Related papers: Mechanizing the Metatheory of LF
Type theories can be formalized using the intrinsically (hard) or the extrinsically (soft) typed style. In large libraries of type theoretical features, often both styles are present, which can lead to code duplication and integration…
Large language models (LLMs) achieve strong performance and have revolutionized NLP, but their lack of explainability keeps them treated as black boxes, limiting their use in domains that demand transparency and trust. A promising direction…
Data programming (DP) has proven to be an attractive alternative to costly hand-labeling of data. In DP, users encode domain knowledge into \emph{labeling functions} (LF), heuristics that label a subset of the data noisily and may have…
Although most of the automated theorem-proving approaches depend on formal proof systems, informal theorem proving can align better with large language models' (LLMs) strength in natural language processing. In this work, we identify a…
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
Information flow properties express the capability for an agent to infer information about secret behaviours of a partially observable system. In a language-theoretic setting, where the system behaviour is described by a language, we define…
Decidability of definitional equality and conversion of terms into canonical form play a central role in the meta-theory of a type-theoretic logical framework. Most studies of definitional equality are based on a confluent,…
We give new proofs of soundness (all representable functions on base types lies in certain complexity classes) for Elementary Affine Logic, LFPL (a language for polytime computation close to realistic functional programming introduced by…
A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…
The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…
Modern functional-logic programming languages like Toy or Curry feature non-strict non-deterministic functions that behave under call-time choice semantics. A standard formulation for this semantics is the CRWL logic, that specifies a proof…
Autoformalization, the process of translating informal statements into formal logic, has gained renewed interest with the emergence of powerful Large Language Models (LLMs). While LLMs show promise in generating structured outputs from…
We introduce MTT, a dependent type theory which supports multiple modalities. MTT is parametrized by a mode theory which specifies a collection of modes, modalities, and transformations between them. We show that different choices of mode…
This is an overview of the Isabelle technology behind the Archive of Formal Proofs (AFP). Interactive development and quasi-interactive build jobs impose significant demands of scalability on the logic (usually Isabelle/HOL), on Isabelle/ML…
This paper presents a formalisation of pGCL in Isabelle/HOL. Using a shallow embedding, we demonstrate close integration with existing automation support. We demonstrate the facility with which the model can be extended to incorporate…
Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…
For formulas F of propositional calculus I introduce a "metavariable" MF and show how it can be used to define an algorithm for testing satisfiability. MF is a formula which is true/false under all possible truth assignments iff F is…
Gradual dependent types can help with the incremental adoption of dependently typed code by providing a principled semantics for imprecise types and proofs, where some parts have been omitted. Current theories of gradual dependent types,…
This paper presents a comprehensive evaluation of the capabilities of Large Language Models (LLMs) in metaphor interpretation across multiple datasets, tasks, and prompt configurations. Although metaphor processing has gained significant…
This paper addresses the current lack of a unified formal framework in machine learning theory, as well as the absence of robust theoretical foundations for interpretability and ethical safety assurance. We first construct a formal…