Ontic: a knowledge representation system for mathematics
Ontic: a knowledge representation system for mathematics
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
On the Implementation of an Extensible Declarative Proof Language
TPHOLs '99 Proceedings of the 12th International Conference on Theorem Proving in Higher Order Logics
Computer-Assisted Mathematics at Work (The Hahn-Banach Theorem in Isabelle/Isar)
TYPES '99 Selected papers from the International Workshop on Types for Proofs and Programs
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
Composable discovery engines for interactive theorem proving
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
A Certified Proof of the Cartan Fixed Point Theorems
Journal of Automated Reasoning
An investigation of hilbert's implicit reasoning through proof discovery in idle-time
ADG'10 Proceedings of the 8th international conference on Automated Deduction in Geometry
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There are two different approaches to formalizing proofs in a computer: the procedural approach (which is the one of the HOL system) and the declarative approach (which is the one of the Mizar system). Most provers are procedural. However declarative proofs are much closer in style to informal mathematical reasoning than procedural ones. There have been attempts to put declarative interfaces on top of procedural proof assistants, like John Harrison's Mizar mode for HOL and Markus Wenzel's Isar mode for Isabelle. However in those cases the declarative assistant is a layer on top of the procedural basis, having a separate syntax and a different 'feel' from the underlying system. This paper shows that the procedural and the declarative ways of proving are related and can be integrated seamlessly. It presents an implementation of the Mizar proof language on top of HOL that consists of only 41 lines of ML. This shows how close the procedural and declarative styles of proving really are.