# Towards Lean Proof Checking

@inproceedings{Barthe1996TowardsLP, title={Towards Lean Proof Checking}, author={Gilles Barthe and Hugo Elbers}, booktitle={DISCO}, year={1996} }

Logical formal systems are ineecient at computations. In order to increase their eeciency, we aim to extend these systems with computational power. In this paper, we suggest a general, powerful syntax, called oracle types, to extend type theories with computational power; the resulting systems, which combine the logical abilities of logical formal systems and the computational power of term rewriting systems, provide a suitable environment for theorem proving. As a practical application, we…

## 6 Citations

Congruence Types

- Computer Science, MathematicsCSL
- 1995

A type theoretical framework in which canon term rewriting systems can be represented faithfully both from the logical and the computational points of view and improves on existing work to combine type theories with algebraic rewriting.

Studies in mechanical verification of mathematical proofs

- Computer Science
- 1999

This thesis is about proof checking in type theory and investigates the question how to mechanically verify mathematical proofs by developing a library of formalized mathematics.

On the Subject Reduction Property for Algebraic Type Systems

- Mathematics, Computer ScienceCSL
- 1996

A general technique to prove Subject Reduction for a large class of algebraic type systems by considering for every (functional) algebraictype system a labelled syntax for which Subject Reduction is easy to prove and proving the equivalence between the labelled and standard syntaxes whenever the labelled system is strongly normalising.

A Two-Level Approach Towards Lean Proof-Checking

- Computer ScienceTYPES
- 1995

A simple and effective methodology for equational reasoning in proof checkers based on a two-level approach distinguishing between syntax and semantics of mathematical theories.

Generation and presentation of formal mathematical documents

- Computer Science
- 2001

The field of formal mathematics is interesting for mathematicians and computer scientists who are not in the first place interested in the logical foundations of mathematics, however, the 2000 years of existence of mathematics are not directed towards full formalization.

A Scheduling Strategy for Parallel Proof Checking and Verification

- Computer Science2008 IEEE International Conference on Networking, Sensing and Control
- 2008

This paper first deals with scheduling issues related to parallel proof checking, then applies the obtained result and similar idea to parallel verifications and is based on INCAPS, an interactive deduction system of temporal logic.

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A simple and effective methodology for equational reasoning in proof checkers based on a two-level approach distinguishing between syntax and semantics of mathematical theories.

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