemporary reinforcement learning with verifiable reward methods post-train language models on multi-step reasoning by assigning a single outcome reward uniformly across all tokens in a trajectory. Such uniform assignment ignores which…
Reinforcement learning has been widely applied to enhance the reasoning capabilities of large language models. Extending the inference limits of smaller models has become a prominent research focus. However, algorithms such as Group…
We introduce a new symbolic representation based on an original generalization of counter abstraction. Unlike classical counter abstraction (used in the analysis of parameterized systems with unordered or unstructured topologies) the new…
We present a unifying framework for type systems for process calculi. The core of the system provides an accurate correspondence between essentially functional processes and linear logic proofs; fragments of this system correspond to…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
Policy optimization (PO) algorithms are used to refine Large Language Models for complex, multi-step reasoning. Current state-of-the-art pipelines enforce a strict think-then-answer format to elicit chain-of-thought (CoT); however, the…
This paper studies the design of programming languages with handlers of higher-order effectful operations -- effectful operations that may take in computations as arguments or return computations as output. We present and analyse a core…
Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…
This article presents a general solution to the problem of computational complexity. First, it gives a historical introduction to the problem since the revival of the foundational problems of mathematics at the end of the 19th century.…
Reasoning language models have shown an uncanny ability to improve performance at test-time by ``thinking longer''-that is, by generating longer chain-of-thought sequences and hence using more compute. However, the length of their…
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…