research-article

Synthesizing geometry constructions

Authors:

Vijay Anand Korthikanti,

Ashish TiwariAuthors Info & Claims

PLDI '11: Proceedings of the 32nd ACM SIGPLAN Conference on Programming Language Design and Implementation

Pages 50 - 61

https://doi.org/10.1145/1993498.1993505

Published: 04 June 2011 Publication History

Abstract

In this paper, we study the problem of automatically solving ruler/compass based geometry construction problems. We first introduce a logic and a programming language for describing such constructions and then phrase the automation problem as a program synthesis problem. We then describe a new program synthesis technique based on three key insights: (i) reduction of symbolic reasoning to concrete reasoning (based on a deep theoretical result that reduces verification to random testing), (ii) extending the instruction set of the programming language with higher level primitives (representing basic constructions found in textbook chapters, inspired by how humans use their experience and knowledge gained from chapters to perform complicated constructions), and (iii) pruning the forward exhaustive search using a goal-directed heuristic (simulating backward reasoning performed by humans). Our tool can successfully synthesize constructions for various geometry problems picked up from high-school textbooks and examination papers in a reasonable amount of time. This opens up an amazing set of possibilities in the context of making classroom teaching interactive.

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Lahiri SKalita PChittora AVankudre VRoy SFilkov VRay BZhou M(2024)Program Synthesis Meets Visual What-Comes-Next PuzzlesProceedings of the 39th IEEE/ACM International Conference on Automated Software Engineering10.1145/3691620.3695015(418-429)Online publication date: 27-Oct-2024
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Li XZhou XDong RZhang YWang X(2024)Efficient Bottom-Up Synthesis for Programs with Local VariablesProceedings of the ACM on Programming Languages10.1145/36328948:POPL(1540-1568)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632894
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cover image ACM Conferences

PLDI '11: Proceedings of the 32nd ACM SIGPLAN Conference on Programming Language Design and Implementation

June 2011

668 pages

ISBN:9781450306638

DOI:10.1145/1993498

General Chair:
Mary Hall
University of Utah
,
Program Chair:
David Padua
University of Illinois at Urbana-Champaign

ACM SIGPLAN Notices Volume 46, Issue 6
PLDI '11
June 2011
652 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/1993316
Issue’s Table of Contents

Copyright © 2011 ACM.

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Published: 04 June 2011

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PLDI '11: ACM SIGPLAN Conference on Programming Language Design and Implementation

June 4 - 8, 2011

California, San Jose, USA

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Overall Acceptance Rate 406 of 2,067 submissions, 20%

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https://dl.acm.org/doi/10.1145/3691620.3695015
Li XZhou XDong RZhang YWang X(2024)Efficient Bottom-Up Synthesis for Programs with Local VariablesProceedings of the ACM on Programming Languages10.1145/36328948:POPL(1540-1568)Online publication date: 5-Jan-2024
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https://doi.org/10.1007/s10472-023-09850-5
Kalita PPotanin A(2022)Program Synthesis for Artifacts beyond ProgramsCompanion Proceedings of the 2022 ACM SIGPLAN International Conference on Systems, Programming, Languages, and Applications: Software for Humanity10.1145/3563768.3565544(13-16)Online publication date: 29-Nov-2022
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Marinković VŠukilović TMarić F(2021)On Automating Triangle Constructions in Absolute and Hyperbolic GeometryElectronic Proceedings in Theoretical Computer Science10.4204/EPTCS.352.3352(14-26)Online publication date: 30-Dec-2021
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