5,780 research outputs found
Asynchronous processing of Coq documents: from the kernel up to the user interface
The work described in this paper improves the reactivity of the Coq system by
completely redesigning the way it processes a formal document. By subdividing
such work into independent tasks the system can give precedence to the ones of
immediate interest for the user and postpones the others. On the user side, a
modern interface based on the PIDE middleware aggregates and present in a
consistent way the output of the prover. Finally postponed tasks are processed
exploiting modern, parallel, hardware to offer better scalability.Comment: in Proceedings of ITP, Aug 2015, Nanjing, Chin
Graph Representations for Higher-Order Logic and Theorem Proving
This paper presents the first use of graph neural networks (GNNs) for
higher-order proof search and demonstrates that GNNs can improve upon
state-of-the-art results in this domain. Interactive, higher-order theorem
provers allow for the formalization of most mathematical theories and have been
shown to pose a significant challenge for deep learning. Higher-order logic is
highly expressive and, even though it is well-structured with a clearly defined
grammar and semantics, there still remains no well-established method to
convert formulas into graph-based representations. In this paper, we consider
several graphical representations of higher-order logic and evaluate them
against the HOList benchmark for higher-order theorem proving
Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar
This paper presents a combination of several automated reasoning and proof
presentation tools with the Mizar system for formalization of mathematics. The
combination forms an online service called MizAR, similar to the SystemOnTPTP
service for first-order automated reasoning. The main differences to
SystemOnTPTP are the use of the Mizar language that is oriented towards human
mathematicians (rather than the pure first-order logic used in SystemOnTPTP),
and setting the service in the context of the large Mizar Mathematical Library
of previous theorems,definitions, and proofs (rather than the isolated problems
that are solved in SystemOnTPTP). These differences poses new challenges and
new opportunities for automated reasoning and for proof presentation tools.
This paper describes the overall structure of MizAR, and presents the automated
reasoning systems and proof presentation tools that are combined to make MizAR
a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial
Intelligence and Symbolic Computation AISC 201
- …