research-article

A Modular Type Reconstruction Algorithm

Author:

Florian RabeAuthors Info & Claims

ACM Transactions on Computational Logic (TOCL), Volume 19, Issue 4

Article No.: 24, Pages 1 - 43

https://doi.org/10.1145/3234693

Published: 08 December 2018 Publication History

Abstract

Mmt is a framework for designing and implementing formal systems in a way that systematically abstracts from theoretical and practical aspects of their type of theoretical and logical foundations. Thus, definitions, theorems, and algorithms can be stated independently of the foundation, and language designers can focus on the essentials of a particular foundation and inherit a large-scale implementation from Mmt at low cost. Going beyond the similarly motivated approach of meta-logical frameworks, Mmt does not even commit to a particular meta-logic—that makes Mmt level results harder to obtain but also more general.

We present one such result: a type reconstruction algorithm that realizes the foundation-independent aspects generically relative to a set of rules that supply the foundation-specific knowledge. Maybe surprisingly, we see that the former covers most of the algorithm, including the most difficult details. Thus, we can easily instantiate our algorithm with rule sets for several important language features including, e.g., dependent function types. Moreover, our design is modular such that we obtain a type reconstruction algorithm for any combination of these features.

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Cited By

Rothgang CRabe FBenzmüller C(2023)Theorem Proving in Dependently-Typed Higher-Order LogicAutomated Deduction – CADE 2910.1007/978-3-031-38499-8_25(438-455)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-38499-8_25
Kaliszyk CRabe F(2020)A Survey of Languages for Formalizing MathematicsIntelligent Computer Mathematics10.1007/978-3-030-53518-6_9(138-156)Online publication date: 26-Jul-2020
https://dl.acm.org/doi/10.1007/978-3-030-53518-6_9
Bauer AHaselwarter PPetković A(2020)Equality Checking for General Type Theories in Andromeda 2Mathematical Software – ICMS 202010.1007/978-3-030-52200-1_25(253-259)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.1007/978-3-030-52200-1_25
Show More Cited By

Index Terms

A Modular Type Reconstruction Algorithm
1. Theory of computation
  1. Logic

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Published In

cover image ACM Transactions on Computational Logic

ACM Transactions on Computational Logic Volume 19, Issue 4

October 2018

277 pages

ISSN:1529-3785

EISSN:1557-945X

DOI:10.1145/3293495

Editor:
Orna Kupferman
School of Computer Science and Engineering, Hebrew University, Israel

Issue’s Table of Contents

Copyright © 2018 ACM.

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Publication History

Published: 08 December 2018

Accepted: 01 June 2018

Revised: 01 January 2018

Received: 01 April 2017

Published in TOCL Volume 19, Issue 4

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Cited By

Rothgang CRabe FBenzmüller C(2023)Theorem Proving in Dependently-Typed Higher-Order LogicAutomated Deduction – CADE 2910.1007/978-3-031-38499-8_25(438-455)Online publication date: 1-Jul-2023
https://dl.acm.org/doi/10.1007/978-3-031-38499-8_25
Kaliszyk CRabe F(2020)A Survey of Languages for Formalizing MathematicsIntelligent Computer Mathematics10.1007/978-3-030-53518-6_9(138-156)Online publication date: 26-Jul-2020
https://dl.acm.org/doi/10.1007/978-3-030-53518-6_9
Bauer AHaselwarter PPetković A(2020)Equality Checking for General Type Theories in Andromeda 2Mathematical Software – ICMS 202010.1007/978-3-030-52200-1_25(253-259)Online publication date: 13-Jul-2020
https://dl.acm.org/doi/10.1007/978-3-030-52200-1_25
Kohlhase MRabe FSacerdoti Coen CSchaefer J(2020)Logic-Independent Proof Search in Logical FrameworksAutomated Reasoning10.1007/978-3-030-51074-9_22(395-401)Online publication date: 1-Jul-2020
https://dl.acm.org/doi/10.1007/978-3-030-51074-9_22
Müller DRabe F(2019)Rapid Prototyping Formal Systems in MMT: 5 Case StudiesElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.307.5307(40-54)Online publication date: 12-Oct-2019
https://doi.org/10.4204/EPTCS.307.5
Rabe FSharoda Y(2019)Diagram Combinators in MMTIntelligent Computer Mathematics10.1007/978-3-030-23250-4_15(211-226)Online publication date: 3-Jul-2019
https://doi.org/10.1007/978-3-030-23250-4_15
Müller DRabe FSacerdoti Coen C(2019)The Coq Library as a Theory GraphIntelligent Computer Mathematics10.1007/978-3-030-23250-4_12(171-186)Online publication date: 3-Jul-2019
https://doi.org/10.1007/978-3-030-23250-4_12

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