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Recent research has investigated the underlying mechanisms of in-context learning (ICL) both theoretically and empirically, often using data generated from simple function classes. However, the existing work often focuses on the sequence…
We establish a formal correspondence between resource calculi an appropriate linear multicategories. We consider the cases of (symmetric) representable, symmetric closed and autonomous multicategories. For all these structures, we prove…
We introduce a self-play framework for semantic equivalence in Haskell, utilizing formal verification to guide adversarial training between a generator and an evaluator. The framework leverages Liquid Haskell proofs for validating…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…
Using a categorial version of Fra\"iss\'e's theorem due to Droste and G\"obel, we derive a criterion for a comma-category to have universal homogeneous objects. As a first application we give new existence result for universal structures…
As it follows from G\"odel's incompleteness theorems, any consistent formal system of axioms and rules of inference should imply a true unprovable statement. Actually, this fundamental principle can be efficiently applicable in…
We consider the problem of explaining the predictions of an arbitrary blackbox model $f$: given query access to $f$ and an instance $x$, output a small set of $x$'s features that in conjunction essentially determines $f(x)$. We design an…
For years, Integrated Development Environments have demonstrated their usefulness in order to ease the development of software. High-level security or safety systems require proofs of compliance to standards, based on analyses such as code…
Coherence, a strictly quantum phenomenon, has found many applications, from quantum information theory and thermodynamics to quantum foundations and biology. When physical constraints are taken into consideration creation of coherence in a…
Destination-passing style programming introduces destinations, which represent the address of a write-once memory cell. These destinations can be passed as function parameters, allowing the caller to control memory management: the callee…
A number of first-order calculi employ an explicit model representation formalism for automated reasoning and for detecting satisfiability. Many of these formalisms can represent infinite Herbrand models. The first-order fragment of…
A key part of implementing high-level languages is providing built-in and default data structures. Yet selecting good defaults is hard. A mutable data structure's workload is not known in advance, and it may shift over its lifetime - e.g.,…
The literature on concurrency theory offers a wealth of examples of characteristic-formula constructions for various behavioural relations over finite labelled transition systems and Kripke structures that are defined in terms of fixed…
Formal reasoning about the time complexity of algorithms and data structures is usually done in interactive theorem provers like Isabelle/HOL. This includes reasoning about amortized time complexity which looks at the worst case performance…
CLASS is a proof-of-concept general purpose linear programming language, flexibly supporting realistic concurrent programming idioms, and featuring an expressive linear type system ensuring that programs (1) never misuse or leak stateful…
Several practical tools for automatically verifying functional programs (e.g., Liquid Haskell and Leon for Scala programs) rely on a heuristic based on unrolling recursive function definitions followed by quantifier-free reasoning using SMT…
The Shapes Constraint Language (SHACL) is the recent W3C recommendation language for validating RDF data, by verifying certain shapes on graphs. Previous work has largely focused on the validation problem and the standard decision problems…
It is a strength of graph-based data formats, like RDF, that they are very flexible with representing data. To avoid run-time errors, program code that processes highly-flexible data representations exhibits the difficulty that it must…
First-order resolution has been used for type inference for many years, including in Hindley- Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show…
SHACL is a W3C-proposed schema language for expressing structural constraints on RDF graphs. Recent work on formalizing this language has revealed a striking relationship to description logics. SHACL expressions can use three fundamental…