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Autoregressive multimodal large language models have recently gained popularity for image generation, driven by advances in foundation models. To enhance alignment and detail, newer approaches employ chain-of-thought (CoT) reasoning,…
In sequential functional languages, sized types enable termination checking of programs with complex patterns of recursion in the presence of mixed inductive-coinductive types. In this paper, we adapt sized types and their metatheory to the…
We propose a computational modeling framework for inducing combinatory categorial grammars from arbitrary behavioral data. This framework provides the analyst fine-grained control over the assumptions that the induced grammar should conform…
We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…
Symmetric monoidal categories (SMCs) are a common framework for reasoning about computation, focusing on the parallel and sequential compositionality of operations. String diagrams are a ubiquitous and powerful tool for reasoning about…
Dependent types allow us to express precisely what a function is intended to do. Recent work on Quantitative Type Theory (QTT) extends dependent type systems with linearity, also allowing precision in expressing when a function can run.…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
To ensure decidability and consistency of its type theory, a proof assistant should only accept terminating recursive functions and productive corecursive functions. Most proof assistants enforce this through syntactic conditions, which can…
We describe a framework for inducing probabilistic grammars from corpora of positive samples. First, samples are {\em incorporated} by adding ad-hoc rules to a working grammar; subsequently, elements of the model (such as states or…
We propose a novel, semi-supervised approach towards domain taxonomy induction from an input vocabulary of seed terms. Unlike all previous approaches, which typically extract direct hypernym edges for terms, our approach utilizes a novel…
We give a new criterion guaranteeing existence of model structures left-induced along a functor admitting both adjoints. This works under the hypothesis that the functor induces idempotent adjunctions at the homotopy category level. As an…
Text-to-image AI are capable of generating novel images for inspiration, but their applications for 3D design workflows and how designers can build 3D models using AI-provided inspiration have not yet been explored. To investigate this, we…
These notes provide a quick introduction to the Coq system and show how it can be used to define logical concepts and functions and reason about them. It is designed as a tutorial, so that readers can quickly start their own experiments,…
This paper defines and develops useful concepts related to the several kinds of inductances employed in any comprehensive design-oriented ferrite-based inductor model, which is required to properly design and control high-frequency operated…
We propose to use Church encodings in typed lambda-calculi as the basis for an automata-theoretic counterpart of implicit computational complexity, in the same way that monadic second-order logic provides a counterpart to descriptive…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…
We introduce ProjectQ, an open source software effort for quantum computing. The first release features a compiler framework capable of targeting various types of hardware, a high-performance simulator with emulation capabilities, and…
Side effects are a core part of practical programming. However, they are often hard to reason about, particularly in a concurrent setting. We propose a foundation for reasoning about concurrent side effects using sessions. Primarily, we…
This paper is concerned with the foundations of the Calculus of Algebraic Constructions (CAC), an extension of the Calculus of Constructions by inductive data types. CAC generalizes inductive types equipped with higher-order primitive…