research-article

The geometry of types

Authors:

Barbara PetitAuthors Info & Claims

ACM SIGPLAN Notices, Volume 48, Issue 1

Pages 167 - 178

https://doi.org/10.1145/2480359.2429090

Published: 23 January 2013 Publication History

Abstract

We show that time complexity analysis of higher-order functional programs can be effectively reduced to an arguably simpler (although computationally equivalent) verification problem, namely checking first-order inequalities for validity. This is done by giving an efficient inference algorithm for linear dependent types which, given a PCF term, produces in output both a linear dependent type and a cost expression for the term, together with a set of proof obligations. Actually, the output type judgement is derivable iff all proof obligations are valid. This, coupled with the already known relative completeness of linear dependent types, ensures that no information is lost, i.e., that there are no false positives or negatives. Moreover, the procedure reflects the difficulty of the original problem: simple PCF terms give rise to sets of proof obligations which are easy to solve. The latter can then be put in a format suitable for automatic or semi-automatic verification by external solvers. Ongoing experimental evaluation has produced encouraging results, which are briefly presented in the paper.

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Cited By

Grosen JKahn DHoffmann J(2023)Automatic Amortized Resource Analysis with Regular Recursive Types2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175720(1-14)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175720
Suzanne HChailloux E(2023)A Reusable Machine-Calculus for Automated Resource AnalysesLogic-Based Program Synthesis and Transformation10.1007/978-3-031-45784-5_5(61-79)Online publication date: 16-Oct-2023
https://doi.org/10.1007/978-3-031-45784-5_5
Dal Lago U(2022)Implicit computation complexity in higher-order programming languagesMathematical Structures in Computer Science10.1017/S0960129521000505(1-17)Online publication date: 15-Mar-2022
https://doi.org/10.1017/S0960129521000505
Show More Cited By

Index Terms

The geometry of types
1. Theory of computation
  1. Semantics and reasoning
    1. Program reasoning
      1. Program analysis
    2. Program semantics

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The geometry of types
POPL '13: Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages

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Linear dependent types in a call-by-value scenario

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 48, Issue 1

POPL '13

January 2013

561 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/2480359

Issue’s Table of Contents

POPL '13: Proceedings of the 40th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
January 2013
586 pages
ISBN:9781450318327
DOI:10.1145/2429069
General Chair:
Roberto Giacobazzi
Università di Verona, Italy
,
Program Chair:
Radhia Cousot
École normale supérieure CNRS & INRIA, France

Copyright © 2013 ACM.

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Association for Computing Machinery

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Publication History

Published: 23 January 2013

Published in SIGPLAN Volume 48, Issue 1

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Cited By

Grosen JKahn DHoffmann J(2023)Automatic Amortized Resource Analysis with Regular Recursive Types2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175720(1-14)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175720
Suzanne HChailloux E(2023)A Reusable Machine-Calculus for Automated Resource AnalysesLogic-Based Program Synthesis and Transformation10.1007/978-3-031-45784-5_5(61-79)Online publication date: 16-Oct-2023
https://doi.org/10.1007/978-3-031-45784-5_5
Dal Lago U(2022)Implicit computation complexity in higher-order programming languagesMathematical Structures in Computer Science10.1017/S0960129521000505(1-17)Online publication date: 15-Mar-2022
https://doi.org/10.1017/S0960129521000505
Ceresa MJaskelioff M(2022)Effectful improvement theoryScience of Computer Programming10.1016/j.scico.2022.102792217:COnline publication date: 1-May-2022
https://dl.acm.org/doi/10.1016/j.scico.2022.102792
Kahn DHoffmann J(2021)Automatic amortized resource analysis with the Quantum physicist’s methodProceedings of the ACM on Programming Languages10.1145/34735815:ICFP(1-29)Online publication date: 19-Aug-2021
https://dl.acm.org/doi/10.1145/3473581
Baillot PBarthe GDal Lago U(2019)Implicit Computational Complexity of Subrecursive Definitions and Applications to Cryptographic ProofsJournal of Automated Reasoning10.1007/s10817-019-09530-2Online publication date: 31-Jul-2019
https://doi.org/10.1007/s10817-019-09530-2
Baillot PBarthe GLago U(2015)Implicit Computational Complexity of Subrecursive Definitions and Applications toźCryptographic ProofsProceedings of the 20th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning - Volume 945010.1007/978-3-662-48899-7_15(203-218)Online publication date: 24-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-662-48899-7_15
Hoffmann JShao Z(2015)Automatic Static Cost Analysis for Parallel ProgramsProceedings of the 24th European Symposium on Programming on Programming Languages and Systems - Volume 903210.1007/978-3-662-46669-8_6(132-157)Online publication date: 11-Apr-2015
https://dl.acm.org/doi/10.1007/978-3-662-46669-8_6
Ghica DSmith A(2014)Bounded Linear Types in a Resource SemiringProceedings of the 23rd European Symposium on Programming Languages and Systems - Volume 841010.1007/978-3-642-54833-8_18(331-350)Online publication date: 5-Apr-2014
https://dl.acm.org/doi/10.1007/978-3-642-54833-8_18
Scherer GHoffmann J(2013)Tracking Data-Flow with Open Closure TypesLogic for Programming, Artificial Intelligence, and Reasoning10.1007/978-3-642-45221-5_47(710-726)Online publication date: 2013
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