2 research outputs found
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions
A Proof Planning Framework For Isabelle
Centre for Intelligent Systems and their ApplicationsProof planning is a paradigm for the automation of proof that focuses on encoding intelligence
to guide the proof process. The idea is to capture common patterns of reasoning which can be
used to derive abstract descriptions of proofs known as proof plans. These can then be executed
to provide fully formal proofs.
This thesis concerns the development and analysis of a novel approach to proof planning
that focuses on an explicit representation of choices during search. We embody our approach
as a proof planner for the generic proof assistant Isabelle and use the Isar language, which is
human-readable and machine-checkable, to represent proof plans. Within this framework we
develop an inductive theorem prover as a case study of our approach to proof planning.
Our prover uses the difference reduction heuristic known as rippling to automate the step
cases of the inductive proofs. The development of a flexible approach to rippling that supports
its various modifications and extensions is the second major focus of this thesis. Here, our
inductive theorem prover provides a context in which to evaluate rippling experimentally.
This work results in an efficient and powerful inductive theorem prover for Isabelle as well
as proposals for further improving the efficiency of rippling. We also draw observations in order
to direct further work on proof planning. Overall, we aim to make it easier for mathematical
techniques, and those specific to mechanical theorem proving, to be encoded and applied to
problems