81 research outputs found
Adventures in the (not so) Complex Space
International audienceWe report on the progress of a constructive mechanization for a small subset of signal processing theory, built upon the SSREFLECT and MATHCOMP libraries.The development was started to provide mechanized semantics for audio programming languages. Currently, we have formalized several standard properties of the Discrete Fourier Transform, such as its unitary matrix form and its power and convolution theorems. Future goals include transfer functions and constant overlap-add processing.At the workshop, we aim to discuss the needs and limits of our current approach, surveying some mathematical concepts not covered by existing libraries, and similar efforts in other frameworks and theorem provers
Matching concepts across HOL libraries
Many proof assistant libraries contain formalizations of the same
mathematical concepts. The concepts are often introduced (defined) in different
ways, but the properties that they have, and are in turn formalized, are the
same. For the basic concepts, like natural numbers, matching them between
libraries is often straightforward, because of mathematical naming conventions.
However, for more advanced concepts, finding similar formalizations in
different libraries is a non-trivial task even for an expert.
In this paper we investigate automatic discovery of similar concepts across
libraries of proof assistants. We propose an approach for normalizing
properties of concepts in formal libraries and a number of similarity measures.
We evaluate the approach on HOL based proof assistants HOL4, HOL Light and
Isabelle/HOL, discovering 398 pairs of isomorphic constants and types
LLMSTEP: LLM proofstep suggestions in Lean
We present LLMSTEP, a tool for integrating a language model into the Lean
proof assistant. LLMSTEP is a Lean 4 tactic that sends a user's proof state to
a server hosting a language model. The language model generates suggestions,
which are checked in Lean and displayed to a user in their development
environment. We provide a baseline language model, along with code for
fine-tuning and evaluation to support further development. We provide server
implementations that run on CPU, a CUDA GPU, or a Google Colab notebook, as a
step towards fast, effective language model suggestions for any user
Extensional Higher-Order Paramodulation in Leo-III
Leo-III is an automated theorem prover for extensional type theory with
Henkin semantics and choice. Reasoning with primitive equality is enabled by
adapting paramodulation-based proof search to higher-order logic. The prover
may cooperate with multiple external specialist reasoning systems such as
first-order provers and SMT solvers. Leo-III is compatible with the TPTP/TSTP
framework for input formats, reporting results and proofs, and standardized
communication between reasoning systems, enabling e.g. proof reconstruction
from within proof assistants such as Isabelle/HOL. Leo-III supports reasoning
in polymorphic first-order and higher-order logic, in all normal quantified
modal logics, as well as in different deontic logics. Its development had
initiated the ongoing extension of the TPTP infrastructure to reasoning within
non-classical logics.Comment: 34 pages, 7 Figures, 1 Table; submitted articl
Teaching Intuitionistic and Classical Propositional Logic Using Isabelle
We describe a natural deduction formalization of intuitionistic and classical
propositional logic in the Isabelle/Pure framework. In contrast to earlier
work, where we explored the pedagogical benefits of using a deep embedding
approach to logical modelling, here we employ a logical framework modelling.
This gives rise to simple and natural teaching examples and we report on the
role it played in teaching our Automated Reasoning course in 2020 and 2021.Comment: In Proceedings ThEdu'21, arXiv:2202.0214
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