Communications of the ACM
An overview of the Tecton proof system
Theoretical Computer Science - Special issue on formal methods in databases and software engineering
Diagrams and the concept of logical system
Logical reasoning with diagrams
System Description: Proof Planning in Higher-Order Logic with Lambda-Clam
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
Higher Dimensional Multigraphs
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
A Tactic Language for Hiproofs
Proceedings of the 9th AISC international conference, the 15th Calculemas symposium, and the 7th international MKM conference on Intelligent Computer Mathematics
Towards formal proof script refactoring
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
Automated theorem provers: a practical tool for the working mathematician?
Annals of Mathematics and Artificial Intelligence
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
CICM'12 Proceedings of the 11th international conference on Intelligent Computer Mathematics
An operational foundation for the tactic language of Coq
Proceedings of the 15th Symposium on Principles and Practice of Declarative Programming
Capturing hiproofs in HOL light
CICM'13 Proceedings of the 2013 international conference on Intelligent Computer Mathematics
European collaboration on automated reasoning
AI Communications - ECAI 2012 Turing and Anniversary Track
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Motivated by the concerns of theorem-proving, we generalise the notion of proof tree to that of hierarchical proof tree. Hierarchical trees extend ordinary trees by adding partial order structure to the set of nodes: that allows us to visualise a node as a rectangle in the plane rather than as a point, letting us use the containment relation to express structure additional to that given by a tree. A hierarchical proof tree, or hiproof for short, is a hierarchical tree with nodes labelled by tactics. We motivate the details of our definition by reference to the behaviour of tactics in tactical theorem proving. We characterise the construction of the ordinary proof tree underlying a hierarchical proof tree as a left adjoint. We then analyse the notion of proof refinement with respect to hierarchy, and we give a characterisation of hiproofs that is more directly suited to implementation.